info large_stringlengths 120 50k | question large_stringlengths 504 10.4k | avg@8_qwen3_4b_instruct_2507 float64 0 0.88 |
|---|---|---|
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\"0100\\n0001\\n10100\\n10001\\n0011011\\n0011\\n111111\\n#\", \"0100\\n1101\\n10000\\n10001\\n0001011\\n1011\\n011110\\n#\", \"0100\\n0101\\n10101\\n10011\\n0011010\\n0011\\n011110\\n#\", \"0100\\n0111\\n10100\\n00001\\n0011011\\n1000\\n011110\\n#\", \"0100\\n0100\\n11100\\n00001\\n0011011\\n1101\\n011110\\n#\", \"0100\\n1000\\n10100\\n10011\\n0011011\\n1101\\n011111\\n#\", \"0100\\n1110\\n10100\\n10011\\n0011011\\n1000\\n011110\\n#\", \"0100\\n0110\\n10110\\n10011\\n0011011\\n1100\\n111111\\n#\", \"0100\\n0110\\n10100\\n10010\\n0011111\\n1010\\n011110\\n#\", \"0100\\n0111\\n10100\\n00000\\n0101011\\n0111\\n011010\\n#\", \"0100\\n0101\\n00100\\n11000\\n0101011\\n0001\\n010110\\n#\", \"0100\\n1101\\n11110\\n11000\\n0101011\\n0011\\n011100\\n#\", \"0100\\n1101\\n00000\\n11000\\n0001001\\n0011\\n011010\\n#\", \"0100\\n1001\\n10100\\n10010\\n0001010\\n0011\\n011111\\n#\", \"0100\\n1101\\n00011\\n10000\\n0001011\\n0010\\n011110\\n#\", \"0100\\n0001\\n10100\\n10001\\n1011011\\n0011\\n111111\\n#\", \"0100\\n0101\\n10101\\n10011\\n0011010\\n0010\\n011110\\n#\", \"0100\\n0111\\n10100\\n00011\\n0011011\\n1000\\n011110\\n#\", \"0100\\n0100\\n11100\\n00001\\n0011010\\n1101\\n011110\\n#\", \"0100\\n0110\\n10100\\n10011\\n0011011\\n1000\\n011110\\n#\", \"0100\\n0110\\n10110\\n10011\\n0011011\\n1110\\n111111\\n#\", \"0100\\n0110\\n10100\\n00000\\n0101011\\n0111\\n011010\\n#\", \"0100\\n0101\\n01100\\n11000\\n0101011\\n0001\\n010110\\n#\", \"0100\\n1101\\n00000\\n11000\\n0001001\\n0010\\n011010\\n#\", \"0100\\n1001\\n10100\\n10010\\n0001000\\n0011\\n011111\\n#\", \"0100\\n0101\\n10100\\n01000\\n0101011\\n0011\\n011111\\n#\"], \"outputs\": [\"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\n\", \"Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nYes\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\n\", \"Yes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\"]}", "source": "primeintellect"} | Aka Beko, trying to escape from 40 bandits, got lost in the city of A. Aka Beko wants to go to City B, where the new hideout is, but the map has been stolen by a bandit.
Kobborg, one of the thieves, sympathized with Aka Beko and felt sorry for him. So I secretly told Aka Beko, "I want to help you go to City B, but I want to give you direct directions because I have to keep out of my friends, but I can't tell you. I can answer. "
When Kobborg receives the question "How about the route XX?" From Aka Beko, he answers Yes if it is the route from City A to City B, otherwise. Check the directions according to the map below.
<image>
Each city is connected by a one-way street, and each road has a number 0 or 1. Aka Beko specifies directions by a sequence of numbers. For example, 0100 is the route from City A to City B via City X, Z, and W. If you choose a route that is not on the map, you will get lost in the desert and never reach City B. Aka Beko doesn't know the name of the city in which she is, so she just needs to reach City B when she finishes following the directions.
Kobborg secretly hired you to create a program to answer questions from Aka Beko. If you enter a question from Aka Beko, write a program that outputs Yes if it is the route from City A to City B, otherwise it outputs No.
input
The input consists of multiple datasets. The end of the input is indicated by a single # (pound) line. Each dataset is given in the following format.
p
A sequence of numbers 0, 1 indicating directions is given on one line. p is a string that does not exceed 100 characters.
The number of datasets does not exceed 100.
output
Print Yes or No on one line for each dataset.
Example
Input
0100
0101
10100
01000
0101011
0011
011111
#
Output
Yes
No
Yes
No
Yes
No
Yes
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[4.5], [7.1], [19.00384], [109.1], [66.4], [\"pippi\"], [{}]], \"outputs\": [[\"X--X--X\\n-X-X-X-\\n--XXX--\\nXXXXXXX\\n--XXX--\\n-X-X-X-\\nX--X--X\"], [\"X--XX--X\\n-X-XX-X-\\n--XXXX--\\nXXXXXXXX\\nXXXXXXXX\\n--XXXX--\\n-X-XX-X-\\nX--XX--X\"], [\"X--------XX--------X\\n-X-------XX-------X-\\n--X------XX------X--\\n---X-----XX-----X---\\n----X----XX----X----\\n-----X---XX---X-----\\n------X--XX--X------\\n-------X-XX-X-------\\n--------XXXX--------\\nXXXXXXXXXXXXXXXXXXXX\\nXXXXXXXXXXXXXXXXXXXX\\n--------XXXX--------\\n-------X-XX-X-------\\n------X--XX--X------\\n-----X---XX---X-----\\n----X----XX----X----\\n---X-----XX-----X---\\n--X------XX------X--\\n-X-------XX-------X-\\nX--------XX--------X\"], [\"X-----------------------------------------------------XX-----------------------------------------------------X\\n-X----------------------------------------------------XX----------------------------------------------------X-\\n--X---------------------------------------------------XX---------------------------------------------------X--\\n---X--------------------------------------------------XX--------------------------------------------------X---\\n----X-------------------------------------------------XX-------------------------------------------------X----\\n-----X------------------------------------------------XX------------------------------------------------X-----\\n------X-----------------------------------------------XX-----------------------------------------------X------\\n-------X----------------------------------------------XX----------------------------------------------X-------\\n--------X---------------------------------------------XX---------------------------------------------X--------\\n---------X--------------------------------------------XX--------------------------------------------X---------\\n----------X-------------------------------------------XX-------------------------------------------X----------\\n-----------X------------------------------------------XX------------------------------------------X-----------\\n------------X-----------------------------------------XX-----------------------------------------X------------\\n-------------X----------------------------------------XX----------------------------------------X-------------\\n--------------X---------------------------------------XX---------------------------------------X--------------\\n---------------X--------------------------------------XX--------------------------------------X---------------\\n----------------X-------------------------------------XX-------------------------------------X----------------\\n-----------------X------------------------------------XX------------------------------------X-----------------\\n------------------X-----------------------------------XX-----------------------------------X------------------\\n-------------------X----------------------------------XX----------------------------------X-------------------\\n--------------------X---------------------------------XX---------------------------------X--------------------\\n---------------------X--------------------------------XX--------------------------------X---------------------\\n----------------------X-------------------------------XX-------------------------------X----------------------\\n-----------------------X------------------------------XX------------------------------X-----------------------\\n------------------------X-----------------------------XX-----------------------------X------------------------\\n-------------------------X----------------------------XX----------------------------X-------------------------\\n--------------------------X---------------------------XX---------------------------X--------------------------\\n---------------------------X--------------------------XX--------------------------X---------------------------\\n----------------------------X-------------------------XX-------------------------X----------------------------\\n-----------------------------X------------------------XX------------------------X-----------------------------\\n------------------------------X-----------------------XX-----------------------X------------------------------\\n-------------------------------X----------------------XX----------------------X-------------------------------\\n--------------------------------X---------------------XX---------------------X--------------------------------\\n---------------------------------X--------------------XX--------------------X---------------------------------\\n----------------------------------X-------------------XX-------------------X----------------------------------\\n-----------------------------------X------------------XX------------------X-----------------------------------\\n------------------------------------X-----------------XX-----------------X------------------------------------\\n-------------------------------------X----------------XX----------------X-------------------------------------\\n--------------------------------------X---------------XX---------------X--------------------------------------\\n---------------------------------------X--------------XX--------------X---------------------------------------\\n----------------------------------------X-------------XX-------------X----------------------------------------\\n-----------------------------------------X------------XX------------X-----------------------------------------\\n------------------------------------------X-----------XX-----------X------------------------------------------\\n-------------------------------------------X----------XX----------X-------------------------------------------\\n--------------------------------------------X---------XX---------X--------------------------------------------\\n---------------------------------------------X--------XX--------X---------------------------------------------\\n----------------------------------------------X-------XX-------X----------------------------------------------\\n-----------------------------------------------X------XX------X-----------------------------------------------\\n------------------------------------------------X-----XX-----X------------------------------------------------\\n-------------------------------------------------X----XX----X-------------------------------------------------\\n--------------------------------------------------X---XX---X--------------------------------------------------\\n---------------------------------------------------X--XX--X---------------------------------------------------\\n----------------------------------------------------X-XX-X----------------------------------------------------\\n-----------------------------------------------------XXXX-----------------------------------------------------\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n-----------------------------------------------------XXXX-----------------------------------------------------\\n----------------------------------------------------X-XX-X----------------------------------------------------\\n---------------------------------------------------X--XX--X---------------------------------------------------\\n--------------------------------------------------X---XX---X--------------------------------------------------\\n-------------------------------------------------X----XX----X-------------------------------------------------\\n------------------------------------------------X-----XX-----X------------------------------------------------\\n-----------------------------------------------X------XX------X-----------------------------------------------\\n----------------------------------------------X-------XX-------X----------------------------------------------\\n---------------------------------------------X--------XX--------X---------------------------------------------\\n--------------------------------------------X---------XX---------X--------------------------------------------\\n-------------------------------------------X----------XX----------X-------------------------------------------\\n------------------------------------------X-----------XX-----------X------------------------------------------\\n-----------------------------------------X------------XX------------X-----------------------------------------\\n----------------------------------------X-------------XX-------------X----------------------------------------\\n---------------------------------------X--------------XX--------------X---------------------------------------\\n--------------------------------------X---------------XX---------------X--------------------------------------\\n-------------------------------------X----------------XX----------------X-------------------------------------\\n------------------------------------X-----------------XX-----------------X------------------------------------\\n-----------------------------------X------------------XX------------------X-----------------------------------\\n----------------------------------X-------------------XX-------------------X----------------------------------\\n---------------------------------X--------------------XX--------------------X---------------------------------\\n--------------------------------X---------------------XX---------------------X--------------------------------\\n-------------------------------X----------------------XX----------------------X-------------------------------\\n------------------------------X-----------------------XX-----------------------X------------------------------\\n-----------------------------X------------------------XX------------------------X-----------------------------\\n----------------------------X-------------------------XX-------------------------X----------------------------\\n---------------------------X--------------------------XX--------------------------X---------------------------\\n--------------------------X---------------------------XX---------------------------X--------------------------\\n-------------------------X----------------------------XX----------------------------X-------------------------\\n------------------------X-----------------------------XX-----------------------------X------------------------\\n-----------------------X------------------------------XX------------------------------X-----------------------\\n----------------------X-------------------------------XX-------------------------------X----------------------\\n---------------------X--------------------------------XX--------------------------------X---------------------\\n--------------------X---------------------------------XX---------------------------------X--------------------\\n-------------------X----------------------------------XX----------------------------------X-------------------\\n------------------X-----------------------------------XX-----------------------------------X------------------\\n-----------------X------------------------------------XX------------------------------------X-----------------\\n----------------X-------------------------------------XX-------------------------------------X----------------\\n---------------X--------------------------------------XX--------------------------------------X---------------\\n--------------X---------------------------------------XX---------------------------------------X--------------\\n-------------X----------------------------------------XX----------------------------------------X-------------\\n------------X-----------------------------------------XX-----------------------------------------X------------\\n-----------X------------------------------------------XX------------------------------------------X-----------\\n----------X-------------------------------------------XX-------------------------------------------X----------\\n---------X--------------------------------------------XX--------------------------------------------X---------\\n--------X---------------------------------------------XX---------------------------------------------X--------\\n-------X----------------------------------------------XX----------------------------------------------X-------\\n------X-----------------------------------------------XX-----------------------------------------------X------\\n-----X------------------------------------------------XX------------------------------------------------X-----\\n----X-------------------------------------------------XX-------------------------------------------------X----\\n---X--------------------------------------------------XX--------------------------------------------------X---\\n--X---------------------------------------------------XX---------------------------------------------------X--\\n-X----------------------------------------------------XX----------------------------------------------------X-\\nX-----------------------------------------------------XX-----------------------------------------------------X\"], [\"X--------------------------------X--------------------------------X\\n-X-------------------------------X-------------------------------X-\\n--X------------------------------X------------------------------X--\\n---X-----------------------------X-----------------------------X---\\n----X----------------------------X----------------------------X----\\n-----X---------------------------X---------------------------X-----\\n------X--------------------------X--------------------------X------\\n-------X-------------------------X-------------------------X-------\\n--------X------------------------X------------------------X--------\\n---------X-----------------------X-----------------------X---------\\n----------X----------------------X----------------------X----------\\n-----------X---------------------X---------------------X-----------\\n------------X--------------------X--------------------X------------\\n-------------X-------------------X-------------------X-------------\\n--------------X------------------X------------------X--------------\\n---------------X-----------------X-----------------X---------------\\n----------------X----------------X----------------X----------------\\n-----------------X---------------X---------------X-----------------\\n------------------X--------------X--------------X------------------\\n-------------------X-------------X-------------X-------------------\\n--------------------X------------X------------X--------------------\\n---------------------X-----------X-----------X---------------------\\n----------------------X----------X----------X----------------------\\n-----------------------X---------X---------X-----------------------\\n------------------------X--------X--------X------------------------\\n-------------------------X-------X-------X-------------------------\\n--------------------------X------X------X--------------------------\\n---------------------------X-----X-----X---------------------------\\n----------------------------X----X----X----------------------------\\n-----------------------------X---X---X-----------------------------\\n------------------------------X--X--X------------------------------\\n-------------------------------X-X-X-------------------------------\\n--------------------------------XXX--------------------------------\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n--------------------------------XXX--------------------------------\\n-------------------------------X-X-X-------------------------------\\n------------------------------X--X--X------------------------------\\n-----------------------------X---X---X-----------------------------\\n----------------------------X----X----X----------------------------\\n---------------------------X-----X-----X---------------------------\\n--------------------------X------X------X--------------------------\\n-------------------------X-------X-------X-------------------------\\n------------------------X--------X--------X------------------------\\n-----------------------X---------X---------X-----------------------\\n----------------------X----------X----------X----------------------\\n---------------------X-----------X-----------X---------------------\\n--------------------X------------X------------X--------------------\\n-------------------X-------------X-------------X-------------------\\n------------------X--------------X--------------X------------------\\n-----------------X---------------X---------------X-----------------\\n----------------X----------------X----------------X----------------\\n---------------X-----------------X-----------------X---------------\\n--------------X------------------X------------------X--------------\\n-------------X-------------------X-------------------X-------------\\n------------X--------------------X--------------------X------------\\n-----------X---------------------X---------------------X-----------\\n----------X----------------------X----------------------X----------\\n---------X-----------------------X-----------------------X---------\\n--------X------------------------X------------------------X--------\\n-------X-------------------------X-------------------------X-------\\n------X--------------------------X--------------------------X------\\n-----X---------------------------X---------------------------X-----\\n----X----------------------------X----------------------------X----\\n---X-----------------------------X-----------------------------X---\\n--X------------------------------X------------------------------X--\\n-X-------------------------------X-------------------------------X-\\nX--------------------------------X--------------------------------X\"], [false], [false]]}", "source": "primeintellect"} | Your aged grandfather is tragically optimistic about Team GB's chances in the upcoming World Cup, and has enlisted you to help him make [Union Jack](https://en.wikipedia.org/wiki/Union_Jack) flags to decorate his house with.
## Instructions
* Write a function which takes as a parameter a number which represents the dimensions of the flag. The flags will always be square, so the number 9 means you should make a flag measuring 9x9.
* It should return a *string* of the flag, with _'X' for the red/white lines and '-' for the blue background_. It should include newline characters so that it's not all on one line.
* For the sake of symmetry, treat odd and even numbers differently: odd number flags should have a central cross that is *only one 'X' thick*. Even number flags should have a central cross that is *two 'X's thick* (see examples below).
## Other points
* The smallest flag you can make without it looking silly is 7x7. If you get a number smaller than 7, simply _make the flag 7x7_.
* If you get a decimal, round it _UP to the next whole number_, e.g. 12.45 would mean making a flag that is 13x13.
* If you get something that's not a number at all, *return false*.
Translations and comments (and upvotes) welcome!
## Examples:
```python
union_jack(9) # (9 is odd, so the central cross is 1'X' thick)
"X---X---X
-X--X--X-
--X-X-X--
---XXX---
XXXXXXXXX
---XXX---
--X-X-X--
-X--X--X-
X---X---X"
union_jack(10) # (10 is even, so the central cross is 2 'X's thick)
'X---XX---X
-X--XX--X-
--X-XX-X--
---XXXX---
XXXXXXXXXX
XXXXXXXXXX
---XXXX---
--X-XX-X--
-X--XX--X-
X---XX---X
union_jack(1) # (the smallest possible flag is 7x7)
"X--X--X
-X-X-X-
--XXX--
XXXXXXX
--XXX--
-X-X-X-
X--X--X"
union_jack('string') #return false.
```
Write your solution by modifying this code:
```python
def union_jack(n):
```
Your solution should implemented in the function "union_jack". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"2008 2 29\\n2015 1 1\", \"1505 9 9\\n2001 11 3\", \"1505 9 9\\n2619 11 3\", \"1505 13 9\\n2619 11 3\", \"573 1 44\\n2015 1 1\", \"595 2 44\\n2015 2 1\", \"597 2 44\\n2015 2 1\", \"246 21 0\\n2619 11 5\", \"246 21 0\\n5129 11 5\", \"431 21 0\\n5129 11 5\", \"597 2 19\\n895 -2 1\", \"51 16 1\\n5129 11 5\", \"77 16 1\\n5129 11 5\", \"77 16 1\\n1852 11 5\", \"941 4 28\\n895 -2 1\", \"941 4 28\\n1419 -2 1\", \"77 10 0\\n496 9 2\", \"77 10 0\\n117 9 2\", \"941 -1 28\\n1419 0 1\", \"0 10 -1\\n117 9 2\", \"1321 -1 28\\n1419 -1 1\", \"0 10 -1\\n135 9 3\", \"2137 -1 28\\n1419 -2 1\", \"1 10 -1\\n135 9 5\", \"2137 -1 28\\n1818 -1 1\", \"2 10 -1\\n135 9 5\", \"2137 -1 28\\n3039 -1 1\", \"167 -1 28\\n3039 -1 0\", \"167 -2 19\\n3039 -1 0\", \"4 15 -1\\n135 15 7\", \"167 -2 33\\n1934 -1 0\", \"167 -2 16\\n1934 -2 1\", \"0 9 -1\\n135 40 7\", \"161 -2 3\\n1934 -2 1\", \"161 -2 3\\n1934 -1 1\", \"161 -2 1\\n980 -1 2\", \"-1 -1 0\\n135 2 12\", \"161 -2 1\\n476 0 2\", \"-1 -1 0\\n140 2 12\", \"10 -2 1\\n476 0 2\", \"-2 1 0\\n140 1 16\", \"10 -6 0\\n128 1 1\", \"4 -6 3\\n128 1 1\", \"-2 0 1\\n227 0 31\", \"4 -6 3\\n119 0 1\", \"-2 -1 1\\n126 0 41\", \"2 -2 3\\n119 -1 1\", \"-4 -2 1\\n126 0 41\", \"-4 -2 1\\n240 0 41\", \"-3 -2 1\\n240 0 41\", \"-6 -2 1\\n240 0 41\", \"-9 -3 1\\n240 0 23\", \"-9 -3 3\\n94 0 44\", \"0 -1 1\\n107 -11 0\", \"-9 -1 3\\n176 0 1\", \"-9 -1 3\\n84 0 1\", \"1 -1 1\\n107 -15 0\", \"-9 -1 3\\n58 0 1\", \"-9 0 3\\n58 0 1\", \"1 0 1\\n201 -24 0\", \"2 0 1\\n201 -24 0\", \"2 0 1\\n299 -24 0\", \"3 0 1\\n299 -24 0\", \"-9 0 -1\\n41 -1 2\", \"0 1 1\\n241 -24 0\", \"-3 1 -1\\n41 -1 4\", \"-1 1 -1\\n41 -1 2\", \"-1 0 -1\\n41 0 1\", \"0 1 2\\n12 0 0\", \"0 1 2\\n2 0 0\", \"-2 0 -2\\n61 0 0\", \"0 -1 2\\n2 0 0\", \"-2 1 -2\\n61 0 0\", \"-1 1 -2\\n61 0 0\", \"0 0 2\\n4 0 0\", \"0 1 2\\n1 0 0\", \"-1 0 -4\\n86 2 0\", \"-1 0 -4\\n144 4 0\", \"-2 0 -8\\n144 4 0\", \"0 -1 -8\\n144 4 0\", \"0 1 -7\\n144 0 0\", \"0 1 -7\\n160 -1 0\", \"-1 1 -7\\n160 -1 0\", \"-1 1 -7\\n96 0 0\", \"0 1 -7\\n96 0 0\", \"1 2 -2\\n96 -1 0\", \"0 -2 -3\\n13 2 -1\", \"-1 -2 -3\\n13 2 -1\", \"0 -2 -3\\n7 2 -1\", \"0 -2 -3\\n5 1 -1\", \"0 -2 -3\\n4 1 -1\", \"21 -1 -1\\n0 0 1\", \"21 -2 -1\\n1 -1 1\", \"20 -4 -2\\n1 0 1\", \"5 0 1\\n-4 -23 0\", \"13 0 1\\n-4 -23 0\", \"7 0 1\\n-1 0 0\", \"14 0 1\\n-1 0 0\", \"0 -1 -7\\n10 1 -4\", \"0 0 -3\\n0 0 -3\", \"2008 2 29\\n2015 3 1\", \"1999 9 9\\n2001 11 3\"], \"outputs\": [\"7\\n\", \"497\\n\", \"1115\\n\", \"1114\\n\", \"1442\\n\", \"1420\\n\", \"1418\\n\", \"2373\\n\", \"4883\\n\", \"4698\\n\", \"298\\n\", \"5078\\n\", \"5052\\n\", \"1775\\n\", \"47\\n\", \"478\\n\", \"419\\n\", \"40\\n\", \"479\\n\", \"117\\n\", \"98\\n\", \"135\\n\", \"719\\n\", \"134\\n\", \"320\\n\", \"133\\n\", \"902\\n\", \"2872\\n\", \"2873\\n\", \"132\\n\", \"1768\\n\", \"1767\\n\", \"136\\n\", \"1773\\n\", \"1774\\n\", \"820\\n\", \"137\\n\", \"316\\n\", \"142\\n\", \"467\\n\", \"143\\n\", \"119\\n\", \"125\\n\", \"230\\n\", \"116\\n\", \"129\\n\", \"118\\n\", \"131\\n\", \"245\\n\", \"244\\n\", \"247\\n\", \"250\\n\", \"104\\n\", \"107\\n\", \"186\\n\", \"94\\n\", \"106\\n\", \"68\\n\", \"67\\n\", \"200\\n\", \"199\\n\", \"297\\n\", \"296\\n\", \"50\\n\", \"241\\n\", \"44\\n\", \"42\\n\", \"43\\n\", \"12\\n\", \"2\\n\", \"64\\n\", \"3\\n\", \"63\\n\", \"62\\n\", \"4\\n\", \"1\\n\", \"88\\n\", \"146\\n\", \"147\\n\", \"145\\n\", \"144\\n\", \"160\\n\", \"161\\n\", \"97\\n\", \"96\\n\", \"95\\n\", \"14\\n\", \"15\\n\", \"8\\n\", \"6\\n\", \"5\\n\", \"21\\n\", \"20\\n\", \"19\\n\", \"10\\n\", \"18\\n\", \"9\\n\", \"16\\n\", \"11\\n\", \"0\\n\", \"8\", \"3\"]}", "source": "primeintellect"} | A trick of fate caused Hatsumi and Taku to come to know each other. To keep the encounter in memory, they decided to calculate the difference between their ages. But the difference in ages varies depending on the day it is calculated. While trying again and again, they came to notice that the difference of their ages will hit a maximum value even though the months move on forever.
Given the birthdays for the two, make a program to report the maximum difference between their ages. The age increases by one at the moment the birthday begins. If the birthday coincides with the 29th of February in a leap year, the age increases at the moment the 1st of March arrives in non-leap years.
Input
The input is given in the following format.
y_1 m_1 d_1
y_2 m_2 d_2
The first and second lines provide Hatsumi’s and Taku’s birthdays respectively in year y_i (1 ≤ y_i ≤ 3000), month m_i (1 ≤ m_i ≤ 12), and day d_i (1 ≤ d_i ≤ Dmax) format. Where Dmax is given as follows:
* 28 when February in a non-leap year
* 29 when February in a leap-year
* 30 in April, June, September, and November
* 31 otherwise.
It is a leap year if the year represented as a four-digit number is divisible by 4. Note, however, that it is a non-leap year if divisible by 100, and a leap year if divisible by 400.
Output
Output the maximum difference between their ages.
Examples
Input
1999 9 9
2001 11 3
Output
3
Input
2008 2 29
2015 3 1
Output
8
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . - . . .\\n5\\n0 50 5 10\\n1 20 0 10\\n2 10 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . . . . .\\n5\\n0 50 8 10\\n0 20 0 10\\n2 10 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 0 3 3\\nP . . . . .\\n5\\n0 50 5 10\\n1 20 0 10\\n2 10 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . - . . .\\n5\\n0 50 5 10\\n1 20 0 10\\n2 10 5 15\\n3 150 3 10\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . . . . .\\n5\\n0 50 8 10\\n0 20 0 10\\n2 12 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 / .\\n. . 2 2 3 3\\nP . . . . .\\n5\\n0 50 8 10\\n0 20 0 10\\n2 18 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 1 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . - . . .\\n5\\n0 50 5 10\\n1 31 0 10\\n2 10 5 15\\n6 150 3 5\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 / 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . . . . .\\n5\\n0 50 8 3\\n1 20 0 10\\n2 10 5 15\\n3 150 3 2\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 1 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . - 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. . .\\n5\\n0 50 5 10\\n1 20 0 2\\n2 10 5 15\\n3 150 3 10\\n4 100 8 9\\n0 0\", \"6 5\\n1 1 . 0 0 4\\n1 . . . . .\\n. . 2 2 . .\\n. . 2 2 3 3\\nP . . . . .\\n5\\n0 50 5 10\\n1 20 0 10\\n2 10 5 15\\n3 150 3 5\\n4 100 8 9\\n0 0\"], \"outputs\": [\"180\\n\", \"160\\n\", \"210\\n\", \"330\\n\", \"162\\n\", \"168\\n\", \"191\\n\", \"130\\n\", \"192\\n\", \"178\\n\", \"310\\n\", \"268\\n\", \"230\\n\", \"215\\n\", \"166\\n\", \"306\\n\", \"157\\n\", \"60\\n\", \"150\\n\", \"133\\n\", \"171\\n\", \"156\\n\", \"161\\n\", \"165\\n\", \"58\\n\", \"278\\n\", \"127\\n\", \"107\\n\", \"249\\n\", \"17\\n\", \"170\\n\", \"30\\n\", \"14\\n\", \"20\\n\", \"11\\n\", \"260\\n\", \"337\\n\", \"292\\n\", \"244\\n\", \"159\\n\", \"141\\n\", \"131\\n\", \"27\\n\", \"167\\n\", \"102\\n\", \"32\\n\", \"180\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"180\\n\", \"180\\n\", \"180\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"162\\n\", \"160\\n\", \"180\\n\", \"180\\n\", \"180\\n\", \"160\\n\", \"162\\n\", \"130\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"160\\n\", \"210\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"160\\n\", \"191\\n\", \"130\\n\", \"180\\n\", \"130\\n\", \"160\\n\", \"160\\n\", \"180\\n\", \"310\\n\", \"180\"]}", "source": "primeintellect"} | Better things, cheaper. There is a fierce battle at the time sale held in some supermarkets today. "LL-do" here in Aizu is one such supermarket, and we are holding a slightly unusual time sale to compete with other chain stores. In a general time sale, multiple products are cheaper at the same time, but at LL-do, the time to start the time sale is set differently depending on the target product.
The Sakai family is one of the households that often use LL-do. Under the leadership of his wife, the Sakai family will hold a strategy meeting for the time sale to be held next Sunday, and analyze in what order the shopping will maximize the discount. .. The Sakai family, who are familiar with the inside of the store, drew a floor plan of the sales floor and succeeded in grasping where the desired items are, how much the discount is, and the time until they are sold out. The Sakai family was perfect so far, but no one could analyze it. So you got to know the Sakai family and decided to write a program. The simulation is performed assuming that one person moves.
There are 10 types of products, which are distinguished by the single-digit product number g. The time sale information includes the item number g, the discount amount d, the start time s of the time sale, and the sold-out time e.
The inside of the store is represented by a two-dimensional grid consisting of squares X in width and Y in height, and either a passage or a product shelf is assigned to each square. There is one type of product on a shelf, which is distinguished by item number g. You can buy any item, but you must not buy more than one item with the same item number. From the product shelves, you can pick up products in any direction as long as they are in the aisle squares that are adjacent to each other.
You can pick up items from the time when the time sale starts, but you cannot pick up items from the time when they are sold out. Also, the time starts from 0 when you enter the store.
You can move from the current square to the adjacent aisle squares on the top, bottom, left, and right, but you cannot move to the squares on the product shelves. You can't even go outside the store represented by the grid. One unit time elapses for each move. Also, do not consider the time to pick up the product.
Please create a program that outputs the maximum value of the total discount amount of the products that you could get by inputting the floor plan of the store, the initial position of the shopper and the time sale information of the product.
input
Given multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:
X Y
m1,1 m2,1 ... mX,1
m1,2 m2,2 ... mX,2
::
m1, Y m2, Y ... mX, Y
n
g1 d1 s1 e1
g2 d2 s2 e2
::
gn dn sn en
The first line gives the store sizes X, Y (3 ≤ X, Y ≤ 20). In the following Y row, the store information mi, j in the i-th column and j-th row is given with the following contents.
. (Period): Aisle square
Number: Product number
P: The initial position of the shopper
The following line is given the number of timesale information n (1 ≤ n ≤ 8). The next n lines are given the i-th time sale information gi di si ei (0 ≤ gi ≤ 9, 1 ≤ di ≤ 10000, 0 ≤ si, ei ≤ 100).
The number of datasets does not exceed 50.
output
For each data set, the maximum value of the total discount amount of the products that can be taken is output on one line.
Example
Input
6 5
1 1 . 0 0 4
1 . . . . .
. . 2 2 . .
. . 2 2 3 3
P . . . . .
5
0 50 5 10
1 20 0 10
2 10 5 15
3 150 3 5
4 100 8 9
0 0
Output
180
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"############################++#\\n+++++++++++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"##.#####.################\\n.........++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"##.#####.################\\n.........++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"################.#####.##\\n+L++++++++++++++.........\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"############################..#\\n+L++++++++++++++++++++++++++...\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"##.#############.########\\n+L.......................\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"############################..#\\n+L++++++++++++++++++++++++++...\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"##.##########.###########\\n+L.......................\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"##.#####.################\\n.........++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"################.#####.##\\n+L++++++++++++++.........\\n\", \"#..############################\\n...++++++++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"############################++#\\n+++++++++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"######################++#\\n+++++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#..######################\\n...++++++++++++++++++++L+\\n\", \"#++######################\\n+L+++++++++++++++++++++++\\n\", \"######################..#\\n+L++++++++++++++++++++...\\n\", \"...\\n.L.\\n...\\n#++++\\n..##L\\n...#+\\n...++\\nL\\n++++L++#.\\n\"]}", "source": "primeintellect"} | There is a grid, consisting of n rows and m columns. Each cell of the grid is either free or blocked. One of the free cells contains a lab. All the cells beyond the borders of the grid are also blocked.
A crazy robot has escaped from this lab. It is currently in some free cell of the grid. You can send one of the following commands to the robot: "move right", "move down", "move left" or "move up". Each command means moving to a neighbouring cell in the corresponding direction.
However, as the robot is crazy, it will do anything except following the command. Upon receiving a command, it will choose a direction such that it differs from the one in command and the cell in that direction is not blocked. If there is such a direction, then it will move to a neighbouring cell in that direction. Otherwise, it will do nothing.
We want to get the robot to the lab to get it fixed. For each free cell, determine if the robot can be forced to reach the lab starting in this cell. That is, after each step of the robot a command can be sent to a robot such that no matter what different directions the robot chooses, it will end up in a lab.
Input
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.
The first line of each testcase contains two integers n and m (1 ≤ n, m ≤ 10^6; n ⋅ m ≤ 10^6) — the number of rows and the number of columns in the grid.
The i-th of the next n lines provides a description of the i-th row of the grid. It consists of m elements of one of three types:
* '.' — the cell is free;
* '#' — the cell is blocked;
* 'L' — the cell contains a lab.
The grid contains exactly one lab. The sum of n ⋅ m over all testcases doesn't exceed 10^6.
Output
For each testcase find the free cells that the robot can be forced to reach the lab from. Given the grid, replace the free cells (marked with a dot) with a plus sign ('+') for the cells that the robot can be forced to reach the lab from. Print the resulting grid.
Example
Input
4
3 3
...
.L.
...
4 5
#....
..##L
...#.
.....
1 1
L
1 9
....L..#.
Output
...
.L.
...
#++++
..##L
...#+
...++
L
++++L++#.
Note
In the first testcase there is no free cell that the robot can be forced to reach the lab from. Consider a corner cell. Given any direction, it will move to a neighbouring border grid that's not a corner. Now consider a non-corner free cell. No matter what direction you send to the robot, it can choose a different direction such that it ends up in a corner.
In the last testcase, you can keep sending the command that is opposite to the direction to the lab and the robot will have no choice other than move towards the lab.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3 3 2\", \"3 3 3\", \"3 2 3\", \"1 2 3\", \"1 4 3\", \"1 4 5\", \"1 6 5\", \"1 6 4\", \"1 8 4\", \"1 1 4\", \"3 2 1\", \"2 5 2\", \"6 3 2\", \"6 3 3\", \"3 2 6\", \"1 2 2\", \"1 3 3\", \"1 5 4\", \"3 3 1\", \"2 6 2\", \"6 3 6\", \"3 4 3\", \"1 2 1\", \"1 6 3\", \"2 5 4\", \"1 1 1\", \"3 5 1\", \"2 6 4\", \"6 1 6\", \"2 1 1\", \"3 5 2\", \"2 1 2\", \"1 5 2\", \"2 2 4\", \"4 2 4\", \"2 1 5\", \"4 1 5\", \"2 2 2\", \"3 6 3\", \"2 6 3\", \"1 5 3\", \"1 6 1\", \"6 2 1\", \"2 8 2\", \"3 3 4\", \"9 3 3\", \"1 6 7\", \"3 1 1\", \"6 6 6\", \"3 4 5\", \"2 4 4\", \"3 4 1\", \"6 1 5\", \"3 1 2\", \"4 1 1\", \"5 1 1\", \"2 3 4\", \"7 2 4\", \"7 1 10\", \"2 4 2\", \"4 3 3\", \"2 2 3\", \"1 11 1\", \"1 8 2\", \"9 3 2\", \"2 6 7\", \"6 6 12\", \"3 6 5\", \"3 4 4\", \"6 3 1\", \"3 1 4\", \"2 3 3\", \"7 2 2\", \"6 2 5\", \"7 2 10\", \"4 4 4\", \"5 3 3\", \"1 3 2\", \"8 3 2\", \"2 6 5\", \"6 7 12\", \"3 8 5\", \"3 2 4\", \"6 6 1\", \"4 4 3\", \"7 2 1\", \"6 2 3\", \"7 4 10\", \"4 3 5\", \"8 4 2\", \"2 11 5\", \"6 2 12\", \"3 8 3\", \"7 6 1\", \"6 4 3\", \"7 3 10\", \"4 1 2\", \"8 4 1\", \"1 11 5\", \"10 2 12\", \"2 2 1\", \"2 3 2\"], \"outputs\": [\"YYG\\nRBB\\nGGY\\n\", \"YRR\\nYYG\\nYBB\\n\", \"RR\\nYR\\nYB\\n\", \"RR\\n\", \"YYRG\\n\", \"RRRR\\n\", \"YYRRRG\\n\", \"YYYRGG\\n\", \"RYYYBGGG\\n\", \"R\\n\", \"RB\\nBR\\nRB\\n\", \"RRBBR\\nYGGYY\\n\", \"YYG\\nRBB\\nGGY\\nBRR\\nYYG\\nRBB\\n\", \"YRR\\nYYG\\nYBB\\nGBB\\nGGY\\nGRR\\n\", \"RR\\nRR\\nRR\\n\", \"YR\\n\", \"YRR\\n\", \"YYRRG\\n\", \"YGY\\nGYG\\nYGY\\n\", \"YRGBYR\\nYBGRYB\\n\", \"RRR\\nRRR\\nRRR\\nYRR\\nYYG\\nYBB\\n\", \"YYRG\\nYYBG\\nRBBB\\n\", \"RB\\n\", \"RYYBGG\\n\", \"YYRRG\\nYYYGG\\n\", \"Y\\n\", \"YGYGY\\nGYGYG\\nYGYGY\\n\", \"YYYRGG\\nYYYBGG\\n\", \"R\\nR\\nR\\nR\\nR\\nY\\n\", \"Y\\nG\\n\", \"RRBBR\\nYGGYY\\nBBRRB\\n\", \"R\\nY\\n\", \"RRBBR\\n\", \"RR\\nRR\\n\", \"RR\\nRR\\nYR\\nYB\\n\", \"R\\nR\\n\", \"R\\nR\\nR\\nR\\n\", \"YR\\nYB\\n\", \"RYYBGG\\nRRBBBR\\nRGGBYY\\n\", \"RYYBGG\\nRRBBBR\\n\", \"YYYGG\\n\", \"RBRBRB\\n\", \"RB\\nBR\\nRB\\nBR\\nRB\\nBR\\n\", \"RYBGRYBG\\nRGBYRGBY\\n\", \"RRR\\nYRR\\nYYG\\n\", \"YRR\\nYYG\\nYBB\\nGBB\\nGGY\\nGRR\\nYRR\\nYYG\\nYBB\\n\", \"RRRRRR\\n\", \"Y\\nG\\nY\\n\", \"YRRRRR\\nYYRRRG\\nYYYRGG\\nYYYBGG\\nYYBBBG\\nYBBBBB\\n\", \"RRRR\\nYRRR\\nYYRG\\n\", \"YRRR\\nYYRG\\n\", \"RBRB\\nBRBR\\nRBRB\\n\", \"R\\nR\\nR\\nR\\nY\\nB\\n\", \"R\\nY\\nB\\n\", \"Y\\nG\\nY\\nG\\n\", \"Y\\nG\\nY\\nG\\nY\\n\", \"RRR\\nYRR\\n\", \"RR\\nRR\\nYR\\nYB\\nBB\\nBB\\nGB\\n\", \"R\\nR\\nR\\nR\\nR\\nR\\nR\\n\", \"RYBG\\nRGBY\\n\", \"YRR\\nYYG\\nYBB\\nGBB\\n\", \"RR\\nYR\\n\", \"YGYGYGYGYGY\\n\", \"RYBGRYBG\\n\", \"YYG\\nRBB\\nGGY\\nBRR\\nYYG\\nRBB\\nGGY\\nBRR\\nYYG\\n\", \"RRRRRR\\nYRRRRR\\n\", \"RRRRRR\\nRRRRRR\\nRRRRRR\\nRRRRRR\\nRRRRRR\\nRRRRRR\\n\", \"YYRRRG\\nYYYRGG\\nYYYBGG\\n\", \"YRRR\\nYYRG\\nYYBG\\n\", \"YGY\\nGYG\\nYGY\\nGYG\\nYGY\\nGYG\\n\", \"R\\nR\\nR\\n\", \"YRR\\nYYG\\n\", \"YR\\nYB\\nGB\\nGR\\nYR\\nYB\\nGB\\n\", \"RR\\nRR\\nRR\\nYR\\nYB\\nBB\\n\", \"RR\\nRR\\nRR\\nRR\\nRR\\nRR\\nRR\\n\", \"YRRR\\nYYRG\\nYYBG\\nYBBB\\n\", \"YRR\\nYYG\\nYBB\\nGBB\\nGGY\\n\", \"YYG\\n\", \"YYG\\nRBB\\nGGY\\nBRR\\nYYG\\nRBB\\nGGY\\nBRR\\n\", \"YYRRRG\\nYYYRGG\\n\", \"RRRRRRR\\nRRRRRRR\\nRRRRRRR\\nRRRRRRR\\nRRRRRRR\\nYRRRRRR\\n\", \"YYYYRGGG\\nYYYYBGGG\\nRYYBBBGG\\n\", \"RR\\nRR\\nYR\\n\", \"RBRBRB\\nBRBRBR\\nRBRBRB\\nBRBRBR\\nRBRBRB\\nBRBRBR\\n\", \"YYRG\\nYYBG\\nRBBB\\nGGBY\\n\", \"RB\\nBR\\nRB\\nBR\\nRB\\nBR\\nRB\\n\", \"RR\\nYR\\nYB\\nBB\\nGB\\nGR\\n\", \"RRRR\\nRRRR\\nRRRR\\nRRRR\\nRRRR\\nRRRR\\nYRRR\\n\", \"RRR\\nRRR\\nYRR\\nYYG\\n\", \"RYBG\\nRGBY\\nBGRY\\nBYRG\\nRYBG\\nRGBY\\nBGRY\\nBYRG\\n\", \"RRYYYBBGGGR\\nRRRYBBBBGRR\\n\", \"RR\\nRR\\nRR\\nRR\\nRR\\nRR\\n\", \"RRRBBBRR\\nYRGGBYYR\\nYBGGRYYB\\n\", \"RBRBRB\\nBRBRBR\\nRBRBRB\\nBRBRBR\\nRBRBRB\\nBRBRBR\\nRBRBRB\\n\", \"YYRG\\nYYBG\\nRBBB\\nGGBY\\nGGRY\\nBRRR\\n\", \"RRR\\nRRR\\nRRR\\nRRR\\nRRR\\nRRR\\nRRR\\n\", \"R\\nY\\nB\\nG\\n\", \"RBRB\\nBRBR\\nRBRB\\nBRBR\\nRBRB\\nBRBR\\nRBRB\\nBRBR\\n\", \"RRYYYBBGGGR\\n\", \"RR\\nRR\\nRR\\nRR\\nRR\\nRR\\nRR\\nRR\\nRR\\nRR\\n\", \"RY\\nGR\", \"RYB\\nRGB\"]}", "source": "primeintellect"} | We have a grid with H rows and W columns of squares. We will represent the square at the i-th row from the top and j-th column from the left as (i,\ j). Also, we will define the distance between the squares (i_1,\ j_1) and (i_2,\ j_2) as |i_1 - i_2| + |j_1 - j_2|.
Snuke is painting each square in red, yellow, green or blue. Here, for a given positive integer d, he wants to satisfy the following condition:
* No two squares with distance exactly d have the same color.
Find a way to paint the squares satisfying the condition. It can be shown that a solution always exists.
Constraints
* 2 ≤ H, W ≤ 500
* 1 ≤ d ≤ H + W - 2
Input
Input is given from Standard Input in the following format:
H W d
Output
Print a way to paint the squares satisfying the condition, in the following format. If the square (i,\ j) is painted in red, yellow, green or blue, c_{ij} should be `R`, `Y`, `G` or `B`, respectively.
c_{11}c_{12}...c_{1W}
:
c_{H1}c_{H2}...c_{HW}
Output
Print a way to paint the squares satisfying the condition, in the following format. If the square (i,\ j) is painted in red, yellow, green or blue, c_{ij} should be `R`, `Y`, `G` or `B`, respectively.
c_{11}c_{12}...c_{1W}
:
c_{H1}c_{H2}...c_{HW}
Examples
Input
2 2 1
Output
RY
GR
Input
2 3 2
Output
RYB
RGB
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[5, 2, 3], [5, 3, 4], [5, 4, 3], [666, 665, 2], [3691401, 1892272, 5]], \"outputs\": [[false], [false], [true], [false], [false]]}", "source": "primeintellect"} | Your task it to return ```true``` if the fractional part (rounded to 1 digit) of the result (```a``` / ```b```) exists, more than ```0``` and is multiple of ```n```.
Otherwise return ```false```. (For Python return True or False)
All arguments are positive digital numbers.
Rounding works like toFixed() method. (if more than...5 rounds up)
Find exapmles below:
```
isMultiple(5, 2, 3) -> false // 2.5 -> 5 is not multiple of 3
isMultiple(5, 3, 4) -> false // 1.7 -> 7 is not multiple of 4
isMultiple(5, 4, 3) -> true // 1.3 -> 3 is multiple of 3
isMultiple(666, 665, 2) -> false // 1.0 -> return false
```
Write your solution by modifying this code:
```python
def isMultiple(a, b, n):
```
Your solution should implemented in the function "isMultiple". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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79 77 85 83 71 91 83 85 81 79 81 81 91 91 87 79 81 91 81 77 87 71 87 91 89 89 77 87 91 87 75 83 87 75 73 83 81 79 77 91 76 76 88 82 88 78 86 72 84 86 72 74 74 88 84 86 80 84 90 80 88 84 82 80 84 74 72 86 86 76 82 80 86 74 84 88 74 82 90 72 86 72 80 80 82 86 88 82 78 72 88\\n\", \"20\\n12 4 12 12 2 10 4 12 18 14 21 21 15 7 17 11 5 11 3 13\\n\", \"88\\n29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 30 30 28 28 30 28 28 28 30 30 30 30 28 30 30 28 28 28 30 28 30 30 30 30 28 30 30 30 28 30 28 28 28 30 30 30 30 28 30 28 30 28\\n\", \"62\\n37 45 41 45 49 37 47 41 39 43 43 39 45 41 43 47 37 41 47 37 47 49 43 39 37 45 45 47 37 47 43 34 42 36 48 36 44 48 44 46 48 44 44 48 36 42 40 38 36 48 48 38 46 48 34 34 46 42 34 36 34 36\\n\", \"148\\n73 53 49 49 65 69 61 67 57 55 53 57 57 59 69 59 71 55 71 49 51 67 57 73 71 55 59 59 61 55 73 69 63 55 59 51 69 73 67 55 61 53 49 69 53 63 71 71 65 63 61 63 65 69 61 63 63 71 71 65 57 63 61 69 49 53 59 51 73 61 55 73 63 65 70 68 68 66 64 56 68 50 68 56 68 70 68 54 70 60 62 68 64 56 52 66 66 64 72 58 70 58 52 50 56 50 56 50 50 72 70 64 50 62 58 70 72 62 62 72 64 52 50 54 56 54 72 64 62 62 72 70 66 70 62 64 50 72 62 58 58 58 56 72 58 52 60 72\\n\", \"76\\n7 7 9 9 9 11 9 11 7 7 9 7 9 9 9 7 11 11 7 11 7 11 7 7 9 11 7 7 7 7 11 7 9 11 11 9 9 11 8 10 8 8 8 10 10 10 10 8 8 8 8 10 10 10 8 8 8 10 8 8 8 8 8 8 10 8 8 10 10 10 10 10 8 10 10 10\\n\", \"52\\n11 33 37 51 27 59 57 55 73 67 13 47 45 39 27 21 23 61 37 35 39 63 69 53 61 55 44 34 64 30 54 48 32 66 32 62 50 44 38 24 22 30 14 54 12 28 40 40 50 54 64 56\\n\", \"60\\n633 713 645 745 641 685 731 645 655 633 703 715 633 739 657 755 657 671 567 699 743 737 667 701 649 721 671 699 697 675 570 570 570 648 684 732 598 558 674 766 720 692 702 756 756 646 568 630 668 742 604 628 628 764 636 600 678 734 638 758\\n\", \"146\\n3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 4 2 4 2 4 2 4 2 2 2 4 2 4 2 4 4 2 4 4 2 2 4 2 2 2 4 4 2 2 2 2 2 2 2 4 4 4 4 4 2 2 4 2 2 2 2 4 4 2 4 4 2 2 2 2 2 2 4 4 4 4 4 4 2 2 2 2 2 2 4 4 4\\n\", \"30\\n2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31\\n\", \"16\\n5 7 7 7 11 11 9 5 4 6 6 10 6 4 10 6\\n\", \"70\\n763 657 799 713 667 531 829 675 799 721 741 549 793 553 723 579 853 713 835 833 581 801 683 551 617 733 611 699 607 565 579 693 897 543 607 848 774 602 544 846 710 722 568 740 548 702 908 572 572 806 834 794 648 770 908 778 748 692 704 624 580 746 780 666 678 822 834 640 548 788\\n\", \"10\\n119 289 109 185 251 184 224 588 360 518\\n\", \"12\\n1751 1909 1655 1583 1867 1841 1740 1584 1518 1806 1664 1518\\n\", \"124\\n135 161 147 135 137 153 145 159 147 129 131 157 163 161 127 129 141 133 133 151 147 169 159 137 137 153 165 137 139 151 149 161 157 149 147 139 145 129 159 155 133 129 139 151 155 145 135 155 135 137 157 141 169 151 163 151 159 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8940 5060 7368 5252 6526 9072 5168 7420 5336 4734 8076 7048 8504 5696 9266 8966 7416 5162\\n\", \"80\\n5599 5365 6251 3777 6887 5077 4987 6925 3663 5457 5063 4077 3531 6359 4293 6305 4585 3641 6737 6403 6863 4839 3765 3767 5807 6657 7275 5625 3635 3939 7035 6945 7167 5023 5949 4295 4899 4595 5725 3863 3750 4020 5096 5232 6566 6194 5524 3702 6876 4464 3720 5782 5160 3712 7028 6204 5378 5896 5494 7084 5290 6784 6408 5410 4260 5082 4210 5336 4110 5064 3664 4964 5202 5410 5634 3990 5034 6774 4956 4806\\n\", \"178\\n5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6\\n\", \"78\\n159 575 713 275 463 365 461 537 301 439 669 165 555 267 571 383 495 375 321 605 367 481 619 675 115 193 447 303 263 421 189 491 591 673 635 309 301 391 379 736 652 704 634 258 708 206 476 408 702 630 650 236 546 328 348 86 96 628 668 426 640 170 434 486 168 640 260 426 186 272 650 616 252 372 442 178 266 464\\n\", \"128\\n3 3 5 3 5 3 5 3 5 5 3 5 3 5 3 5 3 5 5 5 5 5 5 5 5 3 3 3 5 3 5 3 3 3 3 5 3 5 5 3 3 3 3 5 5 5 5 3 5 3 3 5 5 3 5 3 3 5 3 3 5 3 3 3 6 6 6 4 4 4 4 4 6 6 6 6 6 6 4 6 6 4 6 6 4 4 4 6 4 6 6 4 6 4 4 6 4 4 6 4 6 4 6 6 6 6 6 6 4 6 4 6 6 4 4 6 4 6 6 4 6 4 6 4 6 6 4 6\\n\", \"92\\n5 5 3 5 3 3 5 3 5 3 5 5 5 3 3 5 3 5 3 5 3 5 3 5 3 3 3 5 3 5 5 5 5 5 5 3 5 3 3 5 3 5 5 3 3 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n\", \"30\\n25 43 41 17 15 29 29 39 17 19 23 9 39 19 25 26 32 38 12 42 44 44 12 22 26 20 34 12 30 16\\n\", \"98\\n5 5 3 3 3 3 3 5 3 5 3 5 3 3 5 5 5 5 3 5 5 3 3 5 3 3 5 3 3 3 5 5 3 5 3 3 3 5 5 5 3 5 5 5 3 5 5 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n\", \"6\\n681 673 659 656 650 644\\n\", \"90\\n11 9 11 9 9 11 9 9 11 9 11 9 11 11 9 11 11 11 11 9 9 11 11 11 9 9 9 11 11 9 11 11 9 11 9 9 11 11 11 11 9 11 11 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10\\n\", \"38\\n5 7 7 5 7 7 7 5 7 5 7 5 7 5 7 7 5 7 7 4 6 4 8 4 4 8 4 8 4 6 6 8 6 8 6 4 8 6\\n\", \"4\\n2 2 9973 9967\\n\", \"15\\n3 3 0 3 3 3 3 4 2 4 2 2 2 4 2\\n\", \"152\\n29 23 17 25 13 29 29 29 25 23 25 29 19 25 13 25 13 23 21 27 15 29 29 25 27 17 17 19 25 19 13 19 15 13 19 13 17 17 19 17 17 13 25 21 17 13 21 25 25 21 19 23 17 17 29 15 15 17 25 13 25 13 21 13 19 19 13 13 21 25 23 19 19 21 29 29 26 30 22 20 22 28 24 28 18 16 22 18 16 20 12 26 16 20 12 24 20 28 16 16 16 16 12 20 22 12 20 12 22 18 22 12 22 22 24 22 30 28 20 24 30 14 18 12 16 14 18 18 16 22 16 20 20 20 28 30 20 24 12 24 24 28 22 30 24 18 12 20 22 24 12 12\\n\", \"10\\n5 1 7 7 5 6 6 6 6 6\\n\", \"102\\n87 73 87 81 71 83 71 91 75 87 87 79 77 85 83 71 91 83 85 81 79 81 81 91 91 87 79 81 91 81 77 87 71 87 91 89 89 77 87 91 87 75 83 87 75 73 83 81 79 77 91 76 76 88 82 88 78 86 72 84 86 72 74 74 88 84 86 80 84 90 80 88 84 82 80 4 74 72 86 86 76 82 80 86 74 84 88 74 82 90 72 86 72 80 80 82 86 88 82 78 72 88\\n\", \"30\\n2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 41\\n\", \"70\\n763 657 799 713 667 531 829 675 799 721 741 549 793 553 723 579 853 713 835 833 581 801 683 551 617 733 611 699 607 565 579 693 897 543 607 848 774 602 688 846 710 722 568 740 548 702 908 572 572 806 834 794 648 770 908 778 748 692 704 624 580 746 780 666 678 822 834 640 548 788\\n\", \"178\\n5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 12 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6\\n\", \"30\\n25 43 41 17 15 29 29 39 17 19 23 9 39 19 5 26 32 38 12 42 44 44 12 22 26 20 34 12 30 16\\n\", \"38\\n5 7 7 5 7 7 7 5 7 5 7 5 7 5 7 7 5 7 7 4 6 4 8 4 4 8 4 8 4 6 6 8 6 8 6 2 8 6\\n\", \"10\\n5 1 7 7 5 6 6 6 2 6\\n\", \"74\\n3 3 5 3 5 5 3 5 3 3 5 5 3 5 3 3 3 3 3 3 3 5 5 3 5 3 5 3 3 5 5 5 5 3 3 5 3 4 6 6 6 6 4 4 4 6 6 6 6 4 4 4 4 6 6 4 6 4 4 6 6 4 4 4 6 4 4 4 4 6 4 4 4 0\\n\", \"102\\n87 73 87 81 71 83 71 91 75 87 87 79 77 85 83 71 91 83 85 81 79 81 81 91 91 87 79 81 91 81 77 87 71 87 91 89 89 77 87 91 87 75 83 87 75 73 83 81 79 77 91 76 76 88 82 88 78 86 72 84 86 54 74 74 88 84 86 80 84 90 80 88 84 82 80 4 74 72 86 86 76 82 80 86 74 84 88 74 82 90 72 86 72 80 80 82 86 88 82 78 72 88\\n\", \"62\\n37 45 41 45 49 37 47 41 39 43 43 39 45 41 43 47 37 41 47 37 47 49 43 39 37 45 9 47 37 47 43 34 42 36 48 36 44 48 44 46 48 44 44 48 36 42 40 38 36 48 48 38 46 12 34 34 46 42 34 36 34 36\\n\", \"60\\n9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 6 9 9 9 9 9 9 9 9 9 9 8 10 10 10 10 8 10 10 8 10 8 8 10 8 8 10 10 10 8 8 8 8 10 8 10 8 8 8 8 10\\n\", \"20\\n76 38 74 176 106 134 12 88 66 178 63 72 199 99 29 67 135 29 101 47\\n\", \"74\\n3 3 5 3 5 5 3 5 3 3 5 5 3 5 3 3 3 3 3 3 3 5 5 3 5 3 5 3 3 5 5 5 5 3 3 5 3 4 6 6 6 6 4 4 4 6 6 6 6 4 4 4 4 6 6 4 6 4 4 6 6 4 4 4 6 4 4 4 4 6 4 4 4 4\\n\", \"20\\n12 4 12 12 2 10 4 12 18 14 21 4 15 7 17 11 5 11 3 13\\n\", \"88\\n29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 30 30 28 28 30 28 34 28 30 30 30 30 28 30 30 28 28 28 30 28 30 30 30 30 28 30 30 30 28 30 28 28 28 30 30 30 30 28 30 28 30 28\\n\", \"62\\n37 45 41 45 49 37 47 41 39 43 43 39 45 41 43 47 37 41 47 37 47 49 43 39 37 45 9 47 37 47 43 34 42 36 48 36 44 48 44 46 48 44 44 48 36 42 40 38 36 48 48 38 46 48 34 34 46 42 34 36 34 36\\n\", \"148\\n73 53 49 49 65 69 61 67 57 55 53 57 57 59 69 59 71 55 71 49 51 67 57 73 71 55 59 59 61 55 73 69 63 55 59 51 69 73 67 55 61 53 49 69 53 63 71 71 65 63 61 30 65 69 61 63 63 71 71 65 57 63 61 69 49 53 59 51 73 61 55 73 63 65 70 68 68 66 64 56 68 50 68 56 68 70 68 54 70 60 62 68 64 56 52 66 66 64 72 58 70 58 52 50 56 50 56 50 50 72 70 64 50 62 58 70 72 62 62 72 64 52 50 54 56 54 72 64 62 62 72 70 66 70 62 64 50 72 62 58 58 58 56 72 58 52 60 72\\n\", \"76\\n7 7 9 9 9 11 9 11 7 7 9 7 9 9 9 7 11 11 14 11 7 11 7 7 9 11 7 7 7 7 11 7 9 11 11 9 9 11 8 10 8 8 8 10 10 10 10 8 8 8 8 10 10 10 8 8 8 10 8 8 8 8 8 8 10 8 8 10 10 10 10 10 8 10 10 10\\n\", \"52\\n11 33 37 88 27 59 57 55 73 67 13 47 45 39 27 21 23 61 37 35 39 63 69 53 61 55 44 34 64 30 54 48 32 66 32 62 50 44 38 24 22 30 14 54 12 28 40 40 50 54 64 56\\n\", \"146\\n3 3 3 3 3 3 3 3 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 4 2 4 2 4 2 4 2 2 2 4 2 4 2 4 4 2 4 4 2 2 4 2 2 2 4 4 2 2 2 2 2 2 2 4 4 4 4 4 2 2 4 2 2 2 2 4 4 2 4 4 2 2 2 2 2 2 4 4 4 4 4 4 2 2 2 2 2 2 4 4 4\\n\", \"16\\n5 10 7 7 11 11 9 5 4 6 6 10 6 4 10 6\\n\", \"10\\n119 289 109 185 251 184 224 950 360 518\\n\", \"12\\n1751 1909 460 1583 1867 1841 1740 1584 1518 1806 1664 1518\\n\", \"81\\n7627 7425 8929 785 5649 7853 4747 6267 4997 6447 5411 7707 5169 5789 8011 9129 8045 7463 6139 8263 7547 7453 7993 8343 5611 7039 9001 5569 9189 7957 5537 8757 8795 4963 9149 5845 9203 5459 8501 7273 9152 7472 8050 8568 6730 8638 4938 9000 9230 5464 5950 6090 7394 5916 4890 6246 4816 4920 8638 4706 6308 6816 7570 8940 5060 7368 5252 6526 9072 5168 7420 5336 4734 8076 7048 8504 5696 9266 8966 7416 5162\\n\", \"78\\n159 575 713 275 463 365 461 537 301 439 669 165 555 267 571 383 516 375 321 605 367 481 619 675 115 193 447 303 263 421 189 491 591 673 635 309 301 391 379 736 652 704 634 258 708 206 476 408 702 630 650 236 546 328 348 86 96 628 668 426 640 170 434 486 168 640 260 426 186 272 650 616 252 372 442 178 266 464\\n\", \"128\\n3 3 5 3 5 3 5 3 5 5 3 5 3 8 3 5 3 5 5 5 5 5 5 5 5 3 3 3 5 3 5 3 3 3 3 5 3 5 5 3 3 3 3 5 5 5 5 3 5 3 3 5 5 3 5 3 3 5 3 3 5 3 3 3 6 6 6 4 4 4 4 4 6 6 6 6 6 6 4 6 6 4 6 6 4 4 4 6 4 6 6 4 6 4 4 6 4 4 6 4 6 4 6 6 6 6 6 6 4 6 4 6 6 4 4 6 4 6 6 4 6 4 6 4 6 6 4 6\\n\", \"92\\n5 5 3 5 3 3 5 3 5 3 10 5 5 3 3 5 3 5 3 5 3 5 3 5 3 3 3 5 3 5 5 5 5 5 5 3 5 3 3 5 3 5 5 3 3 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n\", \"98\\n5 5 3 3 3 3 3 5 3 5 3 5 3 3 5 5 5 5 3 5 5 3 3 5 3 3 5 3 3 3 5 5 3 5 3 3 3 5 5 5 3 5 5 5 3 3 5 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4\\n\", \"6\\n681 673 659 656 650 619\\n\", \"90\\n11 9 11 9 9 11 9 9 11 9 11 9 11 11 9 11 11 11 11 9 9 11 11 11 9 9 9 11 11 9 11 11 9 11 9 9 11 11 11 11 9 11 11 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 10 10 10 10 10 10\\n\", \"4\\n2 2 9973 9151\\n\", \"5\\n2 1 2 2 2\\n\", \"4\\n3 4 8 0\\n\", \"12\\n2 3 4 8 6 7 8 9 10 11 12 13\\n\", \"24\\n2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 18 19 20 21 22 23 24 25\\n\", \"15\\n3 3 0 3 3 3 3 4 2 4 2 2 2 6 2\\n\", \"152\\n29 23 17 25 13 29 29 29 25 23 25 29 19 25 13 25 13 23 21 27 15 29 29 25 27 17 17 19 25 19 13 19 15 13 19 13 17 17 19 17 17 13 25 21 17 13 21 25 25 21 19 23 17 17 29 15 15 17 25 13 25 13 21 13 19 19 13 13 21 25 23 19 19 21 29 22 26 30 22 20 22 28 24 28 18 16 22 18 16 20 12 26 16 20 12 24 20 28 16 16 16 16 12 20 22 12 20 12 22 18 22 12 22 22 24 22 30 28 20 24 30 14 18 12 16 14 18 18 16 22 16 20 20 20 28 30 20 24 12 24 24 28 22 30 24 18 12 20 22 24 12 12\\n\", \"60\\n9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 6 9 9 9 9 9 14 9 9 9 9 8 10 10 10 10 8 10 10 8 10 8 8 10 8 8 10 10 10 8 8 8 8 10 8 10 8 8 8 8 10\\n\", \"20\\n76 38 74 176 106 134 11 88 66 178 63 72 199 99 29 67 135 29 101 47\\n\", \"20\\n12 4 12 12 2 10 4 12 18 14 21 6 15 7 17 11 5 11 3 13\\n\", \"88\\n29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 24 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 28 30 30 28 28 30 28 34 28 30 30 30 30 28 30 30 28 28 28 30 28 30 30 30 30 28 30 30 30 28 30 28 28 28 30 30 30 30 28 30 28 30 28\\n\", \"148\\n73 53 49 49 65 69 61 67 57 55 53 80 57 59 69 59 71 55 71 49 51 67 57 73 71 55 59 59 61 55 73 69 63 55 59 51 69 73 67 55 61 53 49 69 53 63 71 71 65 63 61 30 65 69 61 63 63 71 71 65 57 63 61 69 49 53 59 51 73 61 55 73 63 65 70 68 68 66 64 56 68 50 68 56 68 70 68 54 70 60 62 68 64 56 52 66 66 64 72 58 70 58 52 50 56 50 56 50 50 72 70 64 50 62 58 70 72 62 62 72 64 52 50 54 56 54 72 64 62 62 72 70 66 70 62 64 50 72 62 58 58 58 56 72 58 52 60 72\\n\", \"5\\n2 2 2 2 2\\n\", \"4\\n3 4 8 9\\n\", \"12\\n2 3 4 5 6 7 8 9 10 11 12 13\\n\", \"24\\n2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25\\n\"], \"outputs\": [\"Impossible\\n\", \"12\\n84 1 78 2 80 3 152 76 151 75 150 73 149 72 147 70 146 71 148 74 77 19 92 20 97 25 100 29 101 31 102 33 109 32 110 34 115 36 117 38 119 40 120 41 121 42 118 46 123 49 125 47 116 44 114 43 113 39 111 35 112 37 107 27 104 26 106 23 103 22 96 17 93 16 89 15 86 14 87 13 84 11 82 5 83\\n4 4 79 9 81\\n4 6 85 7 88\\n4 8 91 12 95\\n4 10 90 18 94\\n4 21 98 24 99\\n4 28 105 30 108\\n4 45 122 48 124\\n4 50 129 56 130\\n28 51 127 52 126 53 132 54 133 58 134 63 137 69 143 66 142 61 139 65 141 64 140 62 138 60 136 55 128\\n4 57 131 59 135\\n4 67 144 68 145\\n\", \"15\\n4 1 31 2 32\\n4 3 33 4 34\\n4 5 35 6 36\\n4 7 37 8 38\\n4 9 39 10 40\\n4 11 41 12 42\\n4 13 43 14 44\\n4 15 45 16 46\\n4 17 47 18 48\\n4 19 49 20 50\\n4 21 51 22 52\\n4 23 53 24 54\\n4 25 55 26 56\\n4 27 57 28 58\\n4 29 59 30 60\\n\", \"2\\n6 1 7 2 6 5 10\\n4 3 8 4 9\\n\", \"Impossible\\n\", \"18\\n6 1 43 2 38 37 74\\n4 3 39 5 40\\n4 4 44 7 45\\n4 6 41 8 42\\n4 9 50 10 52\\n4 11 46 12 47\\n4 13 53 15 56\\n4 14 48 22 49\\n4 16 58 17 59\\n4 18 62 19 63\\n4 20 64 21 66\\n4 23 51 25 54\\n4 24 67 26 68\\n4 27 55 30 57\\n4 28 69 29 71\\n4 31 60 32 61\\n4 33 65 36 70\\n4 34 72 35 73\\n\", \"7\\n52 1 52 41 97 39 95 34 94 33 92 32 83 26 75 16 71 11 68 10 67 7 57 5 61 3 58 4 55 8 54 9 56 12 59 13 62 14 65 17 70 24 72 19 74 20 79 22 80 23 81 44 53\\n28 2 69 21 102 27 73 36 76 37 77 31 101 25 78 29 82 28 84 30 89 35 87 40 90 43 86 46 100\\n4 6 60 15 63\\n4 18 64 47 66\\n4 38 85 42 88\\n6 45 96 48 99 51 98\\n4 49 91 50 93\\n\", \"3\\n12 1 14 2 20 9 18 8 17 4 16 3 15\\n4 5 11 6 12\\n4 7 13 10 19\\n\", \"Impossible\\n\", \"Impossible\\n\", \"13\\n88 1 142 6 139 74 138 71 131 67 127 60 129 54 119 53 120 40 117 49 118 44 114 37 111 32 101 23 103 30 102 26 100 18 99 10 95 13 94 21 91 5 144 14 148 8 89 12 84 11 90 4 88 3 79 73 77 62 76 57 137 56 136 52 128 50 123 46 113 45 109 35 108 33 106 28 104 27 92 25 87 19 85 17 83 16 81 15 145\\n4 2 80 9 82\\n8 7 75 61 146 63 78 70 86\\n4 20 93 22 98\\n4 24 96 29 97\\n12 31 112 38 121 43 122 41 116 39 110 34 115\\n4 36 105 42 107\\n4 47 125 48 133\\n4 51 132 55 134\\n4 58 143 59 147\\n4 64 130 68 135\\n4 65 124 66 126\\n4 69 140 72 141\\n\", \"16\\n4 1 40 2 44\\n6 3 41 38 39 4 76\\n4 5 42 6 43\\n4 7 45 9 46\\n14 8 48 11 47 10 52 12 53 15 51 14 50 13 49\\n4 16 54 19 58\\n4 17 55 18 56\\n4 20 57 22 59\\n4 21 65 23 68\\n4 24 69 27 70\\n4 25 60 26 61\\n4 28 71 29 72\\n4 30 74 32 75\\n4 31 62 33 63\\n4 34 64 35 66\\n4 36 67 37 73\\n\", \"1\\n52 1 30 6 27 23 48 22 49 24 44 20 45 18 46 21 43 15 47 16 39 17 40 11 34 25 32 8 31 9 50 26 28 3 29 2 51 19 42 10 41 14 38 13 36 12 37 7 35 4 33 5 52\\n\", \"4\\n44 1 37 6 55 27 60 24 56 26 57 4 38 9 34 5 59 3 54 30 58 28 53 25 52 20 49 13 51 19 42 16 44 11 41 14 50 15 40 17 46 8 47 10 39\\n4 2 31 7 32\\n4 12 35 29 36\\n8 18 43 22 33 23 48 21 45\\n\", \"36\\n6 1 75 2 74 73 146\\n4 3 76 4 77\\n4 5 78 6 79\\n4 7 80 8 81\\n4 9 82 10 83\\n4 11 84 12 85\\n4 13 86 14 87\\n4 15 88 16 89\\n4 17 90 18 91\\n4 19 92 20 93\\n4 21 94 22 95\\n4 23 96 24 97\\n4 25 98 26 99\\n4 27 100 28 101\\n4 29 102 30 103\\n4 31 104 32 105\\n4 33 106 34 107\\n4 35 108 36 109\\n4 37 110 38 111\\n4 39 112 40 113\\n4 41 114 42 115\\n4 43 116 44 117\\n4 45 118 46 119\\n4 47 120 48 121\\n4 49 122 50 123\\n4 51 124 52 125\\n4 53 126 54 127\\n4 55 128 56 129\\n4 57 130 58 131\\n4 59 132 60 133\\n4 61 134 62 135\\n4 63 136 64 137\\n4 65 138 66 139\\n4 67 140 68 141\\n4 69 142 70 143\\n4 71 144 72 145\\n\", \"4\\n4 1 2 25 26\\n10 3 6 5 4 23 28 29 30 27 24\\n10 7 8 9 12 15 14 13 16 11 10\\n6 17 18 21 20 19 22\\n\", \"2\\n8 1 10 6 16 5 13 8 11\\n8 2 9 3 15 4 12 7 14\\n\", \"5\\n44 1 39 30 67 26 64 27 58 8 36 15 54 18 55 24 49 22 48 6 47 16 42 21 45 20 52 28 61 17 57 14 65 13 51 7 46 10 56 19 60 5 63 4 40\\n10 2 38 33 41 12 44 34 69 11 68\\n4 3 43 9 53\\n8 23 50 25 59 31 70 32 62\\n4 29 37 35 66\\n\", \"Impossible\\n\", \"Impossible\\n\", \"4\\n4 1 64 4 65\\n90 2 121 15 122 56 116 59 68 10 71 60 118 7 69 17 67 62 124 57 120 49 119 47 115 48 117 53 114 55 110 51 112 54 111 52 103 44 106 40 95 41 98 35 100 43 99 39 109 45 107 46 102 33 89 30 88 27 76 16 74 26 72 23 84 21 85 14 97 32 104 34 101 31 96 28 94 25 82 24 77 11 81 12 79 13 75 5 73 50 123\\n26 3 70 6 63 8 66 61 113 58 108 42 105 38 93 37 91 36 92 22 90 29 87 20 83 9 78\\n4 18 80 19 86\\n\", \"10\\n6 1 57 12 53 44 92\\n4 2 86 49 97\\n6 3 55 38 62 9 59\\n4 4 54 5 58\\n38 6 51 48 89 21 67 25 72 28 73 29 76 36 77 37 80 34 81 42 85 45 63 13 60 23 69 33 79 32 84 35 91 20 65 14 94 15 52\\n4 7 75 22 83\\n18 8 50 27 71 30 82 24 74 10 68 40 93 31 98 11 61 19 56\\n8 16 66 43 96 26 95 17 78\\n6 18 64 39 90 41 70\\n4 46 87 47 88\\n\", \"Impossible\\n\", \"2\\n76 1 41 7 49 5 48 6 47 9 68 27 57 31 46 37 55 13 54 4 74 10 58 32 60 22 67 26 62 28 72 29 70 16 63 11 43 12 52 23 45 15 59 35 71 30 64 33 61 34 69 21 75 40 76 24 66 36 73 2 79 18 65 25 56 17 50 20 78 38 77 8 80 39 44 3 42\\n4 14 51 19 53\\n\", \"44\\n6 1 91 2 90 89 178\\n4 3 92 4 93\\n4 5 94 6 95\\n4 7 96 8 97\\n4 9 98 10 99\\n4 11 100 12 101\\n4 13 102 14 103\\n4 15 104 16 105\\n4 17 106 18 107\\n4 19 108 20 109\\n4 21 110 22 111\\n4 23 112 24 113\\n4 25 114 26 115\\n4 27 116 28 117\\n4 29 118 30 119\\n4 31 120 32 121\\n4 33 122 34 123\\n4 35 124 36 125\\n4 37 126 38 127\\n4 39 128 40 129\\n4 41 130 42 131\\n4 43 132 44 133\\n4 45 134 46 135\\n4 47 136 48 137\\n4 49 138 50 139\\n4 51 140 52 141\\n4 53 142 54 143\\n4 55 144 56 145\\n4 57 146 58 147\\n4 59 148 60 149\\n4 61 150 62 151\\n4 63 152 64 153\\n4 65 154 66 155\\n4 67 156 68 157\\n4 69 158 70 159\\n4 71 160 72 161\\n4 73 162 74 163\\n4 75 164 76 165\\n4 77 166 78 167\\n4 79 168 80 169\\n4 81 170 82 171\\n4 83 172 84 173\\n4 85 174 86 175\\n4 87 176 88 177\\n\", \"4\\n64 1 42 2 45 39 74 37 41 9 48 6 46 3 44 7 47 4 77 13 78 20 55 10 50 5 43 8 51 11 54 38 49 21 57 16 53 15 40 34 72 24 63 18 70 19 62 27 61 23 65 29 67 28 59 17 58 22 60 25 64 30 66 31 71\\n4 12 52 14 56\\n6 26 68 35 73 32 69\\n4 33 75 36 76\\n\", \"Impossible\\n\", \"Impossible\\n\", \"2\\n26 1 19 4 16 3 25 9 23 10 24 12 26 11 29 2 30 15 28 14 27 13 17 5 18 6 20\\n4 7 21 8 22\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"4\\n10 1 23 4 26 8 28 10 37 17 34\\n18 2 20 3 22 5 24 6 25 7 27 9 29 11 30 19 38 18 21\\n6 12 31 13 33 14 32\\n4 15 35 16 36\\n\", \"Impossible\\n\", \"Impossible\\n\", \"10\\n116 1 78 2 80 3 152 76 151 75 150 73 149 72 147 70 146 71 148 74 77 19 92 20 97 25 100 29 101 31 102 33 109 32 110 34 115 36 117 38 119 40 120 41 121 42 118 46 123 48 124 45 122 52 126 53 132 54 133 58 134 63 137 69 143 66 142 61 139 65 141 64 140 62 138 60 136 55 128 51 127 49 125 47 116 44 114 43 113 39 111 35 112 37 107 27 104 26 106 23 103 22 96 17 93 16 89 15 86 14 87 13 84 11 82 5 83 \\n4 4 79 9 81 \\n4 6 85 7 88 \\n4 8 91 12 95 \\n4 10 90 18 94 \\n4 21 98 24 99 \\n4 28 105 30 108 \\n4 50 129 56 130 \\n4 57 131 59 135 \\n4 67 144 68 145 \\n\", \"2\\n6 1 7 2 6 5 10 \\n4 3 8 4 9 \\n\", \"6\\n52 1 52 41 97 39 95 34 94 33 92 32 83 26 75 16 71 11 68 10 67 7 57 5 61 3 58 4 55 8 54 9 56 12 59 13 62 14 65 17 70 24 72 19 74 20 79 22 80 23 81 44 53 \\n8 2 69 47 64 18 66 46 100 \\n4 6 60 15 63 \\n8 21 101 31 77 36 73 27 102 \\n26 25 78 29 82 28 84 30 89 35 87 40 90 43 86 37 85 38 88 42 76 45 96 48 99 51 98 \\n4 49 91 50 93 \\n\", \"3\\n14 1 2 27 24 3 6 5 4 23 28 29 30 25 26 \\n10 7 8 9 12 15 14 13 16 11 10 \\n6 17 18 21 20 19 22 \\n\", \"3\\n14 1 39 34 69 11 58 27 65 13 37 29 66 35 40 \\n50 2 41 33 38 8 36 15 54 18 55 24 49 22 50 23 62 32 70 31 59 25 64 26 67 30 51 7 46 10 56 19 60 5 63 4 44 12 45 20 52 28 61 17 57 14 53 9 43 3 68 \\n6 6 47 16 42 21 48 \\n\", \"44\\n6 1 91 2 90 89 178 \\n4 3 92 4 93 \\n4 5 94 6 95 \\n4 7 96 8 97 \\n4 9 98 10 99 \\n4 11 100 12 101 \\n4 13 102 14 103 \\n4 15 104 16 105 \\n4 17 106 18 107 \\n4 19 108 20 109 \\n4 21 110 22 111 \\n4 23 112 24 113 \\n4 25 114 26 115 \\n4 27 116 28 117 \\n4 29 118 30 119 \\n4 31 120 32 121 \\n4 33 122 34 123 \\n4 35 124 36 125 \\n4 37 126 38 127 \\n4 39 128 40 129 \\n4 41 130 42 131 \\n4 43 132 44 133 \\n4 45 134 46 135 \\n4 47 136 48 137 \\n4 49 138 50 139 \\n4 51 140 52 141 \\n4 53 142 54 143 \\n4 55 144 56 145 \\n4 57 146 58 147 \\n4 59 148 60 149 \\n4 61 150 62 151 \\n4 63 152 64 153 \\n4 65 154 66 155 \\n4 67 156 68 157 \\n4 69 158 70 159 \\n4 71 160 72 161 \\n4 73 162 74 163 \\n4 75 164 76 165 \\n4 77 166 78 167 \\n4 79 168 80 169 \\n4 81 170 82 171 \\n4 83 172 84 173 \\n4 85 174 86 175 \\n4 87 176 88 177 \\n\", \"2\\n26 1 19 4 16 3 17 13 27 14 28 15 25 9 23 10 24 12 26 11 29 2 30 5 18 6 20 \\n4 7 21 8 22 \\n\", \"5\\n10 1 23 4 26 8 28 10 36 17 34 \\n16 2 20 3 22 5 24 6 25 7 27 9 29 11 30 18 21 \\n4 12 32 14 37 \\n4 13 31 19 33 \\n4 15 35 16 38 \\n\", \"2\\n6 1 7 2 6 5 9 \\n4 3 8 4 10 \\n\", \"18\\n6 1 43 2 38 37 73 \\n4 3 39 5 40 \\n4 4 44 7 45 \\n4 6 41 8 42 \\n4 9 50 10 51 \\n4 11 46 12 47 \\n4 13 52 15 53 \\n4 14 48 22 49 \\n4 16 56 17 58 \\n4 18 59 19 62 \\n4 20 63 21 64 \\n4 23 54 25 55 \\n4 24 66 26 67 \\n4 27 57 30 60 \\n4 28 68 29 69 \\n4 31 61 32 65 \\n4 33 70 36 74 \\n4 34 71 35 72 \\n\", \"3\\n90 1 52 41 97 39 95 34 94 33 92 32 83 26 75 16 71 11 68 10 67 7 57 5 61 3 58 4 55 8 54 9 56 12 59 13 101 50 93 49 91 40 90 43 86 46 100 2 66 47 62 6 60 15 63 18 64 31 77 36 73 37 85 38 88 42 76 45 96 48 99 51 98 25 78 24 70 17 65 14 72 19 74 20 79 22 80 23 81 44 53 \\n4 21 69 27 102 \\n8 28 82 29 87 35 89 30 84 \\n\", \"6\\n28 1 32 6 33 30 34 7 36 31 47 15 49 16 46 17 53 20 55 24 56 25 57 23 60 28 62 29 61 \\n10 2 37 4 39 9 42 12 43 13 48 \\n12 3 35 5 38 8 41 14 44 18 51 22 50 \\n4 10 40 11 45 \\n4 19 54 21 58 \\n4 26 52 27 59 \\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"1\\n4 1 2 4 3\\n\", \"1\\n12 1 2 3 6 5 12 9 8 7 10 11 4\\n\", \"3\\n8 1 2 3 24 5 6 23 4\\n10 7 8 9 12 15 14 13 16 11 10\\n6 17 18 21 20 19 22\\n\"]}", "source": "primeintellect"} | Fox Ciel is participating in a party in Prime Kingdom. There are n foxes there (include Fox Ciel). The i-th fox is ai years old.
They will have dinner around some round tables. You want to distribute foxes such that:
1. Each fox is sitting at some table.
2. Each table has at least 3 foxes sitting around it.
3. The sum of ages of any two adjacent foxes around each table should be a prime number.
If k foxes f1, f2, ..., fk are sitting around table in clockwise order, then for 1 ≤ i ≤ k - 1: fi and fi + 1 are adjacent, and f1 and fk are also adjacent.
If it is possible to distribute the foxes in the desired manner, find out a way to do that.
Input
The first line contains single integer n (3 ≤ n ≤ 200): the number of foxes in this party.
The second line contains n integers ai (2 ≤ ai ≤ 104).
Output
If it is impossible to do this, output "Impossible".
Otherwise, in the first line output an integer m (<image>): the number of tables.
Then output m lines, each line should start with an integer k -=– the number of foxes around that table, and then k numbers — indices of fox sitting around that table in clockwise order.
If there are several possible arrangements, output any of them.
Examples
Input
4
3 4 8 9
Output
1
4 1 2 4 3
Input
5
2 2 2 2 2
Output
Impossible
Input
12
2 3 4 5 6 7 8 9 10 11 12 13
Output
1
12 1 2 3 6 5 12 9 8 7 10 11 4
Input
24
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Output
3
6 1 2 3 6 5 4
10 7 8 9 12 15 14 13 16 11 10
8 17 18 23 22 19 20 21 24
Note
In example 1, they can sit around one table, their ages are: 3-8-9-4, adjacent sums are: 11, 17, 13 and 7, all those integers are primes.
In example 2, it is not possible: the sum of 2+2 = 4 is not a prime number.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"9\\npair int int int pair pair int int int int int pair pair pair pair pair pair int\\n\", \"2\\npair int int\\n\", \"4\\npair pair pair int int int int\\n\", \"5\\npair pair pair pair int int int int int\\n\", \"10\\npair int int int pair pair pair int int pair int pair int int int pair pair pair int\\n\", \"56\\npair pair pair int int pair pair pair pair pair int pair int int pair pair int pair pair pair int pair int int pair int pair int pair pair pair pair int pair pair int int pair int int pair int int int int int pair pair pair pair pair pair pair pair pair int pair pair int pair pair pair pair int int int pair pair pair pair pair pair pair pair int int int int pair pair pair int int pair pair int int pair pair int int int int int int int int int int int int int int int int int int int int int int\\n\", \"1\\nint pair pair\\n\", \"10\\npair pair pair pair pair pair pair pair pair int int int int int int int int int int\\n\", \"6\\npair pair pair pair pair int int int int int int\\n\", \"55\\npair pair int int pair int pair int pair pair pair int int pair int int pair int pair int pair int pair int pair int pair int pair int pair int pair int pair int pair int pair int pair pair pair pair int int pair pair pair pair pair pair int pair pair int pair pair pair int int int int int pair pair pair pair pair int int pair int pair int int int int pair int pair int pair int pair int int pair int pair int pair int pair pair int pair pair int pair int int int int int int int int int\\n\", \"9\\npair pair pair int int pair pair pair int int pair int pair int int int pair int\\n\", \"10\\npair pair pair int pair int pair pair pair pair pair int int int int int int int int\\n\", \"4\\npair pair int int int int\\n\", \"3\\npair pair int int int\\n\", \"4\\npair int pair int int int\\n\", \"1\\npair int pair\\n\", \"2\\nint pair int\\n\", \"3\\npair int int int\\n\", \"1\\nint\\n\", \"4\\npair int int int int\\n\", \"9\\npair pair int int int int pair int pair int pair pair pair pair int pair int int\\n\", \"5\\npair pair int pair int pair int int int\\n\", \"10\\npair int pair int pair int pair int pair int pair int pair int pair int pair int int\\n\", \"2\\nint int\\n\", \"3\\npair int pair int int\\n\", \"4\\npair pair int int pair int int\\n\", \"10\\npair pair int pair int int pair int pair int pair int pair pair int int pair int int\\n\", \"10\\npair pair pair int pair int pair int int pair int int pair int int pair int pair int\\n\", \"40\\npair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair pair int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int int\\n\", \"9\\npair pahr int int int int pair int pair int pair pair pair pair int pair int int\\n\", \"1\\npair iot\\n\", \"9\\npair int int int pair pais int int int int int pair pair pair pair pair pair int\\n\", \"10\\npair int int int pair pais pair int int pair int pair int int int pair pair pair int\\n\", \"4\\npair int pajr int int int\\n\", \"10\\npair int int int pair pais pair int int pair int pair int int int pair pair pari int\\n\", \"9\\npair pair int int int int pair int pair int pair pajr pair pair int pair int int\\n\", \"1\\npair ins\\n\", \"9\\npair int int int pair pais ins int int int int pair pair pair pair pair pair int\\n\", \"10\\npair int int int pair pais pair ins int pair int pair int int int pair pair pair int\\n\", \"10\\npair int int int pair pais pair ins int pair itn pair int int int pair pair pair int\\n\", \"9\\npair int int int pair pair ins int int int int pair pair pair pair pair pair int\\n\", \"4\\npair pahr int int int int\\n\", \"10\\npair pair pair int pair int pair int int pair int int pair int int pair int p`ir int\\n\", \"9\\npair pahr int int imt int pair int pair int pair pair pair pair int pair int int\\n\", \"9\\npair int int int pair pais int int inu int int pair pair pair pair pair pair int\\n\", \"10\\npair int int int pair pais pair imt int pair int pair int int int pair pair pari int\\n\", \"3\\npair pair int int int\\n\", \"1\\npair int\\n\"], \"outputs\": [\"Error occurred\\n\", \"pair<int,int>\\n\", \"pair<pair<pair<int,int>,int>,int>\\n\", \"pair<pair<pair<pair<int,int>,int>,int>,int>\\n\", \"Error occurred\\n\", \"pair<pair<pair<int,int>,pair<pair<pair<pair<pair<int,pair<int,int>>,pair<pair<int,pair<pair<pair<int,pair<int,int>>,pair<int,pair<int,pair<pair<pair<pair<int,pair<pair<int,int>,pair<int,int>>>,pair<int,int>>,int>,int>>>>,int>>,pair<pair<pair<pair<pair<pair<pair<pair<pair<int,pair<pair<int,pair<pair<pair<pair<int,int>,int>,pair<pair<pair<pair<pair<pair<pair<pair<int,int>,int>,int>,pair<pair<pair<int,int>,pair<pair<int,int>,pair<pair<int,int>,int>>>,int>>,int>,int>,int>,int>>,int>>,int>>,int>,int>,int>,int>,int>,int>,int>,int>>>,int>,int>,int>>,int>\\n\", \"Error occurred\\n\", \"pair<pair<pair<pair<pair<pair<pair<pair<pair<int,int>,int>,int>,int>,int>,int>,int>,int>,int>\\n\", \"pair<pair<pair<pair<pair<int,int>,int>,int>,int>,int>\\n\", \"pair<pair<int,int>,pair<int,pair<int,pair<pair<pair<int,int>,pair<int,int>>,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<pair<pair<pair<int,int>,pair<pair<pair<pair<pair<pair<int,pair<pair<int,pair<pair<pair<int,int>,int>,int>>,int>>,pair<pair<pair<pair<pair<int,int>,pair<int,pair<int,int>>>,int>,int>,pair<int,pair<int,pair<int,pair<int,int>>>>>>,pair<int,pair<int,pair<int,pair<pair<int,pair<pair<int,pair<int,int>>,int>>,int>>>>>,int>,int>,int>>,int>,int>>>>>>>>>>>>>>>>>\\n\", \"Error occurred\\n\", \"pair<pair<pair<int,pair<int,pair<pair<pair<pair<pair<int,int>,int>,int>,int>,int>>>,int>,int>\\n\", \"Error occurred\\n\", \"pair<pair<int,int>,int>\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"int\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"pair<pair<int,pair<int,pair<int,int>>>,int>\\n\", \"pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,pair<int,int>>>>>>>>>\\n\", \"Error occurred\\n\", \"pair<int,pair<int,int>>\\n\", \"pair<pair<int,int>,pair<int,int>>\\n\", \"pair<pair<int,pair<int,int>>,pair<int,pair<int,pair<int,pair<pair<int,int>,pair<int,int>>>>>>\\n\", \"Error occurred\\n\", \"pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<pair<int,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>,int>\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"Error occurred\\n\", \"pair<pair<int,int>,int>\\n\", \"Error occurred\\n\"]}", "source": "primeintellect"} | Vasya used to be an accountant before the war began and he is one of the few who knows how to operate a computer, so he was assigned as the programmer.
We all know that programs often store sets of integers. For example, if we have a problem about a weighted directed graph, its edge can be represented by three integers: the number of the starting vertex, the number of the final vertex and the edge's weight. So, as Vasya was trying to represent characteristics of a recently invented robot in his program, he faced the following problem.
Vasya is not a programmer, so he asked his friend Gena, what the convenient way to store n integers is. Gena used to code in language X-- and so he can use only the types that occur in this language. Let's define, what a "type" is in language X--:
* First, a type is a string "int".
* Second, a type is a string that starts with "pair", then followed by angle brackets listing exactly two comma-separated other types of language X--. This record contains no spaces.
* No other strings can be regarded as types.
More formally: type := int | pair<type,type>. For example, Gena uses the following type for graph edges: pair<int,pair<int,int>>.
Gena was pleased to help Vasya, he dictated to Vasya a type of language X--, that stores n integers. Unfortunately, Gena was in a hurry, so he omitted the punctuation. Now Gena has already left and Vasya can't find the correct punctuation, resulting in a type of language X--, however hard he tries.
Help Vasya and add the punctuation marks so as to receive the valid type of language X--. Otherwise say that the task is impossible to perform.
Input
The first line contains a single integer n (1 ≤ n ≤ 105), showing how many numbers the type dictated by Gena contains.
The second line contains space-separated words, said by Gena. Each of them is either "pair" or "int" (without the quotes).
It is guaranteed that the total number of words does not exceed 105 and that among all the words that Gena said, there are exactly n words "int".
Output
If it is possible to add the punctuation marks so as to get a correct type of language X-- as a result, print a single line that represents the resulting type. Otherwise, print "Error occurred" (without the quotes). Inside the record of a type should not be any extra spaces and other characters.
It is guaranteed that if such type exists, then it is unique.
Note that you should print the type dictated by Gena (if such type exists) and not any type that can contain n values.
Examples
Input
3
pair pair int int int
Output
pair<pair<int,int>,int>
Input
1
pair int
Output
Error occurred
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"11\\n23\\n0\", \"11\\n45\\n0\", \"11\\n77\\n0\", \"11\\n13\\n0\", \"11\\n17\\n0\", \"11\\n25\\n0\", \"11\\n37\\n0\", \"11\\n5\\n0\", \"11\\n69\\n0\", \"11\\n19\\n0\", \"11\\n21\\n0\", \"11\\n27\\n0\", \"11\\n11\\n0\", \"11\\n31\\n0\", \"11\\n33\\n0\", \"11\\n29\\n0\", \"11\\n7\\n0\", \"11\\n3\\n0\", \"11\\n39\\n0\", \"11\\n43\\n0\", \"11\\n35\\n0\", \"11\\n0\\n0\", \"11\\n49\\n0\", \"11\\n9\\n0\", \"11\\n121\\n0\", \"11\\n59\\n0\", \"11\\n65\\n0\", \"11\\n41\\n0\", \"11\\n61\\n0\", \"11\\n113\\n0\", \"11\\n53\\n0\", \"11\\n83\\n0\", \"11\\n173\\n0\", \"11\\n165\\n0\", \"11\\n47\\n0\", \"11\\n119\\n0\", \"11\\n91\\n0\", \"11\\n73\\n0\", \"11\\n55\\n0\", \"11\\n1\\n0\", \"11\\n0\\n1\", \"11\\n0\\n-1\", \"11\\n-1\\n0\", \"11\\n0\\n-2\", \"11\\n0\\n-3\", \"11\\n0\\n-4\", \"11\\n0\\n2\", \"11\\n0\\n4\", \"11\\n0\\n3\", \"11\\n0\\n8\", \"11\\n0\\n12\", \"11\\n0\\n13\", \"11\\n0\\n19\", \"11\\n0\\n27\", \"11\\n0\\n-5\", \"11\\n0\\n6\", \"11\\n0\\n11\", \"11\\n13\\n0\", \"11\\n1\\n0\", \"11\\n0\\n0\", \"11\\n0\\n1\", \"11\\n0\\n2\", \"11\\n-1\\n0\", \"11\\n0\\n-1\", \"11\\n9\\n0\", \"11\\n0\\n-2\", \"11\\n0\\n3\", \"11\\n0\\n-3\", \"11\\n0\\n-4\", \"11\\n0\\n-5\", \"11\\n0\\n-8\", \"11\\n0\\n-13\", \"11\\n0\\n-25\", \"11\\n0\\n5\", \"11\\n0\\n-10\", \"11\\n0\\n-9\", \"11\\n3\\n0\", \"11\\n0\\n-16\", \"11\\n0\\n-23\", \"11\\n0\\n-45\", \"11\\n21\\n0\", \"11\\n0\\n-7\", \"11\\n0\\n4\", \"11\\n11\\n0\", \"11\\n0\\n-11\", \"11\\n0\\n-50\", \"11\\n0\\n-12\", \"11\\n0\\n-6\", \"11\\n0\\n8\", \"11\\n0\\n-15\", \"11\\n0\\n-21\", \"11\\n0\\n-36\", \"11\\n0\\n-33\", \"11\\n0\\n-32\", \"11\\n0\\n-43\", \"11\\n0\\n-17\", \"11\\n0\\n-14\", \"11\\n0\\n-58\", \"11\\n0\\n-46\", \"11\\n0\\n-72\", \"11\\n15\\n0\"], \"outputs\": [\"4\\n4\\n4\\n4\\n4\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n2\\n6\\n4\\n6\\n12\\n2\\n2\\n16\\n6\\n4\\n6\\n2\\n4\\n18\\n4\\n2\\n8\\n4\\n6\\n12\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n10\\n12\\n12\\n10\\n12\\n10\\n22\\n12\\n10\\n10\\n22\\n12\\n10\\n22\\n10\\n10\\n10\\n12\\n10\\n12\\n22\\n22\\n10\\n10\\n10\\n12\\n12\\n22\\n12\\n12\\n12\\n12\\n22\\n12\\n22\\n10\\n10\\n12\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n6\\n4\\n4\\n6\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n6\\n6\\n8\\n6\\n8\\n8\\n8\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n10\\n10\\n4\\n20\\n4\\n10\\n10\\n4\\n20\\n4\\n10\\n\", \"4\\n4\\n4\\n4\\n4\\n16\\n18\\n16\\n16\\n18\\n18\\n16\\n18\\n16\\n16\\n16\\n16\\n18\\n18\\n18\\n16\\n18\\n18\\n\", \"4\\n4\\n4\\n4\\n4\\n0\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n10\\n12\\n22\\n10\\n10\\n22\\n12\\n12\\n22\\n12\\n10\\n22\\n10\\n10\\n22\\n10\\n10\\n22\\n12\\n10\\n22\\n12\\n22\\n22\\n10\\n12\\n22\\n12\\n12\\n22\\n10\\n12\\n22\\n12\\n\", \"4\\n4\\n4\\n4\\n4\\n8\\n8\\n8\\n8\\n8\\n8\\n8\\n8\\n8\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n4\\n6\\n2\\n2\\n6\\n6\\n4\\n6\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n18\\n4\\n4\\n18\\n4\\n4\\n20\\n4\\n4\\n18\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n10\\n4\\n6\\n10\\n6\\n4\\n10\\n6\\n10\\n10\\n6\\n6\\n10\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n12\\n14\\n14\\n12\\n12\\n12\\n12\\n14\\n12\\n14\\n14\\n14\\n12\\n14\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n2\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n0\\n\", \"4\\n4\\n4\\n4\\n4\\n6\\n6\\n12\\n6\\n6\\n12\\n6\\n6\\n12\\n6\\n6\\n12\\n12\\n6\\n12\\n6\\n6\\n12\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n\", \"4\\n4\\n4\\n4\\n4\\n6\\n4\\n4\\n6\\n10\\n6\\n8\\n4\\n6\\n10\\n6\\n4\\n4\\n12\\n10\\n6\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n16\\n16\\n16\\n16\\n16\\n16\\n42\\n16\\n16\\n16\\n16\\n16\\n16\\n42\\n16\\n16\\n16\\n16\\n16\\n16\\n42\\n16\\n16\\n16\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n2\\n6\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n110\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n110\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n110\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n110\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n110\\n46\\n46\\n46\\n46\\n46\\n\", \"4\\n4\\n4\\n4\\n4\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n\", \"4\\n4\\n4\\n4\\n4\\n12\\n6\\n8\\n12\\n18\\n12\\n6\\n6\\n12\\n20\\n12\\n8\\n14\\n12\\n18\\n12\\n8\\n6\\n12\\n18\\n12\\n8\\n8\\n12\\n20\\n24\\n8\\n6\\n12\\n20\\n12\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n18\\n18\\n20\\n18\\n18\\n20\\n20\\n18\\n18\\n18\\n20\\n20\\n20\\n20\\n20\\n18\\n20\\n18\\n20\\n18\\n\", \"4\\n4\\n4\\n4\\n4\\n28\\n30\\n28\\n28\\n28\\n30\\n30\\n30\\n28\\n30\\n30\\n28\\n28\\n28\\n28\\n28\\n30\\n30\\n28\\n28\\n30\\n28\\n30\\n30\\n28\\n30\\n28\\n30\\n30\\n30\\n\", \"4\\n4\\n4\\n4\\n4\\n54\\n54\\n56\\n54\\n56\\n56\\n54\\n54\\n54\\n56\\n54\\n56\\n54\\n54\\n54\\n54\\n56\\n54\\n56\\n56\\n56\\n54\\n56\\n56\\n54\\n54\\n56\\n54\\n56\\n54\\n54\\n54\\n56\\n56\\n56\\n54\\n56\\n56\\n56\\n56\\n54\\n56\\n56\\n54\\n56\\n56\\n56\\n56\\n54\\n54\\n54\\n54\\n54\\n56\\n56\\n54\\n\", \"4\\n4\\n4\\n4\\n4\\n24\\n26\\n26\\n24\\n26\\n24\\n24\\n26\\n24\\n24\\n24\\n26\\n24\\n26\\n24\\n24\\n24\\n26\\n26\\n26\\n26\\n26\\n26\\n24\\n24\\n26\\n\", \"4\\n4\\n4\\n4\\n4\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n\", \"4\\n4\\n4\\n4\\n4\\n84\\n86\\n86\\n84\\n86\\n84\\n86\\n86\\n84\\n84\\n86\\n86\\n84\\n84\\n84\\n84\\n86\\n86\\n86\\n86\\n84\\n84\\n84\\n84\\n84\\n86\\n86\\n86\\n84\\n86\\n84\\n86\\n84\\n84\\n84\\n84\\n84\\n84\\n86\\n84\\n84\\n86\\n84\\n86\\n86\\n86\\n84\\n86\\n84\\n86\\n84\\n84\\n86\\n84\\n84\\n84\\n84\\n86\\n86\\n84\\n86\\n86\\n86\\n84\\n86\\n86\\n84\\n86\\n86\\n86\\n86\\n86\\n84\\n86\\n86\\n86\\n84\\n84\\n86\\n86\\n84\\n86\\n84\\n84\\n84\\n86\\n\", \"4\\n4\\n4\\n4\\n4\\n10\\n6\\n12\\n10\\n18\\n22\\n6\\n6\\n22\\n18\\n22\\n12\\n6\\n12\\n34\\n10\\n6\\n12\\n12\\n18\\n22\\n12\\n6\\n22\\n16\\n12\\n12\\n6\\n10\\n34\\n10\\n6\\n24\\n10\\n16\\n22\\n6\\n6\\n22\\n18\\n10\\n12\\n6\\n22\\n34\\n12\\n6\\n12\\n10\\n16\\n22\\n6\\n6\\n22\\n34\\n12\\n12\\n6\\n12\\n34\\n12\\n6\\n12\\n10\\n16\\n44\\n6\\n6\\n22\\n16\\n12\\n12\\n6\\n10\\n34\\n12\\n12\\n12\\n12\\n18\\n22\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n\", \"4\\n4\\n4\\n4\\n4\\n18\\n18\\n16\\n18\\n16\\n16\\n32\\n18\\n18\\n16\\n16\\n16\\n18\\n32\\n18\\n18\\n34\\n18\\n18\\n16\\n36\\n16\\n16\\n16\\n18\\n18\\n16\\n32\\n16\\n18\\n16\\n18\\n18\\n34\\n36\\n18\\n16\\n18\\n16\\n16\\n16\\n36\\n18\\n16\\n16\\n16\\n18\\n16\\n36\\n18\\n34\\n18\\n18\\n16\\n18\\n32\\n16\\n16\\n18\\n\", \"4\\n4\\n4\\n4\\n4\\n14\\n12\\n14\\n14\\n12\\n12\\n24\\n12\\n14\\n14\\n12\\n14\\n26\\n28\\n12\\n14\\n14\\n12\\n12\\n12\\n24\\n14\\n14\\n12\\n14\\n26\\n14\\n24\\n14\\n14\\n12\\n12\\n12\\n12\\n28\\n14\\n12\\n14\\n26\\n14\\n12\\n28\\n14\\n12\\n12\\n\", \"4\\n4\\n4\\n4\\n4\\n34\\n34\\n34\\n34\\n36\\n34\\n36\\n34\\n34\\n36\\n36\\n34\\n36\\n36\\n36\\n34\\n36\\n34\\n34\\n36\\n36\\n36\\n34\\n34\\n34\\n36\\n34\\n36\\n36\\n36\\n36\\n34\\n36\\n36\\n34\\n34\\n\", \"4\\n4\\n4\\n4\\n4\\n10\\n6\\n6\\n10\\n16\\n10\\n6\\n6\\n10\\n16\\n20\\n6\\n6\\n10\\n16\\n10\\n6\\n6\\n10\\n16\\n10\\n12\\n6\\n10\\n16\\n10\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n6\\n4\\n4\\n6\\n6\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n2\\n6\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n0\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n4\\n6\\n2\\n2\\n6\\n6\\n4\\n6\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n4\\n4\\n4\\n2\\n2\\n4\\n2\\n4\\n4\\n2\"]}", "source": "primeintellect"} | A prime number n (11, 19, 23, etc.) that divides by 4 and has 3 has an interesting property. The results of calculating the remainder of the square of a natural number (1, 2, ..., n -1) of 1 or more and less than n divided by n are the same, so they are different from each other. The number is (n -1) / 2.
The set of numbers thus obtained has special properties. From the resulting set of numbers, choose two different a and b and calculate the difference. If the difference is negative, add n to the difference. If the result is greater than (n -1) / 2, subtract the difference from n.
For example, when n = 11, the difference between 1 and 9 is 1 − 9 = −8 → −8 + n = −8 + 11 = 3. The difference between 9 and 1 is also 9 −1 = 8 → n − 8 = 11 − 8 = 3, which is the same value 3. This difference can be easily understood by writing 0, 1, ···, n -1 on the circumference and considering the shorter arc between the two numbers. (See the figure below)
<image>
The "difference" in the numbers thus obtained is either 1, 2, ..., (n -1) / 2, and appears the same number of times.
[Example] When n = 11, it will be as follows.
1. Calculate the remainder of the square of the numbers from 1 to n-1 divided by n.
12 = 1 → 1
22 = 4 → 4
32 = 9 → 9
42 = 16 → 5
52 = 25 → 3
62 = 36 → 3
72 = 49 → 5
82 = 64 → 9
92 = 81 → 4
102 = 100 → 1
2. Calculation of "difference" between a and b
1. Calculate the difference between different numbers for 1, 3, 4, 5, 9 obtained in 1.
2. If the calculation result is negative, add n = 11.
3. In addition, if the result of the calculation is greater than (n-1) / 2 = 5, subtract from n = 11.
3. Find the number of appearances
Count the number of occurrences of the calculation results 1, 2, 3, 4, and 5, respectively.
From these calculation results, we can see that 1, 2, 3, 4, and 5 appear four times. This property is peculiar to a prime number that is 3 when divided by 4, and this is not the case with a prime number that is 1 when divided by 4. To confirm this, a program that takes an odd number n of 10000 or less as an input, executes the calculation as shown in the example (finds the frequency of the difference of the square that is too much divided by n), and outputs the number of occurrences. Please create.
Input
Given multiple datasets. One integer n (n ≤ 10000) is given on one row for each dataset. The input ends with a line containing one 0.
Output
For each data set, output the frequency of occurrence in the following format.
Number of occurrences (integer) of (a, b) where the difference between the squares of the remainder is 1
The number of occurrences (integer) of (a, b) where the difference between the squares of the remainder is 2
::
::
The number of occurrences (integer) of (a, b) where the difference between the squares of the remainder is (n-1) / 2
Example
Input
11
15
0
Output
4
4
4
4
4
2
2
4
2
4
4
2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1\\n6\", \"1\\n8\", \"1\\n12\", \"1\\n16\", \"1\\n1\", \"1\\n13\", \"1\\n25\", \"1\\n5\", \"1\\n2\", \"1\\n3\", \"1\\n10\", \"1\\n19\", \"1\\n23\", \"1\\n9\", \"1\\n17\", \"1\\n7\", \"1\\n18\", \"1\\n20\", \"1\\n21\", \"1\\n11\", \"1\\n29\", \"1\\n15\", \"1\\n14\", \"1\\n26\", \"1\\n28\", \"1\\n24\", \"1\\n30\", \"1\\n22\", \"1\\n27\", \"1\\n010\", \"1\\n001\", \"1\\n011\", \"1\\n5\", \"1\\n3\", \"1\\n7\", \"1\\n6\", \"1\\n2\", \"1\\n11\", \"1\\n14\", \"1\\n8\", \"1\\n1\", \"1\\n20\", \"1\\n19\", \"1\\n12\", \"1\\n21\", \"1\\n9\", \"1\\n16\", \"1\\n23\", \"1\\n10\", \"1\\n15\", \"1\\n17\", \"1\\n22\", \"1\\n24\", \"1\\n25\", \"1\\n29\", \"1\\n18\", \"1\\n28\", \"1\\n26\", \"1\\n13\", \"1\\n27\", \"1\\n30\", \"1\\n010\", \"1\\n011\", \"1\\n001\", \"1\\n4\"], \"outputs\": [\"1\\n26\\n\", \"1\\n80\\n\", \"1\\n728\\n\", \"1\\n6560\\n\", \"1\\n1\\n\", \"1\\n1457\\n\", \"1\\n1062881\\n\", \"1\\n17\\n\", \"1\\n2\\n\", \"1\\n5\\n\", \"1\\n242\\n\", \"1\\n39365\\n\", \"1\\n354293\\n\", \"1\\n161\\n\", \"1\\n13121\\n\", \"1\\n53\\n\", \"1\\n19682\\n\", \"1\\n59048\\n\", \"1\\n118097\\n\", \"1\\n485\\n\", \"1\\n9565937\\n\", \"1\\n4373\\n\", \"1\\n2186\\n\", \"1\\n1594322\\n\", \"1\\n4782968\\n\", \"1\\n531440\\n\", \"1\\n14348906\\n\", \"1\\n177146\\n\", \"1\\n3188645\\n\", \"1\\n242\\n\", \"1\\n1\\n\", \"1\\n485\\n\", \"1\\n17\\n\", \"1\\n5\\n\", \"1\\n53\\n\", \"1\\n26\\n\", \"1\\n2\\n\", \"1\\n485\\n\", \"1\\n2186\\n\", \"1\\n80\\n\", \"1\\n1\\n\", \"1\\n59048\\n\", \"1\\n39365\\n\", \"1\\n728\\n\", \"1\\n118097\\n\", \"1\\n161\\n\", \"1\\n6560\\n\", \"1\\n354293\\n\", \"1\\n242\\n\", \"1\\n4373\\n\", \"1\\n13121\\n\", \"1\\n177146\\n\", \"1\\n531440\\n\", \"1\\n1062881\\n\", \"1\\n9565937\\n\", \"1\\n19682\\n\", \"1\\n4782968\\n\", \"1\\n1594322\\n\", \"1\\n1457\\n\", \"1\\n3188645\\n\", \"1\\n14348906\\n\", \"1\\n242\\n\", \"1\\n485\\n\", \"1\\n1\\n\", \"1\\n8\"]}", "source": "primeintellect"} | An bydrocarbon is an organic compound which contains only carbons and hydrogens. An isomer is a compound that has the same number of carbons but different structures. Heptane, for example, is a hydrocarbon with 7 carbons. It has nine isomers. The structural formula of three are shown in Figure 1. Carbons are represented by the letter C, and bonds between carbons are represented by a straight line. In all figures, hydrogens are not represented for simplicity. Each carbon can be connected to a maximum of 4 carbons.
<image>
---
Figure 1: These three examples of isomers of heptane have the same number of carbons but different structures.
---
Let define a chain in an isomer as a sequence of connected carbons without branches. An isomer can have many chains of the same length. Figure 2 shows the longest chain of carbons for each of the represented isomer. Note that there can be many instances of longest chain in an isomer.
<image>
---
Figure 2: The figures shows one instance of longest chain of carbons in each isomer. The first and the second isomers show longest chains of 5 carbons. The longest chain in the third isomer has 4 carbons.
---
Your task is to identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n (1 ≤ n ≤ 30) carbons.
Input
Each input contains a list of number of carbons, i.e. the length of a carbon chain.
The number of input lines is less than or equal to 30.
Output
For each number n in input, identify the number of carbons of the largest possible carbon compound whose longest carbon chain has n carbons.
Example
Input
1
4
Output
1
8
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"2\\n3 2 7 4\\n9 9 1 9\", \"2\\n3 2 7 4\\n9 3 1 9\", \"2\\n3 2 7 4\\n9 3 1 15\", \"2\\n3 2 7 4\\n7 3 1 15\", \"2\\n3 2 4 4\\n7 3 1 15\", \"2\\n3 2 4 4\\n7 3 1 9\", \"2\\n3 2 6 4\\n7 3 1 9\", \"2\\n3 2 6 4\\n4 3 1 9\", \"2\\n3 2 6 4\\n4 3 2 9\", \"2\\n3 2 6 4\\n4 3 2 4\", \"2\\n3 4 6 4\\n4 3 2 4\", \"2\\n3 4 6 4\\n8 3 2 4\", \"2\\n3 4 6 4\\n8 3 2 5\", \"2\\n3 4 6 3\\n8 3 2 5\", \"2\\n3 8 6 3\\n8 3 2 5\", \"2\\n3 8 6 3\\n8 5 2 5\", \"2\\n3 8 6 0\\n8 5 2 5\", \"2\\n3 3 6 0\\n8 5 2 5\", \"2\\n3 3 7 0\\n8 5 2 5\", \"2\\n3 3 7 0\\n8 2 2 5\", \"2\\n3 3 7 0\\n8 2 2 1\", \"2\\n3 4 7 0\\n8 2 2 1\", \"2\\n3 4 2 0\\n7 2 2 2\", \"2\\n3 2 3 0\\n12 2 2 4\", \"2\\n3 2 3 0\\n12 2 2 6\", \"2\\n3 2 3 0\\n12 2 0 6\", \"2\\n3 2 3 1\\n12 4 0 6\", \"2\\n3 2 7 4\\n0 9 1 9\", \"2\\n3 2 7 8\\n7 3 1 15\", \"2\\n3 2 4 4\\n7 3 1 26\", \"2\\n3 2 4 4\\n7 6 1 9\", \"2\\n3 2 6 4\\n13 3 1 9\", \"2\\n3 2 6 4\\n5 3 2 4\", \"2\\n3 4 6 4\\n4 4 2 4\", \"2\\n3 4 6 4\\n12 3 2 4\", \"2\\n2 8 6 3\\n8 3 2 5\", \"2\\n3 8 5 0\\n8 5 2 5\", \"2\\n3 3 7 0\\n8 3 2 5\", \"2\\n3 3 7 0\\n5 2 2 1\", \"2\\n3 2 7 0\\n8 2 2 1\", \"2\\n0 4 2 0\\n12 2 2 2\", \"2\\n3 4 2 0\\n12 1 2 2\", \"2\\n3 0 2 0\\n12 2 2 2\", \"2\\n3 2 2 0\\n22 2 2 4\", \"2\\n2 2 3 0\\n12 2 0 6\", \"2\\n3 4 3 0\\n12 2 0 6\", \"2\\n3 2 3 0\\n12 4 -1 6\", \"2\\n3 2 3 1\\n12 4 0 10\", \"2\\n6 2 7 2\\n9 3 1 9\", \"2\\n3 2 7 4\\n3 3 1 10\", \"2\\n3 2 7 8\\n12 3 1 15\", \"2\\n6 2 4 4\\n7 3 1 26\", \"2\\n3 2 6 4\\n13 4 1 9\", \"2\\n3 2 2 4\\n4 3 0 9\", \"2\\n3 2 9 4\\n4 0 2 9\", \"2\\n3 2 6 3\\n5 3 2 4\", \"2\\n1 4 6 4\\n4 4 2 4\", \"2\\n4 4 6 4\\n12 3 2 4\", \"2\\n1 8 5 0\\n8 5 2 5\", \"2\\n3 3 7 0\\n8 3 2 10\", \"2\\n3 0 7 0\\n8 2 0 2\", \"2\\n3 4 2 0\\n15 1 2 2\", \"2\\n3 4 1 0\\n12 2 0 6\", \"2\\n0 2 7 8\\n12 3 1 15\", \"2\\n8 2 4 4\\n7 3 1 26\", \"2\\n3 2 6 4\\n13 4 1 5\", \"2\\n0 2 9 4\\n4 0 2 9\", \"2\\n2 4 6 4\\n12 3 2 4\", \"2\\n3 3 7 0\\n8 3 2 15\", \"2\\n3 2 0 1\\n8 2 2 1\", \"2\\n3 7 0 0\\n8 1 2 2\", \"2\\n3 0 2 0\\n12 5 2 2\", \"2\\n3 4 1 0\\n12 2 1 6\", \"2\\n5 2 3 0\\n12 4 0 10\", \"2\\n4 4 7 6\\n9 9 1 4\", \"2\\n6 2 7 1\\n9 3 2 9\", \"2\\n0 2 7 8\\n6 3 1 15\", \"2\\n8 2 4 4\\n7 6 1 26\", \"2\\n1 2 2 4\\n7 3 0 9\", \"2\\n0 2 18 4\\n4 0 2 9\", \"2\\n3 2 4 3\\n9 3 2 4\", \"2\\n1 4 6 0\\n4 4 1 4\", \"2\\n2 8 2 4\\n13 3 2 5\", \"2\\n2 8 5 0\\n13 5 2 5\", \"2\\n3 3 7 0\\n6 3 2 15\", \"2\\n1 0 7 0\\n4 2 0 2\", \"2\\n3 7 0 0\\n0 1 2 2\", \"2\\n3 4 0 0\\n12 2 1 6\", \"2\\n5 2 3 0\\n12 4 0 12\", \"2\\n10 2 7 1\\n9 3 2 9\", \"2\\n2 4 8 4\\n3 3 1 10\", \"2\\n0 2 10 8\\n6 3 1 15\", \"2\\n15 2 4 4\\n7 6 1 26\", \"2\\n3 0 4 4\\n7 6 0 3\", \"2\\n3 2 6 4\\n13 4 1 11\", \"2\\n0 2 35 4\\n4 0 2 9\", \"2\\n3 2 4 3\\n9 4 2 4\", \"2\\n1 4 4 0\\n4 4 1 4\", \"2\\n2 8 6 4\\n12 4 2 4\", \"2\\n2 14 2 4\\n13 3 2 5\", \"2\\n4 2 7 4\\n9 9 1 9\"], \"outputs\": [\"6\\n8\\n\", \"6\\n14\\n\", \"6\\n20\\n\", \"6\\n18\\n\", \"3\\n18\\n\", \"3\\n12\\n\", \"5\\n12\\n\", \"5\\n9\\n\", \"5\\n8\\n\", \"5\\n3\\n\", \"3\\n3\\n\", \"3\\n7\\n\", \"3\\n8\\n\", \"4\\n8\\n\", \"8\\n8\\n\", \"8\\n10\\n\", \"11\\n10\\n\", \"6\\n10\\n\", \"7\\n10\\n\", \"7\\n9\\n\", \"7\\n7\\n\", \"8\\n7\\n\", \"5\\n7\\n\", \"2\\n12\\n\", \"2\\n14\\n\", \"2\\n16\\n\", \"1\\n16\\n\", \"6\\n1\\n\", \"10\\n18\\n\", \"3\\n29\\n\", \"3\\n9\\n\", \"5\\n18\\n\", \"5\\n4\\n\", \"3\\n2\\n\", \"3\\n11\\n\", \"9\\n8\\n\", \"10\\n10\\n\", \"7\\n8\\n\", \"7\\n4\\n\", \"6\\n7\\n\", \"6\\n12\\n\", \"5\\n11\\n\", \"1\\n12\\n\", \"3\\n22\\n\", \"3\\n16\\n\", \"4\\n16\\n\", \"2\\n17\\n\", \"1\\n18\\n\", \"1\\n14\\n\", \"6\\n9\\n\", \"10\\n23\\n\", \"4\\n29\\n\", \"5\\n17\\n\", \"3\\n10\\n\", \"8\\n11\\n\", \"4\\n4\\n\", \"5\\n2\\n\", \"2\\n11\\n\", \"12\\n10\\n\", \"7\\n13\\n\", \"4\\n10\\n\", \"5\\n14\\n\", \"6\\n16\\n\", \"13\\n23\\n\", \"6\\n29\\n\", \"5\\n15\\n\", \"11\\n11\\n\", \"4\\n11\\n\", \"7\\n18\\n\", \"4\\n7\\n\", \"10\\n7\\n\", \"1\\n13\\n\", \"6\\n15\\n\", \"4\\n18\\n\", \"5\\n13\\n\", \"2\\n13\\n\", \"13\\n17\\n\", \"6\\n26\\n\", \"3\\n13\\n\", \"20\\n11\\n\", \"2\\n8\\n\", \"9\\n3\\n\", \"6\\n13\\n\", \"11\\n15\\n\", \"7\\n16\\n\", \"6\\n6\\n\", \"10\\n3\\n\", \"7\\n15\\n\", \"4\\n20\\n\", \"4\\n13\\n\", \"8\\n9\\n\", \"16\\n17\\n\", \"13\\n26\\n\", \"5\\n10\\n\", \"5\\n19\\n\", \"37\\n11\\n\", \"2\\n9\\n\", \"7\\n3\\n\", \"8\\n12\\n\", \"12\\n13\\n\", \"5\\n8\"]}", "source": "primeintellect"} | For a non-negative integer K, we define a fractal of level K as follows:
* A fractal of level 0 is a grid with just one white square.
* When K > 0, a fractal of level K is a 3^K \times 3^K grid. If we divide this grid into nine 3^{K-1} \times 3^{K-1} subgrids:
* The central subgrid consists of only black squares.
* Each of the other eight subgrids is a fractal of level K-1.
For example, a fractal of level 2 is as follows:
A fractal of level 2
In a fractal of level 30, let (r, c) denote the square at the r-th row from the top and the c-th column from the left.
You are given Q quadruples of integers (a_i, b_i, c_i, d_i). For each quadruple, find the distance from (a_i, b_i) to (c_i, d_i).
Here the distance from (a, b) to (c, d) is the minimum integer n that satisfies the following condition:
* There exists a sequence of white squares (x_0, y_0), \ldots, (x_n, y_n) satisfying the following conditions:
* (x_0, y_0) = (a, b)
* (x_n, y_n) = (c, d)
* For every i (0 \leq i \leq n-1), (x_i, y_i) and (x_{i+1}, y_{i+1}) share a side.
Constraints
* 1 \leq Q \leq 10000
* 1 \leq a_i, b_i, c_i, d_i \leq 3^{30}
* (a_i, b_i) \neq (c_i, d_i)
* (a_i, b_i) and (c_i, d_i) are white squares.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
Q
a_1 \ b_1 \ c_1 \ d_1
:
a_Q \ b_Q \ c_Q \ d_Q
Output
Print Q lines. The i-th line should contain the distance from (a_i, b_i) to (c_i, d_i).
Example
Input
2
4 2 7 4
9 9 1 9
Output
5
8
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[2], [3], [4], [5], [6], [-3], [-27]], \"outputs\": [[true], [false], [false], [false], [true], [false], [false]]}", "source": "primeintellect"} | ## Task:
You have to create a function `isPronic` to check whether the argument passed is a Pronic Number and return true if it is & false otherwise.
### Description:
`Pronic Number` -A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n(n + 1).
> The first few Pronic Numbers are - 0, 2, 6, 12, 20, 30, 42...
### Explanation:
0 = 0 × 1 // ∴ 0 is a Pronic Number
2 = 1 × 2 // ∴ 2 is a Pronic Number
6 = 2 × 3 // ∴ 6 is a Pronic Number
12 = 3 × 4 // ∴ 12 is a Pronic Number
20 = 4 × 5 // ∴ 20 is a Pronic Number
30 = 5 × 6 // ∴ 30 is a Pronic Number
42 = 6 × 7 // ∴ 42 is a Pronic Number
Write your solution by modifying this code:
```python
def is_pronic(n):
```
Your solution should implemented in the function "is_pronic". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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719524142056884004\\n10 473299957195528003\\n2 555965798821270052\\n10 492559401050725258\\n\", \"10\\n3 85516593409472003\\n10 55669371794102449\\n1 934934767906835993\\n0 384681214954881520\\n4 684989729845321867\\n7 231000356557573162\\n1 336780423782602481\\n2 300230185318227609\\n9 23423148068105278\\n1 431976751989315128\\n\", \"10\\n1 185031988313502617\\n9 461852423965441269\\n2 296797889599026429\\n3 15306118532047016\\n5 866138600524414105\\n10 587197493269144005\\n2 853266793804812376\\n2 18851629184643095\\n3 29711990269601043\\n0 26848446304372246\\n\", \"10\\n4 1825\\n3 75\\n3 530\\n4 1829\\n4 1651\\n3 187\\n4 584\\n4 255\\n4 774\\n2 474\\n\", \"3\\n1 1\\n1 2\\n1 111111111111\\n\", \"5\\n0 69\\n1 194\\n1 139\\n0 47\\n1 66\\n\"], \"outputs\": [\" e\\\"atdW? e\", \"?usaglrnyh\", \"..........\", \"h... .. d.\", \"oru A\\\" de\\\"\", \"o u lugW? \", \"..........\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"..........\", \"idrd? o nl\", \"..........\", \"donts ly o\", \"ee WWah at\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"?\", \"W\\\"W?\\\"\\\"W?\\\"?\", \" u nrhuiy \", \"W\", \"youni iiee\", \"lohiW ohra\", \"i oio u? \", \"..........\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"oisv\\\"sb ta\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"WonreeuhAn\", \"\\\"?.\\\"?.\\\"?.\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"eunWwdtnA \", \"t?W y wnr\", \"o W rlot\", \"?utaglrnyh\", \"..........\", \"h... .. d.\", \"ouu A\\\" de\\\"\", \"o u lugWe \", \"W\\\"W?\\\" W?\\\"?\", \"W\\\"W?\\\"\\\"W?\\\"?\", \"idrd? o ns\", \"eonts ly o\", \"ee WWah at\", \"W\\\"W?\\\"\\\"W?.?\", \"r\", \"W\\\"W.\\\"\\\"W?\\\"?\", \"W\", \"youni tiee\", \"lrhiW ohra\", \"i oioiu? \", \"WWW?\\\"\\\"W?\\\"?\", \"oisl\\\"sb ta\", \"W\\\"W?\\\"tW?\\\"?\", \"Wo reeuhAn\", \"\\\"?.\\\"b.\\\"?.\", \"W\\\"W?\\\"\\\"W.\\\"?\", \"eu WwdtnA \", \"t?W y wnr\", \"Areyoubus.\", \"ab.ef\", \"?utaglrnuh\", \"ouu A\\\"ude\\\"\", \"eonss ly o\", \"W\\\"Wn\\\"\\\"W?.?\", \"W\\\"W.\\\"rW?\\\"?\", \"lrhia ohra\", \"i oioio? \", \"W\\\"w?\\\"\\\"W?.?\", \"WWWt\\\"\\\"W?\\\"?\", \"oisl\\\"sb?ta\", \"Wo reuuhAn\", \"\\\"?.\\\"b..?.\", \"W\\\"W?\\\"\\\"W.e?\", \"eu WrdtnA \", \"t?W y wne\", \"Areyoubuo.\", \"hb.ef\", \"?u aglrnuh\", \"W\\\"W?\\\" W?s?\", \"idrd? o nh\", \"eo ss ly o\", \"W\\\"Wn.\\\"W?.?\", \"W\\\"W.\\\"rW?\\\".\", \"h\", \"hrhia ohra\", \"i oioi ? \", \"h\\\"w?\\\"\\\"W?.?\", \"WWWt\\\"\\\"W?.?\", \"oisl\\\"sy?ta\", \"Wo reuuhnn\", \"\\\"?.\\\"b..a.\", \"W\\\"W \\\"\\\"W.e?\", \"t?W ys wne\", \"Ar.youbuo.\", \"Wb.ef\", \"?u aglrluh\", \"u... .. d.\", \"W\\\"W?\\\"oW?s?\", \"idyd? o nh\", \"eb ss ly o\", \"..........\", \"..........\", \"..........\", \"..........\", \"W\\\"W?\\\"\\\"W?.?\", \"..........\", \"h... .. d.\", \"..........\", \"W\\\"W?\\\" W?\\\"?\", \"..........\", \"idrd? o ns\", \"..........\", \"ee WWah at\", \"W\", \"..........\", \"W\\\"W?\\\"tW?\\\"?\", \"..........\", \"h... .. d.\", \"..........\", \"..........\", \"..........\", \"ee WWah at\", \"..........\", \"..........\", \"..........\", \"..........\", \"..........\", \"Areyoubusy\", \"Wh.\", \"abdef\"]}", "source": "primeintellect"} | What are you doing at the end of the world? Are you busy? Will you save us?
<image>
Nephren is playing a game with little leprechauns.
She gives them an infinite array of strings, f0... ∞.
f0 is "What are you doing at the end of the world? Are you busy? Will you save us?".
She wants to let more people know about it, so she defines fi = "What are you doing while sending "fi - 1"? Are you busy? Will you send "fi - 1"?" for all i ≥ 1.
For example, f1 is
"What are you doing while sending "What are you doing at the end of the world? Are you busy? Will you save us?"? Are you busy? Will you send "What are you doing at the end of the world? Are you busy? Will you save us?"?". Note that the quotes in the very beginning and in the very end are for clarity and are not a part of f1.
It can be seen that the characters in fi are letters, question marks, (possibly) quotation marks and spaces.
Nephren will ask the little leprechauns q times. Each time she will let them find the k-th character of fn. The characters are indexed starting from 1. If fn consists of less than k characters, output '.' (without quotes).
Can you answer her queries?
Input
The first line contains one integer q (1 ≤ q ≤ 10) — the number of Nephren's questions.
Each of the next q lines describes Nephren's question and contains two integers n and k (0 ≤ n ≤ 105, 1 ≤ k ≤ 1018).
Output
One line containing q characters. The i-th character in it should be the answer for the i-th query.
Examples
Input
3
1 1
1 2
1 111111111111
Output
Wh.
Input
5
0 69
1 194
1 139
0 47
1 66
Output
abdef
Input
10
4 1825
3 75
3 530
4 1829
4 1651
3 187
4 584
4 255
4 774
2 474
Output
Areyoubusy
Note
For the first two examples, refer to f0 and f1 given in the legend.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[3], [5], [-3], [-11], [-25], [0]], \"outputs\": [[\" 111 \\n 222 \\n1233321\\n1233321\\n1233321\\n 222 \\n 111 \"], [\" 11111 \\n 22222 \\n 33333 \\n 44444 \\n1234555554321\\n1234555554321\\n1234555554321\\n1234555554321\\n1234555554321\\n 44444 \\n 33333 \\n 22222 \\n 11111 \"], [\"\"], [\"\"], [\"\"], [\"\"]]}", "source": "primeintellect"} | < PREVIOUS KATA
NEXT KATA >
###Task:
You have to write a function `pattern` which returns the following Pattern(See Examples) upto (3n-2) rows, where n is parameter.
* Note:`Returning` the pattern is not the same as `Printing` the pattern.
####Rules/Note:
* The pattern should be created using only unit digits.
* If `n < 1` then it should return "" i.e. empty string.
* `The length of each line is same`, and is equal to the length of longest line in the pattern i.e. `length = (3n-2)`.
* Range of Parameters (for the sake of CW Compiler) :
+ `n ∈ (-∞,50]`
###Examples:
+ pattern(5) :
11111
22222
33333
44444
1234555554321
1234555554321
1234555554321
1234555554321
1234555554321
44444
33333
22222
11111
+ pattern(11):
11111111111
22222222222
33333333333
44444444444
55555555555
66666666666
77777777777
88888888888
99999999999
00000000000
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
1234567890111111111110987654321
00000000000
99999999999
88888888888
77777777777
66666666666
55555555555
44444444444
33333333333
22222222222
11111111111
>>>LIST OF ALL MY KATAS<<<
Write your solution by modifying this code:
```python
def pattern(n):
```
Your solution should implemented in the function "pattern". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3776.5765005393655\\n1819.0\\n645.2\\n2004.1\\n1208.6\", \"3777.502968017379\\n1819.0\\n645.2\\n2004.1\\n1208.6\", \"3778.4165917426626\\n1819.0\\n645.2\\n2004.2183724359945\\n1208.6\", \"3779.3515835085277\\n1819.169376096264\\n645.2\\n2004.5930566110492\\n1208.6\", \"3779.3515835085277\\n1819.169376096264\\n645.463437143232\\n2005.3577164478409\\n1209.3337144467619\", \"3779.3515835085277\\n1819.169376096264\\n645.8367231919477\\n2005.3577164478409\\n1209.3337144467619\", \"3779.3515835085277\\n1819.169376096264\\n645.8829036094434\\n2005.3577164478409\\n1209.3337144467619\", \"3780.0351746720435\\n1819.169376096264\\n645.8829036094434\\n2005.3577164478409\\n1209.3337144467619\", \"3780.0804815259103\\n1819.169376096264\\n645.8829036094434\\n2005.3577164478409\\n1209.3337144467619\", \"3780.0804815259103\\n1819.169376096264\\n646.6571280527984\\n2005.3577164478409\\n1209.3337144467619\", \"3780.563953034745\\n1819.2106222474372\\n646.6571280527984\\n2006.3750035575931\\n1210.272681011882\", \"3780.563953034745\\n1819.3385445392398\\n647.4136189514501\\n2006.6426405146844\\n1210.272681011882\", \"3781.0767308455193\\n1819.448159511015\\n647.4136189514501\\n2006.6426405146844\\n1210.272681011882\", \"3781.7784257624053\\n1819.448159511015\\n647.4136189514501\\n2006.6426405146844\\n1210.272681011882\", \"3781.7784257624053\\n1820.0897664722077\\n647.9481320421364\\n2008.2343270797455\\n1210.272681011882\", \"3782.7195081942164\\n1820.495707862411\\n647.9481320421364\\n2008.4568072933544\\n1212.9462716401742\", \"3782.7195081942164\\n1820.495707862411\\n648.36993466855\\n2008.4568072933544\\n1212.9462716401742\", \"3782.9841718116804\\n1820.495707862411\\n648.36993466855\\n2008.4568072933544\\n1212.9462716401742\", \"3783.330107938579\\n1821.055914607603\\n648.36993466855\\n2008.4568072933544\\n1212.9462716401742\", \"3783.330107938579\\n1821.5992049377405\\n649.3237125101873\\n2008.4568072933544\\n1213.566768947316\", \"3783.6109384455353\\n1821.5992049377405\\n649.3237125101873\\n2008.8147615323267\\n1214.1371939030753\", \"3784.041950800506\\n1821.5992049377405\\n649.3237125101873\\n2008.8147615323267\\n1214.1371939030753\", \"3784.5476877206565\\n1821.5992049377405\\n649.3237125101873\\n2008.8147615323267\\n1214.1371939030753\", \"3785.1813418386323\\n1821.5992049377405\\n649.3237125101873\\n2009.4416858192994\\n1214.2309349574236\", \"3785.313037222763\\n1821.5992049377405\\n649.3237125101873\\n2010.401652284202\\n1214.2619965197052\", \"3785.313037222763\\n1821.5992049377405\\n649.601739493771\\n2010.401652284202\\n1214.2619965197052\", \"3785.3986278215193\\n1821.5992049377405\\n649.601739493771\\n2010.401652284202\\n1214.2619965197052\", \"3785.5299644769743\\n1821.5992049377405\\n649.601739493771\\n2010.401652284202\\n1214.2619965197052\", \"3785.5299644769743\\n1821.5992049377405\\n650.0662056796525\\n2010.401652284202\\n1214.76561305268\", \"3785.5299644769743\\n1822.8075308723019\\n650.9796685362885\\n2010.401652284202\\n1214.76561305268\", \"3786.2443860959384\\n1822.8075308723019\\n650.9796685362885\\n2010.401652284202\\n1214.76561305268\", \"3786.709448951659\\n1822.8774340497916\\n650.9796685362885\\n2010.8220489349183\\n1214.76561305268\", \"3787.1982701218176\\n1822.8774340497916\\n650.9796685362885\\n2010.8220489349183\\n1214.76561305268\", \"3787.1982701218176\\n1822.8774340497916\\n651.7784719363967\\n2010.8220489349183\\n1214.76561305268\", \"3787.1982701218176\\n1822.8774340497916\\n651.8853622826949\\n2010.8220489349183\\n1214.76561305268\", \"3787.727647960824\\n1823.5256829017794\\n651.8853622826949\\n2011.449941699831\\n1215.4052254391302\", \"3787.7869334799493\\n1824.0674300563485\\n651.8853622826949\\n2011.727618626295\\n1216.3021681144476\", \"3787.7869334799493\\n1824.0674300563485\\n652.2539021259846\\n2011.727618626295\\n1216.3021681144476\", \"3788.1593414877557\\n1824.0674300563485\\n652.2539021259846\\n2011.727618626295\\n1216.3021681144476\", \"3788.1804133310084\\n1824.0674300563485\\n652.2539021259846\\n2011.962105400809\\n1216.3021681144476\", \"3789.073407944056\\n1824.128350837821\\n652.2539021259846\\n2012.4395020468091\\n1216.3021681144476\", \"3789.7275143037896\\n1824.128350837821\\n652.2539021259846\\n2012.4395020468091\\n1217.206813985485\", \"3790.1159613701802\\n1824.8833719624647\\n652.2539021259846\\n2012.4395020468091\\n1217.206813985485\", \"3790.8159250982\\n1824.8833719624647\\n652.2539021259846\\n2012.4395020468091\\n1217.206813985485\", \"3791.457019718548\\n1825.9172310751928\\n652.2539021259846\\n2012.4395020468091\\n1217.206813985485\", \"3791.927492911873\\n1826.5692786422178\\n652.2539021259846\\n2012.5564504356792\\n1217.5021240196654\", \"3791.927492911873\\n1827.5038399003997\\n652.3096761753305\\n2012.5564504356792\\n1217.5021240196654\", \"3791.927492911873\\n1827.5038399003997\\n652.5959415254272\\n2012.5564504356792\\n1217.5021240196654\", \"3791.927492911873\\n1827.5038399003997\\n653.4866711320179\\n2012.5564504356792\\n1217.5021240196654\", \"3791.927492911873\\n1827.5038399003997\\n653.4993645993594\\n2012.5564504356792\\n1218.0326483164713\", \"3792.4209183393\\n1827.5038399003997\\n653.4993645993594\\n2012.5564504356792\\n1218.0326483164713\", \"3792.4209183393\\n1827.5038399003997\\n653.5032494800946\\n2012.5564504356792\\n1218.0326483164713\", \"3792.4209183393\\n1828.2628250796859\\n654.3088726873827\\n2012.5564504356792\\n1218.0326483164713\", \"3792.4209183393\\n1828.2628250796859\\n654.7631010988753\\n2012.6796640894572\\n1218.0326483164713\", \"3792.7691816377633\\n1828.2628250796859\\n654.7631010988753\\n2012.7275421076122\\n1218.0326483164713\", \"3792.7691816377633\\n1828.2628250796859\\n655.5618911545704\\n2013.3606836084307\\n1218.0326483164713\", \"3792.7691816377633\\n1828.2628250796859\\n655.8578152742465\\n2013.3606836084307\\n1218.771776471869\", \"3792.7691816377633\\n1828.2628250796859\\n656.2200978020528\\n2013.3606836084307\\n1219.3586418253283\", \"3792.7691816377633\\n1828.2628250796859\\n656.4591098319041\\n2013.3606836084307\\n1219.3586418253283\", \"3793.633136252094\\n1829.2307458203293\\n656.4591098319041\\n2014.2606949931794\\n1219.3586418253283\", \"3793.633136252094\\n1829.2307458203293\\n657.2776927702541\\n2014.2606949931794\\n1219.3586418253283\", \"3793.633136252094\\n1830.207401996363\\n657.7479998177856\\n2014.2606949931794\\n1219.6801702417647\", \"3793.633136252094\\n1830.7209331462452\\n658.3978619481923\\n2014.847992882431\\n1220.221307204699\", \"3794.631648752604\\n1830.7209331462452\\n658.3978619481923\\n2014.847992882431\\n1220.221307204699\", 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\"3800.753179141307\\n1841.6951842981764\\n664.7519226735278\\n2024.3103661692626\\n1225.2062180779285\", \"3800.753179141307\\n1841.6951842981764\\n664.9396422749081\\n2024.3103661692626\\n1225.2062180779285\", \"3800.753179141307\\n1841.6951842981764\\n665.0356930677984\\n2024.668754274095\\n1225.286238726446\", \"3800.753179141307\\n1841.6951842981764\\n665.7734966978811\\n2024.668754274095\\n1225.286238726446\", \"3801.0780911419797\\n1841.6951842981764\\n665.7734966978811\\n2024.668754274095\\n1225.286238726446\", \"3801.8394636640232\\n1841.726413429015\\n665.7734966978811\\n2024.668754274095\\n1225.286238726446\", \"3801.8394636640232\\n1841.726413429015\\n666.1037345853492\\n2024.668754274095\\n1225.286238726446\", \"3801.8394636640232\\n1841.726413429015\\n666.6314599966545\\n2024.668754274095\\n1225.286238726446\", \"3801.8394636640232\\n1841.726413429015\\n667.4311746474547\\n2024.668754274095\\n1225.286238726446\", \"3776.0\\n1819.0\\n645.2\\n2004.1\\n1208.6\"], \"outputs\": [\"3131.37650054\\n\", \"3132.30296802\\n\", \"3133.21659174\\n\", \"3134.15158351\\n\", \"3133.88814637\\n\", \"3133.51486032\\n\", \"3133.4686799\\n\", \"3134.15227106\\n\", \"3134.19757792\\n\", \"3133.42335347\\n\", \"3133.90682498\\n\", \"3133.15033408\\n\", \"3133.66311189\\n\", \"3134.36480681\\n\", \"3133.83029372\\n\", \"3134.77137615\\n\", \"3134.34957353\\n\", \"3134.61423714\\n\", \"3134.96017327\\n\", \"3134.00639543\\n\", \"3134.28722594\\n\", \"3134.71823829\\n\", \"3135.22397521\\n\", \"3135.85762933\\n\", \"3135.98932471\\n\", \"3135.71129773\\n\", \"3135.79688833\\n\", \"3135.92822498\\n\", \"3135.4637588\\n\", \"3134.55029594\\n\", \"3135.26471756\\n\", \"3135.72978042\\n\", \"3136.21860159\\n\", \"3135.41979819\\n\", \"3135.31290784\\n\", \"3135.84228568\\n\", \"3135.9015712\\n\", \"3135.53303135\\n\", \"3135.90543936\\n\", \"3135.92651121\\n\", \"3136.81950582\\n\", \"3137.47361218\\n\", \"3137.86205924\\n\", \"3138.56202297\\n\", \"3139.20311759\\n\", \"3139.67359079\\n\", \"3139.61781674\\n\", \"3139.33155139\\n\", \"3138.44082178\\n\", \"3138.42812831\\n\", \"3138.92155374\\n\", \"3138.91766886\\n\", \"3138.11204565\\n\", \"3137.65781724\\n\", \"3138.00608054\\n\", \"3137.20729048\\n\", \"3136.91136636\\n\", \"3136.54908384\\n\", \"3136.31007181\\n\", \"3137.17402642\\n\", \"3136.35544348\\n\", \"3135.88513643\\n\", \"3135.2352743\\n\", \"3136.2337868\\n\", \"3137.17819318\\n\", \"3137.06491686\\n\", \"3136.85754907\\n\", \"3136.98729087\\n\", \"3137.15153066\\n\", \"3138.07057588\\n\", \"3137.42685415\\n\", \"3137.65429503\\n\", \"3138.12462169\\n\", \"3138.26169247\\n\", \"3138.1502058\\n\", \"3137.18938129\\n\", \"3136.76966923\\n\", \"3136.11166847\\n\", \"3135.70952317\\n\", \"3134.80813731\\n\", \"3135.63475312\\n\", \"3135.49721077\\n\", \"3134.70674995\\n\", \"3134.97805796\\n\", \"3135.47872424\\n\", \"3135.24684755\\n\", \"3134.9452685\\n\", \"3134.58995037\\n\", \"3135.22810763\\n\", \"3135.10874495\\n\", \"3135.97417557\\n\", \"3136.00125647\\n\", \"3135.81353687\\n\", \"3135.71748607\\n\", \"3134.97968244\\n\", \"3135.30459444\\n\", \"3136.06596697\\n\", \"3135.73572908\\n\", \"3135.20800367\\n\", \"3134.40828902\\n\", \"3130.8\"]}", "source": "primeintellect"} | There is data that records the altitude of mountains that have been climbed so far. Create a program that reads this data and outputs the elevation difference between the highest and lowest mountains.
Input
The input is given in the following format:
Mountain height
...
...
The height of the mountain is given over multiple lines. All values entered are real numbers greater than or equal to 0 and less than or equal to 1,000,000. The number of mountain heights entered is 50 or less.
Output
The elevation difference between the highest mountain and the lowest mountain is output as a real number. The output may contain an error of 0.01 or less.
Example
Input
3776.0
1819.0
645.2
2004.1
1208.6
Output
3130.8
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.5 |
{"tests": "{\"inputs\": [\"3 2\\n2 1 1\\n\", \"3 3\\n2 1 2\\n\", \"7 1\\n4 4 6 6 6 6 5\\n\", \"3 2\\n2 0 1\\n\", \"3 1\\n2 1 1\\n\", \"3 1\\n0 1 2\\n\", \"10 6\\n3 0 0 0 0 0 0 1 0 0\\n\", \"5 5\\n0 1 1 0 0\\n\", \"3 2\\n2 2 1\\n\", \"5 1\\n0 0 1 3 4\\n\", \"2 1\\n1 1\\n\", \"9 1\\n0 0 0 2 5 5 5 5 5\\n\", \"6 1\\n0 1 2 2 0 0\\n\", \"2 2\\n1 0\\n\", \"9 1\\n0 1 1 1 1 1 6 7 8\\n\", \"2 2\\n1 1\\n\", \"3 3\\n1 1 0\\n\", \"3 2\\n2 2 2\\n\", \"2 1\\n0 0\\n\", \"1 1\\n0\\n\", \"3 1\\n0 0 2\\n\", \"6 1\\n5 2 1 3 3 1\\n\", \"2 1\\n1 0\\n\", \"9 1\\n0 1 1 1 1 5 6 7 8\\n\", \"3 3\\n2 1 0\\n\", \"2 2\\n0 1\\n\", \"2 2\\n0 0\\n\", \"2 1\\n0 1\\n\", \"3 1\\n1 2 2\\n\", \"3 1\\n2 0 1\\n\", \"10 6\\n3 1 0 0 0 0 0 1 0 0\\n\", \"5 5\\n0 0 1 0 0\\n\", \"3 3\\n0 1 0\\n\", \"5 5\\n0 0 0 0 0\\n\", \"10 6\\n3 0 1 0 0 0 0 1 0 1\\n\", \"3 2\\n1 0 2\\n\", \"3 3\\n2 2 1\\n\", \"9 1\\n0 0 0 2 5 4 5 5 5\\n\", \"6 1\\n0 1 0 2 0 0\\n\", \"9 1\\n0 1 2 1 1 1 6 7 8\\n\", \"6 1\\n5 2 1 5 3 1\\n\", \"9 1\\n0 1 1 1 1 5 6 2 8\\n\", \"5 4\\n1 0 0 4 1\\n\", \"3 2\\n2 0 0\\n\", \"3 1\\n2 0 0\\n\", \"10 6\\n3 0 0 0 0 0 0 1 0 1\\n\", \"9 1\\n0 1 3 1 1 1 6 7 8\\n\", \"6 1\\n5 2 1 1 3 1\\n\", \"5 4\\n1 1 0 4 1\\n\", \"9 1\\n0 0 3 1 1 1 6 7 8\\n\", \"6 1\\n1 2 1 1 3 1\\n\", \"10 6\\n3 0 1 0 0 0 0 1 0 2\\n\", \"6 1\\n1 2 1 1 5 1\\n\", \"10 6\\n3 0 1 0 0 0 1 1 0 2\\n\", \"6 1\\n1 0 1 1 3 1\\n\", \"10 6\\n3 0 1 1 0 0 1 1 0 2\\n\", \"6 1\\n1 0 0 1 3 1\\n\", \"3 1\\n0 2 2\\n\", \"5 1\\n0 0 1 4 4\\n\", \"9 1\\n1 0 0 2 5 5 5 5 5\\n\", \"3 2\\n1 2 2\\n\", \"9 1\\n0 1 1 1 0 5 6 7 8\\n\", \"5 3\\n0 0 0 4 1\\n\", \"3 1\\n2 1 2\\n\", \"3 3\\n2 1 1\\n\", \"3 3\\n0 0 0\\n\", \"6 1\\n5 2 1 5 1 1\\n\", \"5 4\\n1 0 0 4 2\\n\", \"9 1\\n0 1 3 1 1 1 6 1 8\\n\", \"10 6\\n2 0 1 0 0 0 0 1 0 1\\n\", \"9 1\\n0 0 3 1 1 0 6 7 8\\n\", \"6 1\\n1 2 1 1 0 1\\n\", \"6 1\\n0 2 1 1 5 1\\n\", \"10 6\\n3 0 1 0 0 0 1 1 0 4\\n\", \"6 1\\n1 0 1 2 3 1\\n\", \"3 2\\n0 2 2\\n\", \"9 1\\n1 0 0 2 5 8 5 5 5\\n\", \"6 1\\n5 2 1 1 1 1\\n\", \"9 1\\n0 1 3 1 1 1 2 1 8\\n\", \"6 1\\n1 2 1 2 0 1\\n\", \"6 1\\n1 0 2 2 3 1\\n\", \"9 1\\n1 0 0 2 6 8 5 5 5\\n\", \"6 1\\n5 2 1 1 1 0\\n\", \"9 1\\n0 1 3 1 1 0 2 1 8\\n\", \"9 1\\n1 0 0 2 6 8 5 8 5\\n\", \"6 2\\n5 2 1 1 1 0\\n\", \"5 3\\n1 0 0 4 1\\n\", \"3 2\\n2 0 2\\n\"], \"outputs\": [\"1\\n\", \"1\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"3\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"6\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"5\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"6\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"1\\n\"]}", "source": "primeintellect"} | There are n workers in a company, each of them has a unique id from 1 to n. Exaclty one of them is a chief, his id is s. Each worker except the chief has exactly one immediate superior.
There was a request to each of the workers to tell how how many superiors (not only immediate). Worker's superiors are his immediate superior, the immediate superior of the his immediate superior, and so on. For example, if there are three workers in the company, from which the first is the chief, the second worker's immediate superior is the first, the third worker's immediate superior is the second, then the third worker has two superiors, one of them is immediate and one not immediate. The chief is a superior to all the workers except himself.
Some of the workers were in a hurry and made a mistake. You are to find the minimum number of workers that could make a mistake.
Input
The first line contains two positive integers n and s (1 ≤ n ≤ 2·105, 1 ≤ s ≤ n) — the number of workers and the id of the chief.
The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ n - 1), where ai is the number of superiors (not only immediate) the worker with id i reported about.
Output
Print the minimum number of workers that could make a mistake.
Examples
Input
3 2
2 0 2
Output
1
Input
5 3
1 0 0 4 1
Output
2
Note
In the first example it is possible that only the first worker made a mistake. Then:
* the immediate superior of the first worker is the second worker,
* the immediate superior of the third worker is the first worker,
* the second worker is the chief.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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1\\n! 200\\n\", \"? 3\\n! 619347297\\n\", \"? 3\\n? 9\\n! 978367651\\n\", \"? 3\\n! 411188472\\n\", \"? 3\\n? 5\\n? 1\\n? 4\\n? 2\\n! 673892808\\n\", \"? 3\\n! 844816862\\n\", \"? 3\\n! 97\\n\", \"? 3\\n! 3\\n\", \"? 1\\n! 200\\n\", \"? 3\\n! 619347297\\n\", \"? 3\\n? 9\\n! 978367651\\n\", \"? 3\\n! 411188472\\n\", \"? 1\\n? 2\\n? 3\\n? 4\\n? 5\\n! -1\\n\", \"? 0\\n! -1\\n\", \"? 3\\n! 844816862\\n\", \"? 3\\n! 97\\n\", \"? 3\\n! 3\\n\", \"? 1\\n! 200\\n\", \"? 3\\n! 619347297\\n\", \"? 3\\n? 9\\n! 978367651\\n\", \"? 3\\n! 411188472\\n\", \"? 3\\n? 1\\n? 1\\n? 4\\n? 2\\n! 673892808\\n\", \"? 0\\n! -1\\n\", \"? 2\\n? 1\\n? 1\\n? 4\\n? 2\\n! -1\\n\", \"? 3\\n! 97\\n\"]}", "source": "primeintellect"} | This is an interactive problem.
You are given a sorted in increasing order singly linked list. You should find the minimum integer in the list which is greater than or equal to x.
More formally, there is a singly liked list built on an array of n elements. Element with index i contains two integers: valuei is the integer value in this element, and nexti that is the index of the next element of the singly linked list (or -1, if the current element is the last). The list is sorted, i.e. if nexti ≠ - 1, then valuenexti > valuei.
You are given the number of elements in the list n, the index of the first element start, and the integer x.
You can make up to 2000 queries of the following two types:
* ? i (1 ≤ i ≤ n) — ask the values valuei and nexti,
* ! ans — give the answer for the problem: the minimum integer, greater than or equal to x, or ! -1, if there are no such integers. Your program should terminate after this query.
Write a program that solves this problem.
Input
The first line contains three integers n, start, x (1 ≤ n ≤ 50000, 1 ≤ start ≤ n, 0 ≤ x ≤ 109) — the number of elements in the list, the index of the first element and the integer x.
Output
To print the answer for the problem, print ! ans, where ans is the minimum integer in the list greater than or equal to x, or -1, if there is no such integer.
Interaction
To make a query of the first type, print ? i (1 ≤ i ≤ n), where i is the index of element you want to know information about.
After each query of type ? read two integers valuei and nexti (0 ≤ valuei ≤ 109, - 1 ≤ nexti ≤ n, nexti ≠ 0).
It is guaranteed that if nexti ≠ - 1, then valuenexti > valuei, and that the array values give a valid singly linked list with start being the first element.
Note that you can't ask more than 1999 queries of the type ?.
If nexti = - 1 and valuei = - 1, then it means that you asked more queries than allowed, or asked an invalid query. Your program should immediately terminate (for example, by calling exit(0)). You will receive "Wrong Answer", it means that you asked more queries than allowed, or asked an invalid query. If you ignore this, you can get other verdicts since your program will continue to read from a closed stream.
Your solution will get "Idleness Limit Exceeded", if you don't print anything or forget to flush the output, including the final answer.
To flush you can use (just after printing a query and line end):
* fflush(stdout) in C++;
* System.out.flush() in Java;
* stdout.flush() in Python;
* flush(output) in Pascal;
* For other languages see documentation.
Hacks format
For hacks, use the following format:
In the first line print three integers n, start, x (1 ≤ n ≤ 50000, 1 ≤ start ≤ n, 0 ≤ x ≤ 109).
In the next n lines print the description of the elements of the list: in the i-th line print two integers valuei and nexti (0 ≤ valuei ≤ 109, - 1 ≤ nexti ≤ n, nexti ≠ 0).
The printed structure should be a valid singly linked list. In particular, it should be possible to reach all elements from start by following links nexti, and the last element end should have -1 in the nextend.
Example
Input
5 3 80
97 -1
58 5
16 2
81 1
79 4
Output
? 1
? 2
? 3
? 4
? 5
! 81
Note
You can read more about singly linked list by the following link: <https://en.wikipedia.org/wiki/Linked_list#Singly_linked_list>
The illustration for the first sample case. Start and finish elements are marked dark. <image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.125 |
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\"69027853\\n\", \"124207947\\n\", \"53142566\\n\", \"443476923\\n\", \"718416032\\n\", \"714415413\\n\", \"815058467\\n\", \"19475618\\n\", \"352633440\\n\", \"135616516\\n\", \"512892394\\n\", \"700813158\\n\", \"237580383\\n\", \"343325503\\n\", \"649406940\\n\", \"21724067\\n\", \"966912011\\n\", \"153939035\\n\", \"811442492\\n\", \"762062201\\n\", \"403012329\\n\", \"404492202\\n\", \"913609421\\n\", \"170360480\\n\", \"686672537\\n\", \"293907707\\n\", \"844117763\\n\", \"474176810\\n\", \"589747946\\n\", \"798228603\\n\", \"39324383\\n\", \"968150439\\n\", \"843490134\\n\", \"554797686\\n\", \"773079808\\n\", \"676786376\\n\", \"319784064\\n\", \"352683047\\n\", \"678735347\\n\", \"584919955\\n\", \"82166530\\n\", \"165720483\\n\", \"141968535\\n\", \"519733863\\n\", \"493844566\\n\", \"755573142\\n\", \"360202301\\n\", \"649211171\\n\", \"542396684\\n\", \"328666116\\n\", \"377786574\\n\", \"260021058\\n\", \"920138479\\n\", \"910202272\\n\", \"20621341\\n\", \"546345498\\n\", \"137221551\\n\", \"649675076\\n\", \"983482968\\n\", \"646076029\\n\", \"164333059\\n\", \"956154878\\n\", \"266077197\\n\", \"1427703\\n\", \"801346835\\n\", \"575683518\\n\", \"155392497\\n\", \"139827189\\n\", \"58798180\\n\", \"433940745\\n\", \"245240032\\n\", \"679213445\\n\", \"527738935\\n\", \"862587894\\n\", \"420376581\\n\", \"788739052\\n\", \"82446742\\n\", \"911237016\\n\", \"313097678\\n\", \"607647504\\n\", \"79564153\\n\", \"962975375\\n\", \"472526756\\n\", \"455642499\\n\", \"291957322\\n\", \"813718136\\n\", \"445048429\\n\", \"449206259\\n\", \"477521683\\n\", \"664561971\\n\", \"562801281\\n\", \"823150509\\n\", \"\\n6\", \"\\n1\", \"\\n3\", \"\\n688750769\"]}", "source": "primeintellect"} | Kavi has 2n points lying on the OX axis, i-th of which is located at x = i.
Kavi considers all ways to split these 2n points into n pairs. Among those, he is interested in good pairings, which are defined as follows:
Consider n segments with ends at the points in correspondent pairs. The pairing is called good, if for every 2 different segments A and B among those, at least one of the following holds:
* One of the segments A and B lies completely inside the other.
* A and B have the same length.
Consider the following example:
<image>
A is a good pairing since the red segment lies completely inside the blue segment.
B is a good pairing since the red and the blue segment have the same length.
C is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.
Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo 998244353.
Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.
Input
The single line of the input contains a single integer n (1≤ n ≤ 10^6).
Output
Print the number of good pairings modulo 998244353.
Examples
Input
1
Output
1
Input
2
Output
3
Input
3
Output
6
Input
100
Output
688750769
Note
The good pairings for the second example are:
<image>
In the third example, the good pairings are:
<image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1\\n4 2 2\\n\", \"1\\n1000 999 1\\n\", \"1\\n7 2 1\\n\", \"1\\n1000 1 1\\n\", \"1\\n2 1 1\\n\", \"1\\n1000 1 1000\\n\", \"1\\n8 7 2\\n\", \"1\\n1000 998 1000\\n\", \"1\\n1000 500 123\\n\", \"1\\n1000 1 2\\n\", \"1\\n1000 999 2\\n\", \"1\\n7 2 2\\n\", \"1\\n1100 999 1\\n\", \"1\\n8 2 1\\n\", \"1\\n1000 2 2\\n\", \"1\\n4 1 1\\n\", \"1\\n1001 1 1000\\n\", \"1\\n16 7 2\\n\", \"1\\n1000 784 123\\n\", \"1\\n1001 999 2\\n\", \"2\\n4 3 1\\n5 2 2\\n\", \"1\\n7 2 4\\n\", \"1\\n8 2 2\\n\", \"1\\n1000 4 2\\n\", \"1\\n4 2 1\\n\", \"1\\n23 7 2\\n\", \"1\\n1000 784 30\\n\", \"2\\n8 3 1\\n4 2 2\\n\", \"1\\n8 2 4\\n\", \"1\\n1000 7 2\\n\", \"1\\n21 7 2\\n\", \"1\\n1001 784 30\\n\", \"1\\n8 1 4\\n\", \"1\\n8 4 3\\n\", \"1\\n21 1 2\\n\", \"1\\n1001 822 30\\n\", \"1\\n5 1 4\\n\", \"1\\n13 4 3\\n\", \"1\\n21 1 4\\n\", \"1\\n1001 822 10\\n\", \"1\\n2 1 4\\n\", \"1\\n13 4 1\\n\", \"1\\n1001 822 4\\n\", \"1\\n2 1 3\\n\", \"1\\n13 4 2\\n\", \"1\\n2 1 2\\n\", \"1\\n10 4 2\\n\", \"1\\n1100 999 2\\n\", \"1\\n7 4 1\\n\", \"1\\n1100 1 1000\\n\", \"1\\n1100 998 1000\\n\", \"1\\n1000 2 1\\n\", \"1\\n1000 919 2\\n\", \"1\\n1100 624 1\\n\", \"1\\n8 4 1\\n\", \"1\\n1010 2 2\\n\", \"1\\n7 1 1\\n\", \"1\\n1001 1 1100\\n\", \"1\\n1010 784 123\\n\", \"1\\n7 2 3\\n\", \"1\\n5 2 1\\n\", \"1\\n6 2 1\\n\", \"1\\n23 7 3\\n\", \"2\\n9 3 1\\n4 2 2\\n\", \"1\\n8 2 3\\n\", \"1\\n1000 7 1\\n\", \"1\\n19 7 2\\n\", \"1\\n1001 784 17\\n\", \"1\\n21 1 3\\n\", \"1\\n1001 822 49\\n\", \"1\\n10 1 4\\n\", \"1\\n13 2 3\\n\", \"1\\n42 1 4\\n\", \"1\\n8 4 2\\n\", \"2\\n8 5 1\\n4 2 2\\n\", \"2\\n4 3 1\\n4 2 2\\n\"], \"outputs\": [\"0.6666666667\\n\", \"0.9999989990\\n\", \"1.7948717949\\n\", \"0.9999989990\\n\", \"0.6666666667\\n\", \"0.0000010010\\n\", \"0.9333333333\\n\", \"0.3993597439\\n\", \"0.0660894852\\n\", \"0.2501875781\\n\", \"0.9999959960\\n\", \"0.6140350877\\n\", \"100.0710485339\\n\", \"1.8461538462\\n\", \"0.5007506242\\n\", \"0.9230769231\\n\", \"0.0000010010\\n\", \"2.3119266055\\n\", \"0.2396458892\\n\", \"1.9999680005\\n\", \"0.9230769231\\n0.6521739130\\n\", \"0.1690821256\\n\", \"0.6000000000\\n\", \"1.0030049868\\n\", \"1.3333333333\\n\", \"2.1738396624\\n\", \"3.9590035161\\n\", \"2.4489795918\\n0.6666666667\\n\", \"0.1621621622\\n\", \"1.7592141721\\n\", \"2.2105263158\\n\", \"3.9452933083\\n\", \"0.0707070707\\n\", \"0.7272727273\\n\", \"0.2590993214\\n\", \"4.9658300236\\n\", \"0.0766283525\\n\", \"0.5992317542\\n\", \"0.0654103722\\n\", \"36.5751156839\\n\", \"0.1111111111\\n\", \"3.5187969925\\n\", \"110.2864577327\\n\", \"0.1818181818\\n\", \"1.2446808511\\n\", \"0.3333333333\\n\", \"1.3043478261\\n\", \"97.3839698729\\n\", \"2.2702702703\\n\", \"0.0000010009\\n\", \"0.0107616096\\n\", \"1.9999919840\\n\", \"78.7510949554\\n\", \"357.8696482711\\n\", \"2.6666666667\\n\", \"0.5007431861\\n\", \"0.9767441860\\n\", \"0.0000008273\\n\", \"0.2313523775\\n\", \"0.2928870293\\n\", \"1.5789473684\\n\", \"1.7142857143\\n\", \"1.0450304260\\n\", \"2.5714285714\\n0.6666666667\\n\", \"0.2823529412\\n\", \"6.9996545991\\n\", \"2.2510578279\\n\", \"11.8315954314\\n\", \"0.1159900580\\n\", \"1.8942631128\\n\", \"0.0689127106\\n\", \"0.2565022422\\n\", \"0.0639245675\\n\", \"1.3333333333\\n\", \"2.4489795918\\n0.6666666667\\n\", \"0.9230769231\\n0.6666666667\\n\"]}", "source": "primeintellect"} | Have you ever tasted Martian food? Well, you should.
Their signature dish is served on a completely black plate with the radius of R, flat as a pancake.
First, they put a perfectly circular portion of the Golden Honduras on the plate. It has the radius of r and is located as close to the edge of the plate as possible staying entirely within the plate. I. e. Golden Honduras touches the edge of the plate from the inside. It is believed that the proximity of the portion of the Golden Honduras to the edge of a plate demonstrates the neatness and exactness of the Martians.
Then a perfectly round portion of Pink Guadeloupe is put on the plate. The Guadeloupe should not overlap with Honduras, should not go beyond the border of the plate, but should have the maximum radius. I. e. Pink Guadeloupe should touch the edge of the plate from the inside, and touch Golden Honduras from the outside. For it is the size of the Rose Guadeloupe that shows the generosity and the hospitality of the Martians.
Further, the first portion (of the same perfectly round shape) of Green Bull Terrier is put on the plate. It should come in contact with Honduras and Guadeloupe, should not go beyond the border of the plate and should have maximum radius.
Each of the following portions of the Green Bull Terrier must necessarily touch the Golden Honduras, the previous portion of the Green Bull Terrier and touch the edge of a plate, but should not go beyond the border.
To determine whether a stranger is worthy to touch the food, the Martians ask him to find the radius of the k-th portion of the Green Bull Terrier knowing the radii of a plate and a portion of the Golden Honduras. And are you worthy?
Input
The first line contains integer t (1 ≤ t ≤ 104) — amount of testcases.
Each of the following t lines contain three positive integers: the radii of the plate and a portion of the Golden Honduras R and r (1 ≤ r < R ≤ 104) and the number k (1 ≤ k ≤ 104).
In the pretests 1 ≤ k ≤ 2.
Output
Print t lines — the radius of the k-th portion of the Green Bull Terrier for each test. The absolute or relative error of the answer should not exceed 10 - 6.
Examples
Input
2
4 3 1
4 2 2
Output
0.9230769231
0.6666666667
Note
Dish from the first sample looks like this:
<image>
Dish from the second sample looks like this:
<image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5 1\\n1 1856513539 999999998 999999999 1000000000\", \"16 10\\n1 7 12 27 52 75 731 13856 395504 534840 1276551 903860 9384806 19108104 82684732 535447408\", \"2 100\\n1 13\", \"10 8851025\\n38 87 668 4845 22601 65499 90236 790604 4290609 4894746\", \"16 10\\n1 7 12 27 52 75 731 18298 395504 534840 1276551 903860 9384806 19108104 82684732 535447408\", \"2 100\\n1 25\", \"10 8851025\\n38 87 668 4845 22601 65499 90236 925504 4290609 4894746\", \"16 10\\n1 12 12 27 52 75 731 18298 395504 534840 1276551 903860 9384806 19108104 82684732 535447408\", \"2 101\\n1 25\", \"10 8851025\\n38 87 1130 4845 22601 65499 90236 925504 4290609 4894746\", \"16 10\\n1 12 12 27 52 132 731 18298 395504 534840 1276551 903860 9384806 19108104 82684732 535447408\", \"2 101\\n1 42\", \"10 8851025\\n38 87 1130 4845 22601 65499 90236 398928 4290609 4894746\", \"16 10\\n0 12 12 27 52 132 731 18298 395504 534840 1276551 903860 9384806 19108104 82684732 535447408\", \"16 10\\n0 12 12 27 52 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13856 395504 534840 1276551 716202 8621338 19108104 82684732 1034374634\", \"2 001\\n2 13\", \"10 8851025\\n38 17 1832 4845 22601 65499 90236 790604 3407582 3363505\", \"16 10\\n1 0 9 27 53 75 731 25791 395504 534840 1276551 903860 9384806 19108104 117287972 167456262\", \"16 19\\n0 12 12 27 52 75 731 18298 395504 534840 728898 903860 9384806 19108104 117281461 891323925\", \"16 10\\n1 12 12 17 48 132 812 23157 395504 534840 1276551 903860 9384806 5744546 82684732 588217545\", \"16 10\\n1 12 12 7 52 132 731 18298 395504 105513 1276551 1577724 9384806 37684133 82684732 535447408\", \"16 10\\n0 23 12 27 52 132 1174 18298 395504 534840 605490 903860 1420430 12502570 82684732 11190507\", \"16 10\\n0 13 12 27 77 132 731 3190 631588 534840 1276551 903860 6785357 19108104 82684732 780831445\", \"10 1530195\\n11 87 668 3175 22601 4759 89053 790604 4290609 4750425\", \"2 001\\n0 13\", \"10 8851025\\n4 17 1832 4845 22601 65499 90236 790604 3407582 3363505\", \"16 10\\n1 12 12 17 48 132 812 23157 395504 534840 1276551 903860 9384806 5744546 83163708 588217545\", \"16 10\\n1 12 12 7 52 132 731 18298 395504 105513 177729 1577724 9384806 37684133 82684732 535447408\", \"16 10\\n0 23 12 27 52 132 1174 18298 394717 534840 605490 903860 1420430 12502570 82684732 11190507\", \"5 1\\n1 999999997 999999998 999999999 1000000000\", \"16 10\\n1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408\", \"2 100\\n1 10\", \"10 8851025\\n38 87 668 3175 22601 65499 90236 790604 4290609 4894746\"], \"outputs\": [\"24282567693\\n\", \"3248753070\\n\", \"370\\n\", \"150735186\\n\", \"3248775280\\n\", \"430\\n\", \"151679486\\n\", \"3248775305\\n\", \"433\\n\", \"151687340\\n\", \"3248775590\\n\", \"518\\n\", \"148001308\\n\", \"3248775585\\n\", \"4475695770\\n\", \"4462698525\\n\", \"20906745193\\n\", \"3257897765\\n\", \"358\\n\", \"150709485\\n\", \"3248753065\\n\", \"365\\n\", \"150746406\\n\", \"3248775285\\n\", \"133\\n\", \"151679171\\n\", \"3246037040\\n\", \"151686689\\n\", \"3248775995\\n\", \"131433493\\n\", \"3246500510\\n\", \"4442668100\\n\", \"4462768650\\n\", \"19883079338\\n\", \"3259693880\\n\", \"353\\n\", \"69345636\\n\", \"3244935725\\n\", \"65\\n\", \"150745076\\n\", \"3248775270\\n\", \"3246037035\\n\", \"157675518\\n\", \"3181958205\\n\", \"143760423\\n\", \"3249869830\\n\", \"4439312795\\n\", \"4464441755\\n\", \"20069053868\\n\", \"3259693875\\n\", \"69345680\\n\", \"3244938150\\n\", \"70\\n\", \"146329941\\n\", \"3421791470\\n\", \"3464829020\\n\", \"157680652\\n\", \"3445808890\\n\", \"155509038\\n\", \"3249869835\\n\", \"4399490915\\n\", \"4464441880\\n\", \"20119053868\\n\", \"69370905\\n\", \"3243999860\\n\", \"100\\n\", \"133711841\\n\", \"3421791427\\n\", \"3464829236\\n\", \"3445833185\\n\", \"155942031\\n\", \"3342749980\\n\", \"4399493130\\n\", \"4464296215\\n\", \"68945725\\n\", \"3243999895\\n\", \"73\\n\", \"138673736\\n\", \"3421828892\\n\", \"3637812881\\n\", \"3445833135\\n\", \"3342749880\\n\", \"4399493185\\n\", \"4464296220\\n\", \"68224120\\n\", \"5738636025\\n\", \"78\\n\", \"138682304\\n\", \"1581873162\\n\", \"5198403481\\n\", \"3445833115\\n\", \"3342878320\\n\", \"551288495\\n\", \"4463803535\\n\", \"68192980\\n\", \"68\\n\", \"138681590\\n\", \"3448227995\\n\", \"3337384210\\n\", \"551284560\\n\", \"19999999983\", \"3256017715\", \"355\", \"150710136\"]}", "source": "primeintellect"} | Snuke has decided to use a robot to clean his room.
There are N pieces of trash on a number line. The i-th piece from the left is at position x_i. We would like to put all of them in a trash bin at position 0.
For the positions of the pieces of trash, 0 < x_1 < x_2 < ... < x_{N} \leq 10^{9} holds.
The robot is initially at position 0. It can freely move left and right along the number line, pick up a piece of trash when it comes to the position of that piece, carry any number of pieces of trash and put them in the trash bin when it comes to position 0. It is not allowed to put pieces of trash anywhere except in the trash bin.
The robot consumes X points of energy when the robot picks up a piece of trash, or put pieces of trash in the trash bin. (Putting any number of pieces of trash in the trash bin consumes X points of energy.) Also, the robot consumes (k+1)^{2} points of energy to travel by a distance of 1 when the robot is carrying k pieces of trash.
Find the minimum amount of energy required to put all the N pieces of trash in the trash bin.
Constraints
* 1 \leq N \leq 2 \times 10^{5}
* 0 < x_1 < ... < x_N \leq 10^9
* 1 \leq X \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N X
x_1 x_2 ... x_{N}
Output
Print the answer.
Examples
Input
2 100
1 10
Output
355
Input
5 1
1 999999997 999999998 999999999 1000000000
Output
19999999983
Input
10 8851025
38 87 668 3175 22601 65499 90236 790604 4290609 4894746
Output
150710136
Input
16 10
1 7 12 27 52 75 731 13856 395504 534840 1276551 2356789 9384806 19108104 82684732 535447408
Output
3256017715
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"2\\ntako 2\\nyaki 1\\n0\\ntako yaki\", \"2\\ntako 3\\nyaji 1\\n-1\\noakt yaki\", \"2\\ntako 1\\nyaij 1\\n-2\\noajt yaki\", \"2\\ntako 1\\njiay 0\\n-2\\nouja yakg\", \"2\\npaks 1\\naxii -1\\n-3\\nokua hx`j\", \"2\\npaks 0\\naxii -1\\n-1\\nnkua hx`j\", \"2\\ntako 4\\nyaji 1\\n0\\ntbko yaki\", \"2\\ntbko 6\\nyaji 1\\n-1\\noajs yaki\", \"2\\noakt 1\\njiax 5\\n-2\\noaju ikay\", \"2\\ntcko 6\\nijay 2\\n-1\\noais yaki\", \"2\\noakt 1\\njixa 8\\n-2\\noaju ikay\", \"2\\ntako -1\\njiay -1\\n0\\npuja yakh\", \"2\\npaks -2\\nayhi -1\\n0\\nmauk j`xh\", \"2\\ntako 2\\nyaji 1\\n0\\ntako yaki\", \"2\\ntako 2\\nyaji 1\\n0\\noakt yaki\", \"2\\ntako 2\\nyaji 1\\n-1\\noakt yaki\", \"2\\ntako 3\\nijay 1\\n-1\\noakt yaki\", \"2\\ntako 3\\nijay 1\\n-1\\noajt yaki\", \"2\\ntako 2\\nijay 1\\n-1\\noajt yaki\", \"2\\ntako 2\\nyaji 1\\n-1\\noajt yaki\", \"2\\ntako 2\\nyaji 1\\n-2\\noajt yaki\", \"2\\ntako 2\\nyaij 1\\n-2\\noajt yaki\", \"2\\ntako 3\\nyaij 1\\n-2\\noajt yaki\", \"2\\ntako 1\\nyaij 1\\n-2\\noaju yaki\", \"2\\ntako 1\\nyaij 1\\n-2\\nouja yaki\", \"2\\ntako 1\\njiay 1\\n-2\\nouja yaki\", \"2\\ntako 1\\njiay 1\\n-2\\nouja yakh\", \"2\\ntako 1\\njiay 1\\n-2\\nouja yakg\", \"2\\nsako 1\\njiay 0\\n-2\\nouja yakg\", \"2\\nsako 1\\njiay 0\\n-2\\nouka yakg\", \"2\\nsako 1\\njiay 0\\n-2\\nouka gkay\", \"2\\nsako 1\\njiay 0\\n-2\\nakuo gkay\", \"2\\nsako 1\\njiya 0\\n-2\\nakuo gkay\", \"2\\nsakp 1\\njiya 0\\n-2\\nakuo gkay\", \"2\\nsakp 1\\njiya 1\\n-2\\nakuo gkay\", \"2\\nsakp 1\\njixa 1\\n-2\\nakuo gkay\", \"2\\nsakp 1\\nijxa 1\\n-2\\nakuo gkay\", \"2\\nsakp 1\\nijxa 1\\n-2\\nokua gkay\", \"2\\nsakp 1\\nijxa 0\\n-2\\nokua gkay\", \"2\\nsakp 1\\naxji 0\\n-2\\nokua gkay\", \"2\\nsakp 1\\naxji 0\\n-2\\nokua gkax\", \"2\\nsakp 2\\naxji 0\\n-2\\nokua gkax\", \"2\\nsakp 2\\naxij 0\\n-2\\nokua gkax\", \"2\\nsakp 2\\naxij 0\\n-3\\nokua gkax\", \"2\\nsakp 2\\naxij 0\\n-3\\nokua gk`x\", \"2\\nsakp 2\\naxii 0\\n-3\\nokua gk`x\", \"2\\nsakp 1\\naxii 0\\n-3\\nokua gk`x\", \"2\\nsakp 1\\naxii 0\\n-3\\nokua hk`x\", \"2\\nsakp 1\\naxii 0\\n-3\\nokua hx`k\", \"2\\npaks 1\\naxii 0\\n-3\\nokua hx`k\", \"2\\npaks 1\\naxii 0\\n-3\\nokua k`xh\", \"2\\npaks 1\\naxii 0\\n-3\\nokua hx`j\", \"2\\npaks 1\\naxii -1\\n-1\\nokua hx`j\", \"2\\npaks 2\\naxii -1\\n-1\\nokua hx`j\", \"2\\npaks 2\\naxii -1\\n-1\\nnkua hx`j\", \"2\\npaks 2\\niixa -1\\n-1\\nnkua hx`j\", \"2\\npaks 2\\nayii -1\\n-1\\nnkua hx`j\", \"2\\npaks 2\\nayii 0\\n-1\\nnkua hx`j\", \"2\\npaks 2\\nayii 0\\n-1\\nnkua hxaj\", \"2\\npaks 2\\nayii 0\\n0\\nnkua hxaj\", \"2\\npaks 2\\nayii 0\\n0\\nokua hxaj\", \"2\\npaks 2\\nayii 0\\n0\\nauko hxaj\", \"2\\ntako 2\\nybki 1\\n0\\ntako yaki\", \"2\\ntako 2\\nyaji 1\\n0\\ntbko yaki\", \"2\\ntako 2\\nyaji 1\\n0\\ntkao yaki\", \"2\\ntoka 2\\nyaji 1\\n-1\\noakt yaki\", \"2\\ntako 3\\nyaji 1\\n-1\\ntako yaki\", \"2\\ntako 3\\nijay 1\\n-1\\ntkao yaki\", \"2\\ntako 3\\nyaji 1\\n-1\\noajt yaki\", \"2\\ntako 0\\nijay 1\\n-1\\noajt yaki\", \"2\\ntako 2\\nyaji 1\\n-1\\noajs yaki\", \"2\\ntako 2\\nyaji 1\\n-2\\ntjao yaki\", \"2\\ntako 2\\nyaij 1\\n-2\\nojat yaki\", \"2\\ntako 3\\nyaij 0\\n-2\\noajt yaki\", \"2\\ntako 1\\nyaij 1\\n-2\\noajt ykai\", \"2\\ntako 1\\nyaij 1\\n-2\\noaju ikay\", \"2\\ntako 1\\nyaij 1\\n-2\\najuo yaki\", \"2\\ntako 1\\njiay 2\\n-2\\nouja yaki\", \"2\\ntako 1\\njiay 1\\n-1\\nouja yakh\", \"2\\ntako 1\\njiay 1\\n0\\nouja yakg\", \"2\\ntako 1\\njiay 0\\n-2\\najuo yakg\", \"2\\nsako 1\\njiya 0\\n-2\\nouja yakg\", \"2\\nasko 1\\njiay 0\\n-2\\nouka yakg\", \"2\\nsako 1\\njiay 0\\n-2\\nakuo yakg\", \"2\\nsako 1\\njiay 0\\n-2\\najuo gkay\", \"2\\nsako 1\\njiya 0\\n-2\\naouk gkay\", \"2\\npkas 1\\njiya 0\\n-2\\nakuo gkay\", \"2\\nsakp 1\\njiya 1\\n-2\\nakuo gkby\", \"2\\nsakp 1\\njixa 1\\n-2\\nkauo gkay\", \"2\\nsakp 1\\nijxa 1\\n-4\\nakuo gkay\", \"2\\nsakp 0\\nijxa 1\\n-2\\nokua gkay\", \"2\\nsakp 1\\niixa 0\\n-2\\nokua gkay\", \"2\\nsakp 0\\naxji 0\\n-2\\nokua gkay\", \"2\\npaks 1\\naxji 0\\n-2\\nokua gkax\", \"2\\nsakp 2\\naxii 0\\n-2\\nokua gkax\", \"2\\nsakp 4\\naxij 0\\n-2\\nokua gkax\", \"2\\nsakp 3\\naxij 0\\n-3\\nokua gkax\", \"2\\nsakp 1\\naxij 0\\n-3\\nokua gk`x\", \"2\\ntakp 2\\naxii 0\\n-3\\nokua gk`x\", \"2\\nsakp 1\\naxii 0\\n-3\\nauko gk`x\", \"2\\ntako 2\\nyaki 1\\n1\\ntako yaki\"], \"outputs\": [\"3\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"-1\\n\", \"5\\n\", \"7\\n\", \"6\\n\", \"8\\n\", \"9\\n\", \"-2\\n\", \"-3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\"]}", "source": "primeintellect"} | Problem statement
2D, who is good at cooking, is trying to make lunch. Cooking requires all N ingredients a_ {0}, a_ {1},…, a_ {N−1}.
Now, 2D's refrigerator doesn't contain any ingredients, so I have to go to the supermarket to buy it. At the supermarket, you can buy the material a_ {i} for the price x_ {i} yen.
2D is also a wizard and can use M types of magic. The i-th magic can be changed to the material t_ {i} by applying it to the material s_ {i}, and conversely to s_ {i} by applying it to the material t_ {i}. In addition, you can repeatedly use multiple spells on a single material. For example, you can get r from p using the magic of changing from p to q and the magic of changing from q to r.
2D decided to use the power of magic to prepare the materials as cheaply as possible. Find the minimum sum of the prices of the ingredients that 2D needs to buy to complete the dish.
input
The input is given in the following format.
N
a_ {0} x_ {0}
...
a_ {N−1} x_ {N−1}
M
s_ {0} t_ {0}
...
s_ {M−1} t_ {M−1}
Constraint
* All numbers are integers
* All material names consist of at least 1 and no more than 10 lowercase letters.
* If i ≠ j, then a_ {i} ≠ a_ {j}
* 1 \ ≤ x_ {i} \ ≤ 1,000
* 1 \ ≤ N \ ≤ 5,000
* 0 \ ≤ M \ ≤ {\ rm min} (N (N−1) / 2, 1000)
* s_ {i} ≠ t_ {i}
* There is no duplication in the pair of s_ {i}, t_ {i}
* s_ {i}, t_ {i} are included in a_ {0},…, a_ {N−1}
output
Print the answer in one line.
sample
Sample input 1
2
tako 2
yaki 1
1
tako yaki
You can magically turn a cheap yaki into a tako, so buy two yaki.
Sample output 1
2
Sample input 2
Five
a 1
b 2
c 2
d 4
e 3
Five
b a
a c
c d
e b
c b
Sample output 2
Five
As shown below, all materials can be changed from a.
* a: a as it is
* b: a-> c-> b
* c: a-> c
* d: a-> c-> d
* e: a-> b-> e
<image>
Example
Input
2
tako 2
yaki 1
1
tako yaki
Output
2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.75 |
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5\\n0\\n1\\n0\\n0\\n2\\n0\\n0\\n1\\n1\\n2\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n1\\n0\\n2\\n-1\\n0\\n1\\n-6\", \"7 0\\n1\\n0\\n1\\n3\\n0\\n0\\n2\\n-1\\n0\\n1\\n-6\", \"7 5\\n1\\n1\\n0\\n0\\n2\\n0\\n1\\n1\\n1\\n2\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n0\\n0\\n2\\n-1\\n0\\n1\\n-7\", \"7 5\\n1\\n1\\n0\\n0\\n2\\n0\\n1\\n2\\n1\\n2\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n0\\n0\\n2\\n-2\\n0\\n1\\n-7\", \"7 5\\n1\\n1\\n0\\n0\\n2\\n-1\\n1\\n2\\n1\\n2\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n1\\n0\\n2\\n-2\\n0\\n1\\n-7\", \"7 5\\n1\\n1\\n0\\n0\\n2\\n-1\\n1\\n2\\n1\\n0\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n1\\n0\\n3\\n-2\\n0\\n1\\n-7\", \"7 2\\n1\\n1\\n0\\n0\\n2\\n-1\\n1\\n2\\n1\\n0\\n-3\", \"7 0\\n1\\n0\\n1\\n3\\n1\\n0\\n3\\n-2\\n0\\n1\\n0\", \"7 3\\n1\\n1\\n0\\n0\\n2\\n-1\\n1\\n2\\n1\\n0\\n-3\", \"7 0\\n1\\n-1\\n1\\n3\\n1\\n0\\n3\\n-2\\n0\\n1\\n0\", \"7 3\\n1\\n1\\n0\\n0\\n2\\n-1\\n2\\n2\\n1\\n0\\n-3\", \"7 0\\n1\\n-1\\n1\\n3\\n1\\n0\\n3\\n-2\\n-1\\n1\\n0\", \"7 3\\n1\\n1\\n0\\n0\\n2\\n-1\\n2\\n2\\n1\\n1\\n-3\", \"7 0\\n1\\n-1\\n1\\n3\\n1\\n-1\\n3\\n-2\\n-1\\n1\\n0\", \"7 0\\n1\\n-1\\n1\\n2\\n1\\n-1\\n3\\n-2\\n-1\\n1\\n0\", \"7 5\\n2\\n1\\n1\\n2\\n2\\n1\\n2\\n-1\\n3\\n2\\n-3\", \"7 0\\n2\\n1\\n2\\n3\\n2\\n1\\n2\\n-1\\n3\\n0\\n-3\", \"7 5\\n1\\n0\\n2\\n3\\n2\\n1\\n2\\n-1\\n3\\n2\\n-3\", \"7 5\\n3\\n1\\n1\\n3\\n2\\n1\\n2\\n-1\\n1\\n2\\n-3\", \"7 5\\n2\\n1\\n2\\n3\\n2\\n2\\n2\\n-1\\n3\\n2\\n-1\", \"7 5\\n2\\n0\\n1\\n3\\n2\\n1\\n2\\n-1\\n3\\n1\\n-3\", \"7 5\\n4\\n1\\n1\\n0\\n2\\n1\\n2\\n-1\\n1\\n2\\n-3\", \"7 5\\n2\\n1\\n2\\n5\\n0\\n1\\n2\\n-1\\n3\\n2\\n-1\", \"7 5\\n4\\n1\\n2\\n3\\n0\\n1\\n2\\n-1\\n0\\n1\\n0\", \"7 5\\n2\\n1\\n1\\n3\\n2\\n1\\n3\\n-1\\n1\\n1\\n-3\", \"7 5\\n2\\n0\\n2\\n3\\n3\\n1\\n2\\n0\\n3\\n1\\n-3\", \"7 5\\n1\\n1\\n1\\n0\\n2\\n1\\n2\\n-1\\n1\\n3\\n-3\", \"7 0\\n1\\n1\\n2\\n3\\n2\\n1\\n2\\n-1\\n3\\n1\\n-3\", \"7 5\\n2\\n0\\n1\\n0\\n2\\n0\\n2\\n0\\n1\\n2\\n-3\", \"7 5\\n0\\n1\\n2\\n1\\n2\\n1\\n2\\n-1\\n3\\n1\\n-3\", \"7 5\\n4\\n1\\n2\\n3\\n0\\n1\\n2\\n-1\\n-1\\n0\\n0\", \"7 5\\n2\\n1\\n3\\n3\\n2\\n0\\n2\\n-1\\n3\\n0\\n-3\", \"7 0\\n1\\n-1\\n2\\n3\\n2\\n0\\n2\\n-1\\n3\\n1\\n-3\", \"7 5\\n2\\n0\\n1\\n-1\\n2\\n-1\\n2\\n-1\\n1\\n2\\n-3\", \"7 5\\n0\\n0\\n2\\n1\\n2\\n2\\n2\\n-1\\n3\\n1\\n-4\", \"7 5\\n0\\n1\\n1\\n0\\n2\\n1\\n2\\n0\\n2\\n2\\n-3\", \"7 0\\n1\\n0\\n2\\n3\\n0\\n0\\n2\\n-1\\n3\\n1\\n-3\", \"7 5\\n2\\n0\\n1\\n0\\n2\\n-1\\n2\\n-1\\n2\\n2\\n-2\", \"7 5\\n3\\n1\\n2\\n3\\n-1\\n1\\n2\\n0\\n0\\n0\\n0\", \"7 5\\n0\\n1\\n1\\n0\\n2\\n2\\n0\\n0\\n1\\n2\\n-3\", \"7 0\\n1\\n0\\n2\\n3\\n1\\n0\\n0\\n-1\\n3\\n1\\n-5\", \"7 5\\n4\\n0\\n1\\n0\\n2\\n-1\\n2\\n-1\\n2\\n2\\n-3\", \"7 5\\n2\\n1\\n1\\n3\\n2\\n1\\n2\\n-1\\n3\\n2\\n-3\"], \"outputs\": [\"19\\n\", \"16\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"15\\n\", \"4\\n\", \"13\\n\", \"9\\n\", \"10\\n\", \"23\\n\", \"17\\n\", \"7\\n\", \"0\\n\", \"6\\n\", \"18\\n\", \"5\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"11\\n\", \"22\\n\", \"24\\n\", \"21\\n\", \"20\\n\", \"28\\n\", \"25\\n\", \"14\\n\", \"16\\n\", \"14\\n\", \"14\\n\", \"16\\n\", \"16\\n\", \"4\\n\", \"10\\n\", \"12\\n\", \"8\\n\", \"0\\n\", \"4\\n\", \"10\\n\", \"6\\n\", \"7\\n\", \"0\\n\", \"8\\n\", \"4\\n\", \"0\\n\", \"10\\n\", \"5\\n\", \"4\\n\", \"0\\n\", \"9\\n\", \"0\\n\", \"12\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"6\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"16\\n\", \"0\\n\", \"15\\n\", \"15\\n\", \"16\\n\", \"14\\n\", \"10\\n\", \"14\\n\", \"7\\n\", \"14\\n\", \"18\\n\", \"10\\n\", \"0\\n\", \"8\\n\", \"13\\n\", \"10\\n\", \"18\\n\", \"0\\n\", \"2\\n\", \"10\\n\", \"8\\n\", \"0\\n\", \"7\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"10\\n\", \"18\"]}", "source": "primeintellect"} | problem
You are a traveler traveling on the JOI Highway. The JOI Highway is a road that extends straight from east to west, and there are n post towns on the JOI Highway. Numbered. The westernmost post town on the JOI highway is post town 1, and the easternmost post town is post town n.
You have decided to depart from post town 1 and embark on an m-day journey. Your itinerary is determined according to the sequence a1, a2, ..., am as follows. It is a non-zero integer that represents how to move the eyes. If the post town you depart on day i is post town k, then on day i you move straight from post town k to post town k + ai. Means to do.
The number of post towns n, the number of days of travel m, the information on the distance between post towns, and the sequence a1, a2, ... Create a program that finds the remainder by dividing the sum by 100000 = 105.
Diagram corresponding to the input / output example
<image>
output
The output consists of one line containing the remainder of your total distance traveled in the m-day journey divided by 100000 = 105.
Input / output example
Input example 1
7 5
2
1
1
3
2
1
2
-1
3
2
-3
Output example 1
18
On the first day you move from post town 1 to post town 3. On the second day you move from post town 3 to post town 2. And on the third day you move from post town 2 to post town 5. Move, move from post town 5 to post town 7 on the 4th day, move from post town 7 to post town 4 on the 5th day. Your total travel distance in a 5-day trip is 18.
The above question sentences and the data used for the automatic referee are the question sentences created and published by the Japan Committee for Information Olympics and the test data for scoring.
input
The integers n and m are separated by blanks on the first line. N (2 ≤ n ≤ 100000 = 105) is the number of post towns on the JOI highway, and m (1 ≤ m ≤ 100000 = 105) is Represents the number of days of travel.
The following n − 1 line represents the distance between post towns on the JOI highway. I + 1st line (1 ≤ i ≤ n − 1) is a positive integer si that represents the distance between post town i and post town i + 1. (1 ≤ si ≤ 100) is written.
The following m line contains a sequence of movements for m days. Line i + n (1 ≤ i ≤ m) contains a non-zero integer ai that represents your movement method for day i. Has been.
In the scoring data, it does not move west of post town 1 or east of post town n.
Of the scoring data, 50% of the points are satisfied with n ≤ 100 and m ≤ 100.
Example
Input
7 5
2
1
1
3
2
1
2
-1
3
2
-3
Output
18
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.875 |
{"tests": "{\"inputs\": [[542, 5], [1750, 6], [14990, 7], [3456, 4], [30500, 3], [62550, 5], [568525, 7], [9567100, 8]], \"outputs\": [[547], [1799], [14996], [3462], [30501], [62557], [568531], [9567115]]}", "source": "primeintellect"} | We define the function `f1(n,k)`, as the least multiple of `n` that has all its digits less than `k`.
We define the function `f2(n,k)`, as the least multiple of `n` that has all the digits that are less than `k`.
Each digit may occur more than once in both values of `f1(n,k)` and `f2(n,k)`.
The possible values for `n` and `k` according to these ranges for both functions `f1` and `f2` in this kata:
```
1 <= n <= 1.000.000.000.000
3 <= k <= 9
```
For example, let's see the value of both functions for `n = 71` and `k = 4`:
```
f1(71,4) == 213 # all its digits less than 4
f2(71,4) == 2130 # 0,1,2,3 all of them present
```
The integer `76` is the first integer that has the same values of `f1` and `f2` for `k = 4`.
```
f1(76,4) = f2(76,4) = 10032
```
Let's call these kind of numbers, **forgiving numbers**. (Let's continue with the fashion of attributing personality traits to numbers and, of course, an unknown one)
So, `76` is the smallest forgiving number of order `4`.
In the same way, `485` is the smallest forgiving number of order `5`.
Create a function that given an integer `n` and the order `k`, will output the higher and closest forgiving number to `n` of order `k`.
Let's see some examples:
```
find_f1_eq_f2(500,5) == 547
find_f1_eq_f2(1600,6) == 1799
find_f1_eq_f2(14900,7) == 14996
```
If the number `n` is a forgiving itself for a certain order `k`, the function will never output the same value, remember, closest and **higher** than `n`.
For example, `3456`, is a forgiving one of order `4`,
```
find_f1_eq_f2(3456,4) == 3462
```
**Features of the tests:**
* `n` and `k` will be always valid and positive integers.
* A total of 8 fixed tests.
* A total of 150 random tests in the ranges for `n` and `k` given above.
I'll be waiting your awesome solution. :)
Write your solution by modifying this code:
```python
def find_f1_eq_f2(n,k):
```
Your solution should implemented in the function "find_f1_eq_f2". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n111 SET c 1\\n12 SUB c c 4\\n777 SET a 4\", \"3\\n10 SET c 1\\n193 IF c 10\\n20 HALT\", \"6\\n10 SET c 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n200 HALT\", \"3\\n10 SET c 1\\n193 IF c 11\\n20 HALT\", \"3\\n10 SET c 0\\n193 IF c 11\\n20 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 2\\n777 SET b 4\", \"6\\n10 SET b 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n200 HALT\", \"3\\n111 SET c 0\\n12 SUB c c 5\\n777 SET a 4\", \"3\\n17 SET c 3\\n120 IF c 10\\n34 HALT\", \"3\\n17 SET b 3\\n120 IF c 10\\n34 HALT\", \"3\\n111 SET c 1\\n12 SUB c d 2\\n777 SET a 4\", \"6\\n10 SET c 1\\n20 SET h 7\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 101\\n200 HALT\", \"6\\n10 SET d 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n124 HALT\", \"3\\n10 SET c 2\\n120 IF d 10\\n34 HALT\", \"3\\n17 SET c 2\\n120 IF c 10\\n34 HALT\", \"6\\n10 SET c 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n209 IF j 100\\n200 HALT\", \"6\\n10 SET c 1\\n20 SET h 7\\n100 ADD s s j\\n110 SUB i i c\\n120 IF i 101\\n200 HALT\", \"3\\n111 SET c 0\\n12 SUB c d 3\\n777 SET a 4\", \"3\\n2 SET b 0\\n6 IF c 12\\n28 HALT\", \"3\\n10 SET c 1\\n120 IF d 10\\n20 HALT\", \"6\\n10 SET c 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n76 HALT\", \"3\\n16 SET d 1\\n120 IF c 10\\n34 HALT\", \"3\\n10 SET c 0\\n120 IF d 10\\n34 HALT\", \"3\\n17 SET c 4\\n120 IF c 10\\n34 HALT\", \"6\\n10 SET c 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n209 IF j 100\\n200 HALT\", \"3\\n11 SET c 3\\n120 IF d 7\\n34 HALT\", \"3\\n17 SET b 2\\n120 IF c 10\\n42 HALT\", \"3\\n110 SET c 1\\n12 SUB c c 1\\n777 SET b 4\", \"6\\n7 SET b 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i j c\\n120 IF i 100\\n200 HALT\", \"3\\n111 SET b 0\\n22 SUB c c 5\\n777 SET a 4\", \"3\\n6 SET b 1\\n120 IF c 9\\n20 HALT\", \"3\\n11 SET c 3\\n120 IF e 7\\n34 HALT\", \"3\\n2 SET b 0\\n6 IF d 12\\n23 HALT\", \"3\\n110 SET d 1\\n12 SUB c c 1\\n777 SET b 4\", \"6\\n10 SET c 0\\n20 SET i 5\\n100 ADD s s i\\n111 SUB i i c\\n209 IF j 100\\n200 HALT\", \"3\\n2 SET c 0\\n120 IF e 7\\n34 HALT\", \"3\\n16 SET c 2\\n188 IF b 14\\n34 HALT\", \"6\\n10 SET c 0\\n20 SET i 5\\n100 ADD s s j\\n111 SUB i i c\\n209 IF j 100\\n200 HALT\", \"3\\n9 SET d 2\\n4 IF d 13\\n34 HALT\", \"3\\n9 SET c 2\\n95 IF e 30\\n17 HALT\", \"6\\n10 SET c 1\\n20 SET h 8\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n124 HALT\", \"6\\n10 SET c 1\\n20 SET h 5\\n000 ADD s s i\\n110 SUB i i d\\n120 IF i 100\\n124 HALT\", \"6\\n10 SET a 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n320 HALT\", \"3\\n111 SET c 2\\n16 SUB c c 4\\n1275 SET a 4\", \"3\\n111 SET b 1\\n12 SUB c c 2\\n127 SET a 4\", \"6\\n10 SET c 1\\n20 SET j 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n76 HALT\", \"6\\n7 SET b 2\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n200 HALT\", \"3\\n111 SET c 1\\n3 SUB c c 0\\n777 SET b 4\", \"6\\n10 SET c 0\\n20 SET h 7\\n100 ADD s s i\\n110 SUB h i c\\n120 IF i 101\\n200 HALT\", \"3\\n16 SET d 2\\n120 IF c 10\\n34 HALT\", \"6\\n10 SET c 1\\n31 SET h 5\\n100 ADD s s h\\n110 SUB i j c\\n120 IF i 100\\n124 HALT\", \"3\\n6 SET b 1\\n120 IF b 9\\n20 HALT\", \"3\\n2 SET b 1\\n6 IF d 12\\n23 HALT\", \"3\\n11 SET b 3\\n120 IF e 7\\n6 HALT\", \"3\\n9 SET e 2\\n4 IF d 13\\n34 HALT\", \"3\\n9 SET c 4\\n95 IF d 30\\n32 HALT\", \"3\\n9 SET b 2\\n95 IF d 30\\n17 HALT\", \"3\\n111 SET c 1\\n12 SUB c a 4\\n777 SET b 4\", \"6\\n10 SET d 0\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n184 IF i 100\\n124 HALT\", \"6\\n10 SET c 1\\n20 SET j 5\\n100 ADD r s i\\n110 SUB i i c\\n120 IF i 100\\n76 HALT\", \"6\\n10 SET c 1\\n20 SET h 6\\n000 ADD s s i\\n110 SUB i i c\\n150 IF i 110\\n124 HALT\", \"3\\n110 SET d 2\\n12 SUB c c 1\\n777 SET b 6\", \"6\\n10 SET c 2\\n31 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n172 HALT\", \"3\\n011 SET d 1\\n12 SUB c c 0\\n777 SET b 4\", \"3\\n011 SET c 1\\n12 SUB d c 1\\n1496 SET b 4\", \"3\\n110 SET c 0\\n12 SUB c d 0\\n116 SET a 2\", \"3\\n111 SET b 1\\n3 SUB c c 0\\n777 SET c 4\", \"3\\n111 SET c 1\\n6 SUB c c 1\\n46 SET a 4\", \"6\\n10 SET c 1\\n20 SET h 8\\n100 ADD s s i\\n110 SUB i h c\\n120 IF i 111\\n124 HALT\", \"3\\n6 SET c 5\\n100 IF c 10\\n34 HALT\", \"3\\n111 SET b 2\\n23 SUB c c 3\\n777 SET a 6\", \"6\\n10 SET c 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 101\\n200 HALT\", \"3\\n10 SET c 1\\n120 IF c 10\\n34 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 5\\n777 SET a 4\", \"6\\n10 SET c 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n124 HALT\", \"3\\n10 SET c 0\\n64 IF c 11\\n20 HALT\", \"3\\n011 SET c 1\\n12 SUB c c 2\\n777 SET b 4\", \"3\\n10 SET c 2\\n120 IF c 10\\n34 HALT\", \"6\\n10 SET c 1\\n20 SET h 5\\n000 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n124 HALT\", \"3\\n10 SET c 0\\n64 IF c 5\\n20 HALT\", \"3\\n10 SET c 3\\n120 IF c 10\\n34 HALT\", \"3\\n10 SET c 1\\n120 IF c 9\\n20 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 4\\n777 SET b 4\", \"3\\n10 SET c 1\\n193 IF c 2\\n20 HALT\", \"6\\n10 SET c 1\\n20 SET h 5\\n100 ADD s s i\\n110 SUB i i c\\n209 IF i 100\\n200 HALT\", \"3\\n10 SET c 0\\n193 IF c 6\\n20 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 2\\n830 SET b 4\", \"3\\n16 SET c 1\\n120 IF c 10\\n34 HALT\", \"6\\n10 SET b 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n320 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 3\\n777 SET a 4\", \"3\\n10 SET c 0\\n73 IF c 11\\n20 HALT\", \"3\\n110 SET c 0\\n12 SUB c c 5\\n777 SET a 4\", \"3\\n10 SET c 0\\n64 IF c 2\\n20 HALT\", \"3\\n13 SET c 1\\n120 IF c 9\\n20 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 4\\n1275 SET a 4\", \"3\\n10 SET c 1\\n193 IF c 1\\n20 HALT\", \"3\\n16 SET c 1\\n33 IF c 10\\n34 HALT\", \"3\\n111 SET c 0\\n12 SUB c c 3\\n777 SET a 4\", \"3\\n10 SET c 0\\n73 IF c 12\\n20 HALT\", \"3\\n10 SET c 2\\n120 IF d 7\\n34 HALT\", \"3\\n111 SET c 1\\n12 SUB c c 2\\n777 SET a 4\", \"3\\n10 SET c 1\\n120 IF c 10\\n20 HALT\", \"6\\n10 SET c 1\\n20 SET i 5\\n100 ADD s s i\\n110 SUB i i c\\n120 IF i 100\\n200 HALT\"], \"outputs\": [\"a=0\\nc=1\\n\", \"inf\\n\", \"c=1\\nh=5\\ni=0\\ns=0\\n\", \"c=1\\n\", \"c=0\\n\", \"b=0\\nc=1\\n\", \"b=1\\nc=0\\ni=5\\ns=15\\n\", \"a=0\\nc=0\\n\", \"c=3\\n\", \"b=3\\nc=0\\n\", \"a=0\\nc=1\\nd=0\\n\", \"c=1\\nh=7\\ni=0\\ns=0\\n\", \"c=0\\nd=1\\nh=5\\ni=0\\ns=0\\n\", \"c=2\\nd=0\\n\", \"c=2\\n\", \"c=1\\nh=5\\ni=0\\nj=0\\ns=0\\n\", \"c=1\\nh=7\\ni=0\\nj=0\\ns=0\\n\", \"a=0\\nc=0\\nd=0\\n\", \"b=0\\nc=0\\n\", \"c=1\\nd=0\\n\", \"c=1\\ni=0\\ns=15\\n\", \"c=0\\nd=1\\n\", \"c=0\\nd=0\\n\", \"c=4\\n\", \"c=1\\ni=4\\nj=0\\ns=5\\n\", \"c=3\\nd=0\\n\", \"b=2\\nc=0\\n\", \"b=4\\nc=0\\n\", \"b=1\\nc=0\\ni=0\\nj=0\\ns=5\\n\", \"a=0\\nb=0\\nc=0\\n\", \"b=1\\nc=0\\n\", \"c=3\\ne=0\\n\", \"b=0\\nd=0\\n\", \"b=0\\nc=0\\nd=1\\n\", \"c=0\\ni=5\\nj=0\\ns=5\\n\", \"c=0\\ne=0\\n\", \"b=0\\nc=2\\n\", \"c=0\\ni=5\\nj=0\\ns=0\\n\", \"d=2\\n\", \"c=2\\ne=0\\n\", \"c=1\\nh=8\\ni=0\\ns=0\\n\", \"c=1\\nd=0\\nh=5\\ni=0\\ns=0\\n\", \"a=1\\nc=0\\ni=5\\ns=15\\n\", \"a=0\\nc=2\\n\", \"a=0\\nb=1\\nc=0\\n\", \"c=1\\ni=0\\nj=5\\ns=0\\n\", \"b=2\\nc=0\\ni=5\\ns=15\\n\", \"b=4\\nc=1\\n\", \"c=0\\nh=0\\ni=0\\ns=0\\n\", \"c=0\\nd=2\\n\", \"c=1\\nh=5\\ni=0\\nj=0\\ns=5\\n\", \"b=1\\n\", \"b=1\\nd=0\\n\", \"b=3\\ne=0\\n\", \"d=0\\ne=2\\n\", \"c=4\\nd=0\\n\", \"b=2\\nd=0\\n\", \"a=0\\nb=0\\nc=1\\n\", \"c=0\\nd=0\\nh=5\\ni=0\\ns=0\\n\", \"c=1\\ni=0\\nj=5\\nr=0\\ns=0\\n\", \"c=1\\nh=6\\ni=0\\ns=0\\n\", \"b=0\\nc=0\\nd=2\\n\", \"c=2\\nh=5\\ni=0\\ns=0\\n\", \"b=4\\nc=0\\nd=1\\n\", \"b=4\\nc=1\\nd=0\\n\", \"a=2\\nc=0\\nd=0\\n\", \"b=1\\nc=4\\n\", \"a=4\\nc=0\\n\", \"c=1\\nh=8\\ni=7\\ns=0\\n\", \"c=5\\n\", \"a=0\\nb=2\\nc=0\\n\", \"c=1\\nh=5\\ni=0\\ns=0\\n\", \"inf\\n\", \"a=0\\nc=1\\n\", \"c=1\\nh=5\\ni=0\\ns=0\\n\", \"c=0\\n\", \"b=0\\nc=1\\n\", \"inf\\n\", \"c=1\\nh=5\\ni=0\\ns=0\\n\", \"c=0\\n\", \"inf\\n\", \"c=1\\n\", \"b=0\\nc=1\\n\", \"c=1\\n\", \"c=1\\nh=5\\ni=0\\ns=0\\n\", \"c=0\\n\", \"b=0\\nc=1\\n\", \"c=1\\n\", \"b=1\\nc=0\\ni=5\\ns=15\\n\", \"a=0\\nc=1\\n\", \"c=0\\n\", \"a=0\\nc=0\\n\", \"c=0\\n\", \"c=1\\n\", \"a=0\\nc=1\\n\", \"c=1\\n\", \"c=1\\n\", \"a=0\\nc=0\\n\", \"c=0\\n\", \"c=2\\nd=0\\n\", \"a=0\\nc=1\", \"inf\", \"c=1\\ni=0\\ns=15\"]}", "source": "primeintellect"} | Have you ever had an infinite loop when you ran a hard-working program? It would be convenient to be able to determine in advance whether a program will stop executing without having to execute it.
Unfortunately, it is not possible to make such a decision for any program in the programming language you normally use. However, if you have a programming language that is much less computationally powerful, you may be able to write a program that determines if a program written in that language will stop.
Consider a programming language called TinyPower. Programs in this language are line sequences. On each line of the program, write the line number at the beginning and one sentence after it. The types of sentences that can be written in this language are as follows.
Sentence type | Behavior
--- | ---
ADD var1 var2 var3 | Assign the result of adding the value of variable var2 and the value of var3 to variable var1
ADD var1 var2 con | Assign the result of adding the value of the variable var2 and the constant con to the variable var1
SUB var1 var2 var3 | Assign the result of subtracting the value of var3 from the value of variable var2 to variable var1
SUB var1 var2 con | Substitute the result of subtracting the constant con from the value of the variable var2 into the variable var1
SET var1 var2 | Assign the value of variable var2 to variable var1
SET var1 con | Assign the constant con to the variable var1
IF var1 dest | Jump to line number dest only if the value of variable var1 is non-zero
HALT | Stop the program
Line numbers are positive integers, and the same line number will never appear more than once in the program. Variables are represented by a single lowercase letter, and constants and variable values are integers. No variable declaration is required, the initial value of the variable is 0.
Program execution starts with the first statement, and the statements are executed in the order in which they are lined up. However, as written in the table above, if the value of the variable in the IF statement is not 0, jump to the line specified by the line number written after the variable and start from the statement written in that line. Continue running. The program will stop when:
* When the HALT statement is executed.
* When trying to assign a negative integer or an integer greater than or equal to 16 to a variable (the value of the variable is not updated).
* When trying to jump to a line number that does not appear in the program.
* When you do not jump to any line from the last statement of the program.
Create a program that determines if a TinyPower program, given it, will stop.
Input
The input is given in the following format.
N
stmt1
stmt2
::
stmtN
The number of lines N (1 ≤ N ≤ 50) of the program is given on the first line. The following N lines are given the statement stmti of the TinyPower program. stmti is given in one of the following formats:
line ADD var1 var2 var3
Or
line ADD var1 var2 con
Or
line SUB var1 var2 var3
Or
line SUB var1 var2 con
Or
line SET var1 var2
Or
line SET var1 con
Or
line IF var1 dest
Or
line HALT
line, dest (1 ≤ line, dest ≤ 1000) is the line number, varj (one lowercase letter) is the variable, and con (0 ≤ con ≤ 15) is the constant. The delimiter in stmti is one blank character. It is assumed that one or more variables always appear in the program, and only five different variable names appear.
Output
When the program stops, the results of the variables appearing in the program are output in the lexicographic order of the variable names, separated by line breaks, and when it does not stop, "inf" is output. The result of the variable is output by separating the variable name and the value of the variable with "=".
Examples
Input
6
10 SET c 1
20 SET i 5
100 ADD s s i
110 SUB i i c
120 IF i 100
200 HALT
Output
c=1
i=0
s=15
Input
3
10 SET c 1
120 IF c 10
20 HALT
Output
inf
Input
3
111 SET c 1
12 SUB c c 2
777 SET a 4
Output
a=0
c=1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"outputs\": [\"10\\n12\\n13\\n2020\\n599\\n57577\\n7744444777744474777777774774744777747477444774744744\\n\", \"10\\n12\\n12\\n2020\\n25252\\n57577\\n7744444777744474777777774774744777747477444774744744\\n\", \"10\\n12\\n13\\n2020\\n599\\n57577\\n4422424222424224224222242422242224222444442422222\\n\", \"10\\n12\\n12\\n2020\\n25252\\n57577\\n2242242422424422422242444244422444244422422444244222\\n\", \"10\\n12\\n13\\n177\\n599\\n57577\\n4422424222424224224222242422242224222444442422222\\n\", \"10\\n\", \"10\\n13\\n13\\n177\\n599\\n57577\\n4422424222424224224222242422242224222444442422222\\n\", \"10\\n13\\n15\\n177\\n599\\n57577\\n4422424222424224224222242422242224222444442422222\\n\", \"10\\n13\\n15\\n177\\n599\\n57577\\n5855885585555888855555885855585885858585555585885\\n\", \"10\\n14\\n15\\n177\\n599\\n57577\\n5855885585555888855555885855585885858585555585885\\n\", \"10\\n14\\n15\\n177\\n599\\n57577\\n333133133131111131331113311113133133311313331331\\n\", 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\"10\\n12\\n13\\n2020\\n25252\\n57577\\n7744444777744474777777774774744777747477444774744744\"]}", "source": "primeintellect"} | Number of tanka
Wishing to die in the spring under the flowers
This is one of the famous tanka poems that Saigyo Hoshi wrote. Tanka is a type of waka poem that has been popular in Japan for a long time, and most of it consists of five phrases and thirty-one sounds of 5, 7, 5, 7, and 7.
By the way, the number 57577 consists of two types, 5 and 7. Such a positive integer whose decimal notation consists of exactly two types of numbers is called a tanka number. For example, 10, 12, 57577, 25252 are tanka numbers, but 5, 11, 123, 20180701 are not tanka songs.
A positive integer N is given. Find the Nth smallest tanka number.
Input
The input consists of up to 100 datasets. Each dataset is represented in the following format.
> N
The integer N satisfies 1 ≤ N ≤ 1018.
The end of the input is represented by a single zero line.
Output
For each dataset, output the Nth smallest tanka number on one line.
Sample Input
1
2
3
390
1124
1546
314159265358979323
0
Output for the Sample Input
Ten
12
13
2020
25252
57577
7744444777744474777777774774744777747477444774744744
Example
Input
1
2
3
390
1124
1546
314159265358979323
0
Output
10
12
13
2020
25252
57577
7744444777744474777777774774744777747477444774744744
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[\"wHjMudLwtoPGocnJ\"], [\"eCEHWEPwwnvzMicyaRjk\"], [\"JKniLfLW\"], [\"EWlZlDFsEIBufsalqof\"], [\"IMBAWejlGRTDWetPS\"]], \"outputs\": [[\"Bronze!\"], [\"Bronze!\"], [\"Not even a medal!\"], [\"Silver!\"], [\"Gold!\"]]}", "source": "primeintellect"} | To celebrate the start of the Rio Olympics (and the return of 'the Last Leg' on C4 tonight) this is an Olympic inspired kata.
Given a string of random letters, you need to examine each. Some letters naturally have 'rings' in them. 'O' is an obvious example, but 'b', 'p', 'e', 'A', etc are all just as applicable. 'B' even has two!! Please note for this kata you can count lower case 'g' as only one ring.
Your job is to count the 'rings' in each letter and divide the total number by 2. Round the answer down. Once you have your final score:
if score is 1 or less, return 'Not even a medal!';
if score is 2, return 'Bronze!';
if score is 3, return 'Silver!';
if score is more than 3, return 'Gold!';
Dots over i's and any other letters don't count as rings.
Write your solution by modifying this code:
```python
def olympic_ring(string):
```
Your solution should implemented in the function "olympic_ring". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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After the fighting stopped, Heidi gave them another task to waste their time on.
There are $n$ points on a plane. Given a radius $r$, find the maximum number of points that can be covered by an $L^1$-ball with radius $r$.
An $L^1$-ball with radius $r$ and center $(x_0, y_0)$ in a 2D-plane is defined as the set of points $(x, y)$ such that the Manhattan distance between $(x_0, y_0)$ and $(x, y)$ is at most $r$.
Manhattan distance between $(x_0, y_0)$ and $(x, y)$ is defined as $|x - x_0| + |y - y_0|$.
-----Input-----
The first line contains two integers $n, r$ ($1 \le n \le 300\,000, 1 \le r \le 10^6$), the number of points and the radius of the ball, respectively.
Each of the next $n$ lines contains integers $x_i, y_i$ ($-10^6 \leq x_i, y_i \leq 10^6$), describing the coordinates of the $i$-th point.
It is guaranteed, that all points are distinct.
-----Output-----
Print one integer — the maximum number points that an $L^1$-ball with radius $r$ can cover.
-----Examples-----
Input
5 1
1 1
1 -1
-1 1
-1 -1
2 0
Output
3
Input
5 2
1 1
1 -1
-1 1
-1 -1
2 0
Output
5
-----Note-----
In the first example, a ball centered at $(1, 0)$ covers the points $(1, 1)$, $(1, -1)$, $(2, 0)$.
In the second example, a ball centered at $(0, 0)$ covers all the points.
Note that $x_0$ and $y_0$ need not be integer.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.125 |
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4\\n-234\\n25\\n-55\\n8\\n60\\n-91\\n-127\\n48\\n-61\\n9\\n\", \"10 3\\n-20\\n-35\\n-25\\n45\\n-139\\n-20\\n69\\n-7\\n89\\n-11\\n\", \"5 3\\n1\\n2\\n2\\n3\\n3\\n\", \"6 4\\n3\\n3\\n3\\n4\\n4\\n2\\n\"], \"outputs\": [\"-35\\n91\\n91\\n91\\n-39\\n-39\\n4\\n29\\n\", \"79\\n79\\n86\\n86\\n86\\n13\\n57\\n93\\n\", \"68\\n68\\n57\\n57\\n28\\n28\\n3\\n60\\n\", \"-20\\n45\\n45\\n45\\n79\\n79\\n79\\n70\\n\", \"50\\n50\\n50\\n68\\n68\\n68\\n85\\n85\\n\", \"26\\n26\\n43\\n43\\n80\\n80\\n80\\n45\\n\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\\n\", \"46\\n46\\n46\\n22\\n19\\n44\\n44\\n44\\n\", \"-35\\n91\\n91\\n91\\n-39\\n-39\\n4\\n29\", \"79\\n79\\n86\\n86\\n86\\n13\\n57\\n93\", \"68\\n68\\n57\\n57\\n28\\n28\\n3\\n60\", \"-20\\n45\\n45\\n45\\n79\\n79\\n79\\n70\", \"68\\n68\\n68\\n85\\n85\", \"26\\n26\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"46\\n46\\n46\\n22\\n19\\n44\\n44\\n44\", \"3\\nNothing\", \"4\\nNothing\\n3\", \"68\\n68\\n68\\n68\\n68\", \"1\", \"-35\\n91\\n91\\n91\\n-39\\n-39\\n8\\n29\", \"79\\n79\\n86\\n86\\n86\\n23\\n57\\n93\", \"-20\\n45\\n45\\n45\\n79\\n79\\n89\\n89\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"-35\\n91\\n91\\n91\\n-39\\n-39\\n8\\n26\", \"79\\n79\\n86\\n86\\n86\\n23\\n34\\n93\", \"-35\\n91\\n91\\n91\\n-39\\n-39\\n4\\n26\", \"-6\\n91\\n91\\n91\\n-39\\n-39\\n4\\n26\", \"-20\\n45\\n45\\n45\\n24\\n24\\n89\\n89\", \"25\\n60\\n60\\n60\\n60\\n48\\n48\", \"91\\n91\\n91\\n91\\n-39\\n4\\n26\", \"-20\\n45\\n45\\n45\\n47\\n47\\n89\\n89\", \"-20\\n45\\n45\\n45\\n69\\n69\\n89\\n89\", \"60\\n60\\n60\\n60\\n60\\n48\", \"-35\\n91\\n91\\n91\\n-39\\n-39\\n4\\n29\", \"79\\n79\\n86\\n86\\n86\\n13\\n57\\n93\", \"-20\\n45\\n45\\n45\\n79\\n79\\n79\\n70\", \"26\\n26\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"4\\nNothing\\n3\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"-20\\n45\\n45\\n45\\n79\\n79\\n89\\n89\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"-20\\n45\\n45\\n45\\n79\\n79\\n89\\n89\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"-6\\n91\\n91\\n91\\n-39\\n-39\\n4\\n26\", \"-20\\n45\\n45\\n45\\n24\\n24\\n89\\n89\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"25\\n25\\n60\\n60\\n60\\n48\\n48\\n48\", \"-6\\n91\\n91\\n91\\n-39\\n-39\\n4\\n26\", \"-20\\n45\\n45\\n45\\n24\\n24\\n89\\n89\", \"15\\n15\\n43\\n43\\n80\\n80\\n80\\n45\", \"-6\\n91\\n91\\n91\\n-39\\n-39\\n4\\n26\", \"-20\\n45\\n45\\n45\\n24\\n24\\n89\\n89\", \"25\\n60\\n60\\n60\\n60\\n48\\n48\", \"25\\n60\\n60\\n60\\n60\\n48\\n48\", \"-20\\n45\\n45\\n45\\n69\\n69\\n89\\n89\", \"1\\n3\\n2\\n\", \"4\\nNothing\\n3\\n\"]}", "source": "primeintellect"} | Programmer Sasha has recently begun to study data structures. His coach Stas told him to solve the problem of finding a minimum on the segment of the array in <image>, which Sasha coped with. For Sasha not to think that he had learned all, Stas gave him a new task. For each segment of the fixed length Sasha must find the maximum element of those that occur on the given segment exactly once. Help Sasha solve this problem.
Input
The first line contains two positive integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ n) — the number of array elements and the length of the segment.
Then follow n lines: the i-th one contains a single number ai ( - 109 ≤ ai ≤ 109).
Output
Print n–k + 1 numbers, one per line: on the i-th line print of the maximum number of those numbers from the subarray ai ai + 1 … ai + k - 1 that occur in this subarray exactly 1 time. If there are no such numbers in this subarray, print "Nothing".
Examples
Input
5 3
1
2
2
3
3
Output
1
3
2
Input
6 4
3
3
3
4
4
2
Output
4
Nothing
3
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.5 |
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Elections are coming. You know the number of voters and the number of parties — n and m respectively. For each voter you know the party he is going to vote for. However, he can easily change his vote given a certain amount of money. In particular, if you give i-th voter c_i bytecoins you can ask him to vote for any other party you choose.
The United Party of Berland has decided to perform a statistical study — you need to calculate the minimum number of bytecoins the Party needs to spend to ensure its victory. In order for a party to win the elections, it needs to receive strictly more votes than any other party.
Input
The first line of input contains two integers n and m (1 ≤ n, m ≤ 3000) — the number of voters and the number of parties respectively.
Each of the following n lines contains two integers p_i and c_i (1 ≤ p_i ≤ m, 1 ≤ c_i ≤ 10^9) — the index of this voter's preferred party and the number of bytecoins needed for him to reconsider his decision.
The United Party of Berland has the index 1.
Output
Print a single number — the minimum number of bytecoins needed for The United Party of Berland to win the elections.
Examples
Input
1 2
1 100
Output
0
Input
5 5
2 100
3 200
4 300
5 400
5 900
Output
500
Input
5 5
2 100
3 200
4 300
5 800
5 900
Output
600
Note
In the first sample, The United Party wins the elections even without buying extra votes.
In the second sample, The United Party can buy the votes of the first and the fourth voter. This way The Party gets two votes, while parties 3, 4 and 5 get one vote and party number 2 gets no votes.
In the third sample, The United Party can buy the votes of the first three voters and win, getting three votes against two votes of the fifth party.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"20\\n178461\\n767271\\n143872\\n917783\\n642681\\n496408\\n735441\\n899441\\n265715\\n772194\\n797342\\n833227\\n479407\\n800158\\n613225\\n498438\\n818615\\n750993\\n597881\\n142739\\n\", \"20\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n\", \"20\\n61\\n62\\n63\\n64\\n65\\n66\\n67\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n\", \"20\\n9783\\n879497\\n203664\\n981484\\n588099\\n299151\\n782262\\n108971\\n368524\\n643461\\n815444\\n33663\\n479878\\n908619\\n879890\\n768921\\n703812\\n628957\\n849817\\n569957\\n\", \"20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n\", \"20\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n90\\n91\\n92\\n93\\n94\\n95\\n96\\n97\\n98\\n99\\n100\\n\", \"20\\n27955\\n637815\\n90575\\n561777\\n622205\\n466162\\n379336\\n195938\\n91560\\n894581\\n799253\\n948756\\n448870\\n26762\\n507653\\n176200\\n175215\\n499651\\n82441\\n354697\\n\", \"20\\n89532\\n52860\\n154942\\n702927\\n555262\\n45319\\n154538\\n378417\\n514950\\n823559\\n293517\\n42254\\n465184\\n818182\\n517039\\n54600\\n844697\\n367974\\n240024\\n775492\\n\", \"20\\n264222\\n464589\\n278778\\n512505\\n720206\\n948799\\n760706\\n765895\\n179271\\n919305\\n920275\\n327537\\n100541\\n533079\\n570278\\n502602\\n599706\\n473784\\n928170\\n422924\\n\", \"20\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n\"], \"outputs\": [\"No\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\n\", \"No\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\n\", \"No\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\n\", \"No\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\n\", \"No\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nYes\\nNo\\n\", \"Yes\\nYes\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nYes\\n\", \"Yes\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\", \"No\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nYes\\n\"]}", "source": "primeintellect"} | You need to find if a number can be expressed as sum of two perfect powers. That is, given x find if there exists non negative integers a, b, m, n such that a^m + b^n = x.
Input
First line of the input contains number of test cases T. It is followed by T lines, each line contains a sinle number x.
Output
For each test case, print "Yes" (without quotes) if the number can be expressed as sum of two perfect powers. Otherwise print "No" (without quotes).
Constraints
1 ≤ T ≤ 1000
1 ≤ x ≤ 1000000
m > 1, n > 1
SAMPLE INPUT
5
5
15
9
77
100
SAMPLE OUTPUT
Yes
No
Yes
No
Yes
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[\"i am a frog.\"], [\"can you do it?\"], [\"seems like you understand!\"], [\"multisentence is good. is not it?\"], [\"green, red or orange - we all just frogs, do not you think so?\"]], \"outputs\": [[\"frog a am i.\"], [\"it do you can?\"], [\"understand you like seems!\"], [\"good is multisentence. it not is?\"], [\"so think you not do frogs just all we orange or red green?\"]]}", "source": "primeintellect"} | A little weird green frog speaks in a very strange variation of English: it reverses sentence, omitting all puntuation marks `, ; ( ) - ` except the final exclamation, question or period. We urgently need help with building a proper translator.
To simplify the task, we always use lower-case letters. Apostrophes are forbidden as well.
Translator should be able to process multiple sentences in one go. Sentences are separated by arbitrary amount of spaces.
**Examples**
`you should use python.` -> `python use should you.`
`look, a fly!` -> `fly a look!`
`multisentence is good. is not it?` -> `good is multisentence. it not is?`
Write your solution by modifying this code:
```python
def frogify(s):
```
Your solution should implemented in the function "frogify". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"\\n3\\n0\\n0\\n-1\\n1\\n3\\n\"]}", "source": "primeintellect"} | You are given a sequence $a$ consisting of $n$ integers $a_1, a_2, \dots, a_n$, and an integer $x$. Your task is to make the sequence $a$ sorted (it is considered sorted if the condition $a_1 \le a_2 \le a_3 \le \dots \le a_n$ holds).
To make the sequence sorted, you may perform the following operation any number of times you want (possibly zero): choose an integer $i$ such that $1 \le i \le n$ and $a_i > x$, and swap the values of $a_i$ and $x$.
For example, if $a = [0, 2, 3, 5, 4]$, $x = 1$, the following sequence of operations is possible:
choose $i = 2$ (it is possible since $a_2 > x$), then $a = [0, 1, 3, 5, 4]$, $x = 2$;
choose $i = 3$ (it is possible since $a_3 > x$), then $a = [0, 1, 2, 5, 4]$, $x = 3$;
choose $i = 4$ (it is possible since $a_4 > x$), then $a = [0, 1, 2, 3, 4]$, $x = 5$.
Calculate the minimum number of operations you have to perform so that $a$ becomes sorted, or report that it is impossible.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 500$) — the number of test cases.
Each test case consists of two lines. The first line contains two integers $n$ and $x$ ($1 \le n \le 500$, $0 \le x \le 500$) — the number of elements in the sequence and the initial value of $x$.
The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($0 \le a_i \le 500$).
The sum of values of $n$ over all test cases in the input does not exceed $500$.
-----Output-----
For each test case, print one integer — the minimum number of operations you have to perform to make $a$ sorted, or $-1$, if it is impossible.
-----Examples-----
Input
6
4 1
2 3 5 4
5 6
1 1 3 4 4
1 10
2
2 10
11 9
2 10
12 11
5 18
81 324 218 413 324
Output
3
0
0
-1
1
3
-----Note-----
None
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.625 |
{"tests": "{\"inputs\": [\"8\\n2 4 1 3 4 2 1 2\\n\", \"5\\n1 1 2 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 3 1 2\\n\", \"8\\n2 7 1 3 4 3 1 2\\n\", \"8\\n2 8 2 3 4 3 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 8 1 3 4 6 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 6 2 2\\n\", \"8\\n4 4 1 3 4 6 2 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 7 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"98\\n1 2 3 4 5 6 7 13 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"8\\n2 8 1 3 4 3 1 2\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 6 1 2\\n\", \"8\\n2 3 1 3 4 6 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 15 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 33 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 6 1 3 4 6 1 2\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 54 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n4 4 1 3 1 6 2 2\\n\", \"8\\n2 6 1 4 4 6 1 2\\n\", \"99\\n1 2 3 4 5 6 3 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 54 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 44 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 1 1 2\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 89 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 3 2 2\\n\", \"8\\n2 7 1 3 4 3 1 4\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 13 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 1 1 3 4 6 1 2\\n\", \"8\\n2 8 1 1 4 6 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 38 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 36 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 6 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 5 4 6 2 2\\n\", \"8\\n2 3 2 3 4 6 1 2\\n\", \"98\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 15 68 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\\n\", \"99\\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 71 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\\n\", \"8\\n2 4 1 3 4 2 1 2\\n\", \"5\\n1 1 2 1 2\\n\"], \"outputs\": [\"7\\n\", \"6\\n\", \"98\\n\", \"99\\n\", \"98\\n\", \"99\\n\", \"15\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"40\\n\", \"24\\n\", \"3\\n\", \"35\\n\", \"9\\n\", \"13\\n\", \"2\\n\", \"1\\n\", \"71\\n\", \"7\\n\", \"5\\n\", \"15\\n\", \"4\\n\", \"4\\n\", \"35\\n\", \"9\\n\", \"13\\n\", \"3\\n\", \"13\\n\", \"2\\n\", \"3\\n\", \"6\\n\", \"35\\n\", \"5\\n\", \"15\\n\", \"2\\n\", \"2\\n\", \"15\\n\", \"5\\n\", \"4\\n\", \"35\\n\", \"9\\n\", \"13\\n\", \"1\\n\", \"2\\n\", \"35\\n\", \"13\\n\", \"7\\n\", \"6\\n\"]}", "source": "primeintellect"} | You have an array $a_1, a_2, \dots, a_n$.
Let's call some subarray $a_l, a_{l + 1}, \dots , a_r$ of this array a subpermutation if it contains all integers from $1$ to $r-l+1$ exactly once. For example, array $a = [2, 2, 1, 3, 2, 3, 1]$ contains $6$ subarrays which are subpermutations: $[a_2 \dots a_3]$, $[a_2 \dots a_4]$, $[a_3 \dots a_3]$, $[a_3 \dots a_5]$, $[a_5 \dots a_7]$, $[a_7 \dots a_7]$.
You are asked to calculate the number of subpermutations.
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$).
The second line contains $n$ integers $a_1, a_2, \dots , a_n$ ($1 \le a_i \le n$).
This array can contain the same integers.
-----Output-----
Print the number of subpermutations of the array $a$.
-----Examples-----
Input
8
2 4 1 3 4 2 1 2
Output
7
Input
5
1 1 2 1 2
Output
6
-----Note-----
There are $7$ subpermutations in the first test case. Their segments of indices are $[1, 4]$, $[3, 3]$, $[3, 6]$, $[4, 7]$, $[6, 7]$, $[7, 7]$ and $[7, 8]$.
In the second test case $6$ subpermutations exist: $[1, 1]$, $[2, 2]$, $[2, 3]$, $[3, 4]$, $[4, 4]$ and $[4, 5]$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.375 |
{"tests": "{\"inputs\": [\"5 5 2\\n1 2 100\\n2 3 100\\n3 4 100\\n4 5 20\\n2 5 5\\n5 50\\n4 1\\n\", \"2 1 5\\n1 2 4\\n2 3\\n2 5\\n2 4\\n2 4\\n2 5\\n\", \"3 3 6\\n1 2 499999999\\n2 3 500000000\\n1 3 999999999\\n2 499999999\\n2 500000000\\n2 499999999\\n3 999999999\\n3 1000000000\\n3 1000000000\\n\", \"2 1 1\\n1 2 1\\n2 1000000000\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"3 2 5\\n1 2 2\\n2 3 4\\n3 5\\n3 5\\n3 5\\n3 6\\n3 7\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"3 2 2\\n1 2 100\\n2 3 1\\n2 1\\n3 3\\n\", \"3 2 2\\n1 2 4\\n2 3 4\\n2 2\\n3 6\\n\", \"2 1 1\\n1 2 1\\n2 1100000000\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 1023987090\\n5 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"3 2 5\\n1 2 2\\n2 3 4\\n3 5\\n3 5\\n3 5\\n3 7\\n3 7\\n\", \"3 3 6\\n1 2 499999999\\n2 3 500000000\\n1 3 948187054\\n2 499999999\\n2 500000000\\n2 499999999\\n3 999999999\\n3 1000000000\\n3 1000000000\\n\", \"3 2 2\\n1 3 4\\n2 3 4\\n2 2\\n3 2\\n\", \"3 2 2\\n1 3 4\\n2 3 4\\n2 2\\n3 6\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 1023987090\\n3 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n1 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 5 2\\n1 2 100\\n2 3 100\\n3 4 100\\n4 5 20\\n2 5 5\\n5 50\\n4 2\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"2 2 3\\n1 2 2\\n2 1 3\\n2 2\\n2 2\\n2 3\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 337135251\\n5 1 524524524\\n5 1023987090\\n5 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 786802082\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1001000000\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 864716097\\n2 1001000000\\n\", \"2 1 5\\n1 2 6\\n2 3\\n2 5\\n2 4\\n2 4\\n2 5\\n\", \"3 2 5\\n1 2 2\\n2 3 4\\n3 5\\n3 1\\n3 5\\n3 6\\n3 7\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 943048878\\n5 1 524524524\\n5 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 1\\n2 3 2\\n1 3 3\\n3 4 4\\n1 5 5\\n3 3\\n4 5\\n5 5\\n\", \"2 2 3\\n1 2 2\\n2 1 3\\n2 1\\n2 2\\n2 6\\n\", \"2 1 1\\n1 2 1\\n2 1100000100\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1001000010\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n1 4 529529529\\n5 1 269497518\\n1 4 1000000000\\n5 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 337135251\\n5 1 524524524\\n5 1023987090\\n5 529999999\\n4 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 786802082\\n1 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000010010\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000010\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1001000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 943048878\\n3 1 524524524\\n5 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n4 524444444\\n5 529999999\\n2 1001000010\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000010\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1001000001\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n4 524444444\\n5 529999999\\n2 1000000010\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000010\\n3 4 529529529\\n5 1 448728259\\n5 524444444\\n5 529999999\\n2 1001000001\\n\", \"5 5 2\\n1 2 100\\n2 3 100\\n3 4 100\\n4 5 20\\n2 5 5\\n2 50\\n4 1\\n\", \"2 1 5\\n1 2 4\\n2 3\\n2 1\\n2 4\\n2 4\\n2 5\\n\", \"3 3 6\\n1 2 499999999\\n2 3 500000000\\n1 2 999999999\\n2 499999999\\n2 500000000\\n2 499999999\\n3 999999999\\n3 1000000000\\n3 1000000000\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n5 334857815\\n2 1000000000\\n\", \"3 2 5\\n1 2 2\\n2 3 4\\n3 5\\n3 5\\n3 8\\n3 6\\n3 7\\n\", \"5 5 3\\n1 2 999999999\\n2 2 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 3 1000000000\\n5 524444444\\n5 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 1\\n2 3 2\\n1 3 3\\n3 4 4\\n1 5 5\\n3 5\\n4 5\\n4 5\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 1023987090\\n5 529999999\\n3 1000000000\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1010000000\\n3 4 529529529\\n5 1 524524524\\n5 1023987090\\n3 529999999\\n2 1000000000\\n\", \"5 5 3\\n1 2 999999999\\n2 3 1000000000\\n3 4 529529529\\n5 1 269497518\\n1 3 1000000000\\n5 852325903\\n5 529999999\\n2 1000000010\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 4 529529529\\n5 1 524524524\\n5 524444444\\n4 529999999\\n2 1000000000\\n\", \"3 2 5\\n1 2 2\\n2 3 4\\n3 6\\n3 5\\n3 5\\n3 7\\n3 7\\n\", \"2 2 3\\n1 2 2\\n2 1 3\\n2 4\\n2 2\\n2 3\\n\", \"5 4 3\\n1 2 999999999\\n2 3 1001000000\\n3 4 337135251\\n5 1 524524524\\n5 1023987090\\n5 529999999\\n2 1000000000\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 4 472659023\\n5 1 524524524\\n5 524444444\\n5 529999999\\n2 1001000000\\n\", \"5 4 3\\n1 2 999999999\\n2 4 1000000000\\n3 2 529529529\\n5 1 524524524\\n5 524444444\\n5 864716097\\n2 1001000000\\n\", \"2 1 5\\n1 2 6\\n2 3\\n2 5\\n2 4\\n2 2\\n2 5\\n\", \"5 5 3\\n1 2 1\\n2 3 2\\n1 3 3\\n3 4 4\\n1 5 5\\n3 5\\n4 5\\n5 5\\n\", \"2 2 3\\n1 2 2\\n2 1 3\\n2 1\\n2 2\\n2 3\\n\"], \"outputs\": [\"1\", \"4\", \"6\", \"1\", \"2\", \"4\", \"2\", \"1\", \"1\", \"1\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"6\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"6\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"4\\n\", \"3\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\", \"2\"]}", "source": "primeintellect"} | Jzzhu is the president of country A. There are n cities numbered from 1 to n in his country. City 1 is the capital of A. Also there are m roads connecting the cities. One can go from city ui to vi (and vise versa) using the i-th road, the length of this road is xi. Finally, there are k train routes in the country. One can use the i-th train route to go from capital of the country to city si (and vise versa), the length of this route is yi.
Jzzhu doesn't want to waste the money of the country, so he is going to close some of the train routes. Please tell Jzzhu the maximum number of the train routes which can be closed under the following condition: the length of the shortest path from every city to the capital mustn't change.
Input
The first line contains three integers n, m, k (2 ≤ n ≤ 105; 1 ≤ m ≤ 3·105; 1 ≤ k ≤ 105).
Each of the next m lines contains three integers ui, vi, xi (1 ≤ ui, vi ≤ n; ui ≠ vi; 1 ≤ xi ≤ 109).
Each of the next k lines contains two integers si and yi (2 ≤ si ≤ n; 1 ≤ yi ≤ 109).
It is guaranteed that there is at least one way from every city to the capital. Note, that there can be multiple roads between two cities. Also, there can be multiple routes going to the same city from the capital.
Output
Output a single integer representing the maximum number of the train routes which can be closed.
Examples
Input
5 5 3
1 2 1
2 3 2
1 3 3
3 4 4
1 5 5
3 5
4 5
5 5
Output
2
Input
2 2 3
1 2 2
2 1 3
2 1
2 2
2 3
Output
2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"4\\n5\\n1 2 3 4 5\\n2\\n10\\n2 4 2 4 2 4 2 4 2 4\\n3\\n3\\n-10 -5 -10\\n-8\\n3\\n9 9 -3\\n5\\n\", \"1\\n10\\n5 -9 -1 6 -6 5 -6 -8 5 3\\n0\\n\", \"10\\n1\\n62169\\n62169\\n1\\n49900\\n49900\\n1\\n-45220\\n-45220\\n1\\n45734\\n45734\\n1\\n-77581\\n-77581\\n1\\n-48287\\n-48287\\n1\\n53304\\n53304\\n1\\n13558\\n13558\\n1\\n18202\\n18202\\n1\\n33613\\n33613\\n\", \"10\\n2\\n89390 -71766\\n89390\\n2\\n-14330 18110\\n1890\\n2\\n-51060 -90730\\n-70895\\n2\\n31775 450\\n16112\\n2\\n-50057 -45526\\n-47791\\n2\\n27119 -93868\\n-93868\\n2\\n-63505 9891\\n-63505\\n2\\n46435 -78715\\n-16140\\n2\\n-69774 -64015\\n-66894\\n2\\n-78662 -90415\\n-84538\\n\", \"10\\n3\\n-54528 42942 -6804\\n-54528\\n3\\n18649 67840 -26344\\n43244\\n3\\n13902 51617 -4691\\n32759\\n3\\n77397 -38549 -51828\\n-45188\\n3\\n21750 -55472 -47700\\n-55472\\n3\\n59264 11044 -311\\n35154\\n3\\n-13132 88555 -52791\\n-13132\\n3\\n-82155 25593 -3193\\n-28281\\n3\\n-1405 586 77255\\n586\\n3\\n30756 83299 50338\\n54797\\n\"], \"outputs\": [\"4\\n8\\n2\\n2\\n\", \"6\\n\", \"1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n\", \"1\\n2\\n2\\n2\\n1\\n2\\n2\\n2\\n1\\n1\\n\", \"3\\n2\\n2\\n2\\n3\\n2\\n3\\n3\\n2\\n3\\n\"]}", "source": "primeintellect"} | You are given an array of integers $a_1, a_2, \ldots, a_n$ and an integer $x$.
You need to select the maximum number of elements in the array, such that for every subsegment $a_l, a_{l + 1}, \ldots, a_r$ containing strictly more than one element $(l < r)$, either:
At least one element on this subsegment is not selected, or
$a_l + a_{l+1} + \ldots + a_r \geq x \cdot (r - l + 1)$.
-----Input-----
The first line of input contains one integer $t$ ($1 \leq t \leq 10$): the number of test cases.
The descriptions of $t$ test cases follow, three lines per test case.
In the first line you are given one integer $n$ ($1 \leq n \leq 50000$): the number of integers in the array.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($-100000 \leq a_i \leq 100000$).
The third line contains one integer $x$ ($-100000 \leq x \leq 100000$).
-----Output-----
For each test case, print one integer: the maximum number of elements that you can select.
-----Examples-----
Input
4
5
1 2 3 4 5
2
10
2 4 2 4 2 4 2 4 2 4
3
3
-10 -5 -10
-8
3
9 9 -3
5
Output
4
8
2
2
-----Note-----
In the first example, one valid way to select the elements is $[\underline{1}, 2, \underline{3}, \underline{4}, \underline{5}]$. All subsegments satisfy at least one of the criteria. For example, for the subsegment $l = 1$, $r = 2$ we have that the element $2$ is not selected, satisfying the first criterion. For the subsegment $l = 3$, $r = 5$ we have $3 + 4 + 5 = 12 \ge 2 \cdot 3$, satisfying the second criterion.
We can't select all elements, because in this case for $l = 1$, $r = 2$ all elements are selected and we have $a_1 + a_2 = 3 < 2 \cdot 2$. Thus, the maximum number of selected elements is $4$.
In the second example, one valid solution is $[\underline{2}, \underline{4}, 2, \underline{4}, \underline{2}, \underline{4}, 2, \underline{4}, \underline{2}, \underline{4}]$.
In the third example, one valid solution is $[\underline{-10}, -5, \underline{-10}]$.
In the fourth example, one valid solution is $[\underline{9}, \underline{9}, -3]$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"0\\n2\\n50000000\\n4\\n\", \"2\\n2\\n50005000\\n5\\n\", \"1\\n3\\n50500005\\n8\\n\", \"0\\n2\\n999999999\\n2\\n\", \"2\\n4\\n50050000\\n6\\n\", \"3\\n1\\n50005050\\n2\\n\", \"3\\n2\\n50500000\\n8\\n\", \"3\\n6\\n50050000\\n2\\n\", \"0\\n3\\n50000000\\n2\\n\", \"2\\n3\\n50000000\\n2\\n\", \"1\\n1\\n50000000\\n2\\n\", \"0\\n3\\n50000000\\n2\\n\", \"0\\n1\\n50000000\\n2\\n\", \"2\\n3\\n50050000\\n2\\n\", \"1\\n3\\n50000000\\n2\\n\", \"1\\n1\\n50000000\\n2\\n\", \"0\\n3\\n50000000\\n3\\n\", \"1\\n1\\n50000000\\n2\\n\", \"1\\n4\\n49999999\\n2\\n\", \"0\\n3\\n50000000\\n3\\n\", \"0\\n2\\n50000000\\n2\\n\", \"2\\n3\\n50000000\\n2\\n\", \"0\\n2\\n50000000\\n2\\n\", \"0\\n2\\n50000000\\n3\\n\", \"2\\n3\\n50050000\\n2\\n\", \"2\\n3\\n50005000\\n2\\n\", \"1\\n4\\n50000000\\n2\\n\", \"1\\n3\\n50000000\\n2\\n\", \"1\\n6\\n50000000\\n2\\n\", \"2\\n2\\n50000000\\n2\\n\", \"2\\n2\\n50005000\\n2\\n\", \"0\\n2\\n50000000\\n5\\n\", \"0\\n2\\n50500500\\n2\\n\", \"2\\n3\\n50050000\\n2\\n\", \"2\\n3\\n50000000\\n2\\n\", \"3\\n2\\n999999999\\n2\\n\", \"0\\n2\\n50000000\\n2\\n\", \"0\\n3\\n50000000\\n3\\n\", \"0\\n2\\n50000000\\n2\\n\", \"2\\n2\\n50000000\\n2\\n\", \"1\\n1\\n50000000\\n2\\n\", \"4\\n1\\n50000000\\n2\\n\", \"0\\n2\\n50000000\\n5\\n\", \"0\\n3\\n50000000\\n5\\n\", \"1\\n4\\n50000000\\n2\\n\", \"3\\n3\\n50500000\\n8\\n\", \"1\\n2\\n50000000\\n2\\n\", \"2\\n4\\n50050000\\n4\\n\", \"3\\n2\\n999999999\\n7\\n\", \"0\\n8\\n50000000\\n3\\n\", \"3\\n3\\n50500000\\n8\\n\", \"3\\n3\\n50500000\\n8\\n\", \"2\\n3\\n50005000\\n2\\n\", \"3\\n1\\n50000000\\n2\\n\", \"1\\n6\\n50000000\\n2\\n\", \"0\\n2\\n50000000\\n3\\n\", \"1\\n4\\n49999999\\n2\\n\", \"2\\n1\\n50005000\\n2\\n\", \"0\\n2\\n50500500\\n2\\n\", \"1\\n2\\n50000000\\n2\\n\", \"2\\n1\\n50005000\\n2\\n\", \"2\\n2\\n50000000\\n2\\n\", \"1\\n3\\n50000000\\n2\\n\", \"0\\n3\\n50000000\\n5\\n\", \"2\\n3\\n50050000\\n2\\n\", \"3\\n3\\n50500000\\n8\\n\", \"0\\n2\\n50000000\\n2\\n\", \"2\\n2\\n50000000\\n2\\n\", \"0\\n2\\n50000000\\n5\\n\", \"0\\n3\\n50000000\\n5\\n\", \"1\\n8\\n50000000\\n3\\n\", \"3\\n1\\n50000001\\n2\\n\", \"3\\n2\\n999999999\\n7\\n\", \"2\\n1\\n50005000\\n2\\n\", \"3\\n2\\n50000000\\n2\\n\", \"0\\n3\\n50000000\\n5\\n\", \"0\\n2\\n50000000\\n2\\n\", \"\\n0\\n1\\n999999999\\n2\\n\"]}", "source": "primeintellect"} | Consider an infinite triangle made up of layers. Let's number the layers, starting from one, from the top of the triangle (from top to bottom). The $k$-th layer of the triangle contains $k$ points, numbered from left to right. Each point of an infinite triangle is described by a pair of numbers $(r, c)$ ($1 \le c \le r$), where $r$ is the number of the layer, and $c$ is the number of the point in the layer. From each point $(r, c)$ there are two directed edges to the points $(r+1, c)$ and $(r+1, c+1)$, but only one of the edges is activated. If $r + c$ is even, then the edge to the point $(r+1, c)$ is activated, otherwise the edge to the point $(r+1, c+1)$ is activated. Look at the picture for a better understanding.
Activated edges are colored in black. Non-activated edges are colored in gray.
From the point $(r_1, c_1)$ it is possible to reach the point $(r_2, c_2)$, if there is a path between them only from activated edges. For example, in the picture above, there is a path from $(1, 1)$ to $(3, 2)$, but there is no path from $(2, 1)$ to $(1, 1)$.
Initially, you are at the point $(1, 1)$. For each turn, you can:
Replace activated edge for point $(r, c)$. That is if the edge to the point $(r+1, c)$ is activated, then instead of it, the edge to the point $(r+1, c+1)$ becomes activated, otherwise if the edge to the point $(r+1, c+1)$, then instead if it, the edge to the point $(r+1, c)$ becomes activated. This action increases the cost of the path by $1$;
Move from the current point to another by following the activated edge. This action does not increase the cost of the path.
You are given a sequence of $n$ points of an infinite triangle $(r_1, c_1), (r_2, c_2), \ldots, (r_n, c_n)$. Find the minimum cost path from $(1, 1)$, passing through all $n$ points in arbitrary order.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^4$) is the number of test cases. Then $t$ test cases follow.
Each test case begins with a line containing one integer $n$ ($1 \le n \le 2 \cdot 10^5$) is the number of points to visit.
The second line contains $n$ numbers $r_1, r_2, \ldots, r_n$ ($1 \le r_i \le 10^9$), where $r_i$ is the number of the layer in which $i$-th point is located.
The third line contains $n$ numbers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le r_i$), where $c_i$ is the number of the $i$-th point in the $r_i$ layer.
It is guaranteed that all $n$ points are distinct.
It is guaranteed that there is always at least one way to traverse all $n$ points.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
-----Output-----
For each test case, output the minimum cost of a path passing through all points in the corresponding test case.
-----Examples-----
Input
4
3
1 4 2
1 3 1
2
2 4
2 3
2
1 1000000000
1 1000000000
4
3 10 5 8
2 5 2 4
Output
0
1
999999999
2
-----Note-----
None
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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7\\n21662711\\n77271666\\n89022761\\n156626166\\n127774156\\n166902656\\n298992265\", \"10 6\\n0\\n2\\n3\\n6\\n7\\n9\", \"10 3\\n0\\n12\\n38\", \"234749902 7\\n21662711\\n77271666\\n89022761\\n156626166\\n160332356\\n166902656\\n507697443\", \"5 3\\n1\\n7\\n8\", \"30 3\\n0\\n12\\n29\", \"3 6\\n1\\n2\\n3\\n6\\n7\\n26\", \"20 3\\n2\\n7\\n8\", \"0 3\\n2\\n13\\n61\", \"26 3\\n0\\n7\\n10\", \"28 3\\n2\\n6\\n23\", \"485060065 7\\n35438742\\n77271666\\n89022761\\n156626166\\n160332356\\n166902656\\n453863319\", \"10 3\\n1\\n10\\n11\", \"314159265 7\\n35438742\\n77271666\\n122238627\\n156626166\\n160332356\\n331169608\\n453863319\", \"46 3\\n6\\n7\\n12\", \"3 3\\n2\\n0\\n60\", \"19 3\\n2\\n12\\n47\", \"46 3\\n3\\n7\\n28\", \"19 3\\n2\\n4\\n107\", \"67 3\\n0\\n2\\n29\", \"91633092 7\\n2598354\\n77271666\\n10183080\\n210377502\\n206402248\\n166902656\\n948912880\", \"38 3\\n2\\n10\\n7\", \"171714410 7\\n2598354\\n77271666\\n17352283\\n210377502\\n206402248\\n166902656\\n929754377\", \"118 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7\\n2598354\\n77271666\\n10183080\\n210377502\\n206402248\\n166902656\\n844215766\", \"314159265 7\\n21662711\\n33209238\\n89022761\\n156626166\\n185012774\\n166902656\\n298992265\", \"485060065 7\\n35438742\\n77271666\\n89022761\\n158342418\\n160332356\\n166902656\\n246658695\", \"91633092 7\\n33237643\\n77271666\\n57166710\\n156626166\\n206402248\\n166902656\\n535507862\", \"314159265 7\\n21662711\\n77271666\\n89022761\\n156626166\\n160332356\\n166902656\\n298992265\", \"10 6\\n1\\n2\\n3\\n6\\n7\\n9\", \"10 3\\n2\\n7\\n9\"], \"outputs\": [\"1204124749\\n\", \"13\\n\", \"17\\n\", \"1671081643\\n\", \"20\\n\", \"29\\n\", \"9\\n\", \"28\\n\", \"15\\n\", \"16\\n\", \"1111984965\\n\", \"14\\n\", \"12\\n\", \"44\\n\", \"33\\n\", \"32\\n\", \"18\\n\", \"57\\n\", \"53\\n\", \"10\\n\", \"1180653141\\n\", \"1231676811\\n\", \"507697443\\n\", \"49\\n\", \"111\\n\", \"37\\n\", \"54\\n\", \"40\\n\", \"63\\n\", \"67\\n\", \"34\\n\", \"1073277336\\n\", \"113\\n\", \"90\\n\", \"50\\n\", \"112\\n\", \"1023255587\\n\", \"8\\n\", \"23\\n\", \"84\\n\", \"62\\n\", \"99\\n\", \"86\\n\", \"52\\n\", \"72\\n\", \"64\\n\", \"88\\n\", \"121\\n\", \"96\\n\", \"22\\n\", \"92\\n\", \"176\\n\", \"155\\n\", \"1269241149\\n\", \"25\\n\", \"38\\n\", \"727668571\\n\", \"11\\n\", \"36\\n\", \"26\\n\", \"41\\n\", \"61\\n\", \"51\\n\", \"46\\n\", \"2257081611\\n\", \"19\\n\", \"1040061470\\n\", \"119\\n\", \"60\\n\", \"47\\n\", \"81\\n\", \"107\\n\", \"141\\n\", \"948912880\\n\", \"94\\n\", \"929754377\\n\", \"332\\n\", \"140\\n\", \"1181116293\\n\", \"31\\n\", \"21\\n\", \"629656047\\n\", \"45\\n\", \"2253649107\\n\", \"847056624\\n\", \"538107440\\n\", \"4\\n\", \"91\\n\", \"55\\n\", \"27\\n\", \"79\\n\", \"65\\n\", \"484406296\\n\", \"180\\n\", \"143\\n\", \"82\\n\", \"844215766\\n\", \"1066639057\\n\", \"2492756961\\n\", \"535507862\\n\", \"1204124749\", \"27\", \"15\"]}", "source": "primeintellect"} | Takahashi Lake has a perimeter of L. On the circumference of the lake, there is a residence of the lake's owner, Takahashi. Each point on the circumference of the lake has a coordinate between 0 and L (including 0 but not L), which is the distance from the Takahashi's residence, measured counter-clockwise.
There are N trees around the lake; the coordinate of the i-th tree is X_i. There is no tree at coordinate 0, the location of Takahashi's residence.
Starting at his residence, Takahashi will repeat the following action:
* If all trees are burnt, terminate the process.
* Specify a direction: clockwise or counter-clockwise.
* Walk around the lake in the specified direction, until the coordinate of a tree that is not yet burnt is reached for the first time.
* When the coordinate with the tree is reached, burn that tree, stay at the position and go back to the first step.
Find the longest possible total distance Takahashi walks during the process.
Constraints
* 2 \leq L \leq 10^9
* 1 \leq N \leq 2\times 10^5
* 1 \leq X_1 < ... < X_N \leq L-1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
L N
X_1
:
X_N
Output
Print the longest possible total distance Takahashi walks during the process.
Examples
Input
10 3
2
7
9
Output
15
Input
10 6
1
2
3
6
7
9
Output
27
Input
314159265 7
21662711
77271666
89022761
156626166
160332356
166902656
298992265
Output
1204124749
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1\\n-751115 -925948\\n\", \"1\\n-751115 -1566406\\n\", \"3\\n-1 -1\\n0 2\\n1 0\\n\", \"3\\n0 -1\\n0 2\\n2 0\\n\", \"1\\n-751115 -2469241\\n\", \"3\\n-1 -1\\n0 2\\n2 0\\n\", \"1\\n-751115 -4760337\\n\", \"1\\n-751115 -4345366\\n\", \"3\\n0 -1\\n0 2\\n1 0\\n\", \"1\\n-751115 -8685961\\n\", \"3\\n0 -1\\n0 2\\n1 -1\\n\", \"1\\n-751115 -16747294\\n\", \"3\\n0 -1\\n0 2\\n1 -2\\n\", \"1\\n-751115 -11499666\\n\", \"3\\n-1 -1\\n0 2\\n1 -2\\n\", \"1\\n-751115 -8383059\\n\", \"3\\n-1 -1\\n0 4\\n1 -2\\n\", \"1\\n-751115 -14990265\\n\", \"3\\n-1 -1\\n0 8\\n1 -2\\n\", \"1\\n-867280 -14990265\\n\", \"3\\n-1 -1\\n0 8\\n1 -1\\n\", \"1\\n-867280 -20447796\\n\", \"3\\n-1 -1\\n0 8\\n1 0\\n\", \"1\\n-82347 -20447796\\n\", \"3\\n-1 -1\\n0 9\\n1 0\\n\", \"1\\n-24194 -20447796\\n\", \"3\\n-1 0\\n0 9\\n1 0\\n\", \"1\\n-24194 -21170927\\n\", \"3\\n-1 0\\n0 0\\n1 0\\n\", \"1\\n-24194 -38849773\\n\", \"3\\n-2 0\\n0 0\\n1 0\\n\", \"1\\n-24194 -30101673\\n\", \"3\\n-4 0\\n0 0\\n1 0\\n\", \"1\\n-16781 -30101673\\n\", \"3\\n-4 0\\n0 1\\n1 0\\n\", \"1\\n-16781 -35445070\\n\", \"3\\n-4 0\\n0 2\\n1 0\\n\", \"1\\n-16781 -57795496\\n\", \"3\\n-4 0\\n0 2\\n1 1\\n\", \"1\\n-16781 -69843765\\n\", \"3\\n-4 0\\n0 2\\n2 1\\n\", \"1\\n-16781 -67479162\\n\", \"3\\n-4 0\\n0 4\\n2 1\\n\", \"1\\n-18432 -67479162\\n\", \"1\\n-18432 -114655804\\n\", \"1\\n-18432 -73682181\\n\", \"1\\n-26684 -73682181\\n\", \"1\\n-26684 -44017186\\n\", \"1\\n-5791 -44017186\\n\", \"1\\n-4622 -44017186\\n\", \"1\\n-6491 -44017186\\n\", \"1\\n-6491 -57650128\\n\", \"1\\n-6491 -76071226\\n\", \"1\\n-6177 -76071226\\n\", \"1\\n-6177 -111121793\\n\", \"1\\n-5218 -111121793\\n\", \"1\\n-4051 -111121793\\n\", \"1\\n-4071 -111121793\\n\", \"1\\n-4071 -73927447\\n\", \"1\\n-4071 -30505011\\n\", \"1\\n-6940 -30505011\\n\", \"1\\n-5414 -30505011\\n\", \"1\\n-5414 -33615105\\n\", \"1\\n-5414 -52662403\\n\", \"1\\n-5414 -56071083\\n\", \"1\\n-4910 -56071083\\n\", \"1\\n-4910 -80644888\\n\", \"3\\n-1 0\\n0 2\\n1 0\\n\", \"5\\n1 0\\n1 -1\\n0 -1\\n-1 0\\n-1 -1\\n\"], \"outputs\": [\"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"1\\n\"]}", "source": "primeintellect"} | Recently Vasya learned that, given two points with different x coordinates, you can draw through them exactly one parabola with equation of type y = x^2 + bx + c, where b and c are reals. Let's call such a parabola an U-shaped one.
Vasya drew several distinct points with integer coordinates on a plane and then drew an U-shaped parabola through each pair of the points that have different x coordinates. The picture became somewhat messy, but Vasya still wants to count how many of the parabolas drawn don't have any drawn point inside their internal area. Help Vasya.
The internal area of an U-shaped parabola is the part of the plane that lies strictly above the parabola when the y axis is directed upwards.
Input
The first line contains a single integer n (1 ≤ n ≤ 100 000) — the number of points.
The next n lines describe the points, the i-th of them contains two integers x_i and y_i — the coordinates of the i-th point. It is guaranteed that all points are distinct and that the coordinates do not exceed 10^6 by absolute value.
Output
In the only line print a single integer — the number of U-shaped parabolas that pass through at least two of the given points and do not contain any of the given points inside their internal area (excluding the parabola itself).
Examples
Input
3
-1 0
0 2
1 0
Output
2
Input
5
1 0
1 -1
0 -1
-1 0
-1 -1
Output
1
Note
On the pictures below all U-shaped parabolas that pass through at least two given points are drawn for each of the examples. The U-shaped parabolas that do not have any given point inside their internal area are drawn in red.
<image> The first example. <image> The second example.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.5 |
{"tests": "{\"inputs\": [\"1 2 3 2 5 6\\n6 5 4 3 2 1\", \"1 2 3 2 5 6\\n6 1 4 3 2 1\", \"1 2 3 2 5 6\\n6 0 4 3 2 1\", \"1 2 3 2 5 6\\n6 0 4 3 4 1\", \"1 2 3 2 7 6\\n6 0 4 3 4 1\", \"1 2 3 2 7 3\\n6 0 4 3 4 1\", \"1 2 2 2 7 6\\n6 0 4 3 4 1\", \"1 2 2 2 7 9\\n6 0 4 3 4 1\", \"1 2 2 2 7 9\\n6 0 4 5 4 1\", \"1 0 2 2 7 9\\n6 0 4 5 4 1\", \"2 0 2 2 7 9\\n6 0 4 5 4 1\", \"2 0 2 2 7 9\\n2 0 4 5 4 1\", \"2 0 2 2 7 9\\n2 0 4 5 4 2\", \"2 0 2 2 7 11\\n2 0 4 5 4 2\", \"2 0 2 2 7 11\\n2 0 4 1 4 2\", \"2 0 3 2 7 11\\n2 0 4 1 4 2\", \"2 0 3 2 13 11\\n2 0 4 1 4 2\", \"2 0 3 2 13 11\\n2 0 8 1 4 2\", \"2 0 3 2 13 11\\n3 0 8 1 4 2\", \"2 1 3 2 13 11\\n3 0 8 1 4 2\", \"2 1 3 2 13 0\\n3 0 8 1 4 2\", \"2 1 3 2 17 0\\n3 0 8 1 4 2\", \"2 1 3 2 17 0\\n3 0 8 0 4 2\", \"2 1 3 2 13 0\\n3 0 8 0 4 2\", \"2 1 3 2 13 0\\n3 1 8 0 4 2\", \"2 1 0 2 13 0\\n3 1 8 0 4 2\", \"2 1 0 0 13 0\\n3 1 8 0 4 2\", \"2 1 0 -1 13 0\\n3 1 8 0 4 2\", \"2 1 0 -1 13 0\\n3 1 8 0 5 2\", \"2 2 0 -1 13 0\\n3 1 8 0 5 2\", \"2 2 0 0 13 0\\n3 1 8 0 5 2\", \"2 2 0 0 13 -1\\n3 1 8 0 5 2\", \"2 1 0 0 13 -1\\n3 1 8 0 5 2\", \"2 0 0 0 13 -1\\n3 1 8 0 5 2\", \"2 0 0 0 13 -1\\n3 1 8 0 5 4\", \"2 0 0 0 13 -1\\n3 1 1 0 5 4\", \"2 0 0 0 13 -1\\n3 1 0 0 5 4\", \"2 0 0 0 26 -1\\n3 1 0 0 5 4\", \"2 0 0 0 26 -1\\n3 1 0 0 6 4\", \"2 1 0 0 26 -1\\n3 1 0 0 6 4\", \"2 1 0 0 50 -1\\n3 1 0 0 6 4\", \"2 1 -1 0 50 -1\\n3 1 0 0 6 4\", \"2 1 -1 0 50 -1\\n3 1 0 0 9 4\", \"2 1 -1 1 50 -1\\n3 1 0 0 9 4\", \"2 1 0 1 50 -1\\n3 1 0 0 9 4\", \"2 1 0 1 50 -1\\n3 0 0 0 9 4\", \"2 1 0 1 50 -1\\n5 0 0 0 9 4\", \"2 1 0 0 50 -1\\n5 0 0 0 9 4\", \"2 0 0 0 50 -1\\n5 0 0 0 9 4\", \"2 0 0 0 50 -1\\n5 0 0 1 9 4\", \"2 1 0 0 50 -1\\n5 0 0 1 9 4\", \"2 2 0 0 50 -1\\n5 0 0 1 9 4\", \"2 2 0 0 50 -1\\n5 0 0 1 16 4\", \"2 2 0 0 50 -1\\n5 0 1 1 16 4\", \"1 2 0 0 50 -1\\n5 0 1 1 16 4\", \"1 2 0 0 85 -1\\n5 0 1 1 16 4\", \"1 1 0 0 85 -1\\n5 0 1 1 16 4\", \"1 1 0 0 151 -1\\n5 0 1 1 16 4\", \"1 1 0 0 151 -1\\n10 0 1 1 16 4\", \"0 1 0 0 151 -1\\n10 0 1 1 16 4\", \"0 1 0 0 197 -1\\n10 0 1 1 16 4\", \"0 1 0 -1 197 -1\\n10 0 1 1 16 4\", \"0 1 0 -1 197 -1\\n10 0 1 1 16 1\", \"0 2 0 -1 197 -1\\n10 0 1 1 16 1\", \"0 2 0 -1 197 -1\\n2 0 1 1 16 1\", \"0 2 0 -1 362 -1\\n2 0 1 1 16 1\", \"0 2 0 -1 722 -1\\n2 0 1 1 16 1\", \"0 2 0 -1 722 -1\\n2 0 1 1 16 2\", \"0 2 0 -1 722 -1\\n1 0 1 1 16 2\", \"0 2 0 -1 722 0\\n1 0 1 1 16 2\", \"0 2 0 -1 722 0\\n1 0 1 1 27 2\", \"-1 2 0 -1 722 0\\n1 0 1 1 27 2\", \"-1 2 0 -1 722 0\\n1 0 2 1 27 2\", \"-1 2 -1 -1 722 0\\n1 0 2 1 27 2\", \"-1 2 0 -1 722 1\\n1 0 2 1 27 2\", \"-1 2 0 -1 390 1\\n1 0 2 1 27 2\", \"-1 2 0 -2 390 1\\n1 0 2 1 27 2\", \"-1 2 -1 -1 390 1\\n1 0 2 1 27 2\", \"-1 2 -1 -1 390 1\\n1 0 2 0 27 2\", \"-1 2 -1 -1 390 1\\n1 0 2 0 27 0\", \"-1 2 -1 0 390 1\\n1 0 2 0 27 0\", \"-1 2 -1 0 390 1\\n1 0 4 0 27 0\", \"-1 2 -1 0 390 1\\n2 0 4 0 27 0\", \"-1 2 -1 0 390 1\\n3 0 4 0 27 0\", \"-1 2 -1 0 390 1\\n3 0 4 0 18 0\", \"-1 2 -1 0 390 1\\n3 0 4 0 9 0\", \"-1 2 -1 0 390 0\\n3 0 4 0 9 0\", \"-1 2 -1 0 403 0\\n3 0 4 0 9 0\", \"-1 2 -1 0 485 0\\n3 0 4 0 9 0\", \"-1 2 -2 0 485 0\\n3 0 4 0 9 0\", \"-1 2 -2 0 485 1\\n3 0 4 0 9 0\", \"-1 2 -2 0 485 1\\n3 0 4 0 9 -1\", \"-1 2 -3 0 485 1\\n3 0 4 0 9 -1\", \"-1 2 -3 -1 485 1\\n3 0 4 0 9 -1\", \"-2 2 -3 -1 485 1\\n3 0 4 0 9 -1\", \"-2 2 -3 -1 461 1\\n3 0 4 0 9 -1\", \"-2 2 -3 -1 461 1\\n3 0 4 0 13 -1\", \"-1 2 -3 -1 461 1\\n3 0 4 0 13 -1\", \"-1 2 -3 -1 461 1\\n3 0 6 0 13 -1\", \"-1 2 -3 -1 461 2\\n3 0 6 0 13 -1\", \"1 2 3 4 5 6\\n6 5 4 3 2 1\", \"1 2 3 4 5 6\\n6 2 4 3 5 1\"], \"outputs\": [\"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\", \"Yes\"]}", "source": "primeintellect"} | Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.
Constraints
* $0 \leq $ the integer assigned to a face $ \leq 100$
Input
In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels.
In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.
Output
Print "Yes" if two dices are identical, otherwise "No" in a line.
Examples
Input
1 2 3 4 5 6
6 2 4 3 5 1
Output
Yes
Input
1 2 3 4 5 6
6 5 4 3 2 1
Output
No
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.375 |
{"tests": "{\"inputs\": [\"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 15\\n2 4\\n1 10\\n1\\n1 100\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"1\\n4\\n1 1\\n1 1\\n2 2\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"1\\n4\\n1 1\\n1 1\\n2 2\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"1\\n4\\n2 1\\n1 1\\n2 2\\n3 4\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 26\\n2 4\\n1 10\\n1\\n1 100\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 51\\n2 4\\n1 10\\n1\\n1 100\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n2 100\\n1 1\\n1 1\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 26\\n2 4\\n1 1\\n1\\n1 100\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 6\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 26\\n2 4\\n1 1\\n1\\n1 100\\n\", \"1\\n4\\n1 0\\n1 2\\n2 3\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n2 100\\n1 0\\n2 1\\n\", \"1\\n4\\n2 2\\n1 1\\n1 2\\n3 8\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 8\\n1 6\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 26\\n2 4\\n1 1\\n1\\n1 100\\n\", \"1\\n4\\n1 0\\n2 2\\n2 3\\n3 0\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 97\\n2 4\\n1 10\\n1\\n1 100\\n\", \"1\\n4\\n1 0\\n1 1\\n2 2\\n3 6\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 5\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 26\\n2 4\\n1 1\\n1\\n1 100\\n\", \"1\\n4\\n1 0\\n1 4\\n2 3\\n3 4\\n\", \"1\\n4\\n2 2\\n1 1\\n1 2\\n3 9\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 1\\n1 2\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"1\\n4\\n2 2\\n1 1\\n1 2\\n3 13\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 2\\n1 2\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 1\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 5\\n3\\n1 26\\n2 4\\n1 10\\n1\\n1 100\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 1\\n2 3\\n3\\n1 15\\n2 4\\n1 10\\n1\\n1 100\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 100\\n1 2\\n1 1\\n\", \"1\\n4\\n1 0\\n1 1\\n2 2\\n3 4\\n\", \"1\\n4\\n2 2\\n1 1\\n2 2\\n3 4\\n\", \"1\\n4\\n1 0\\n1 1\\n2 3\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n2 100\\n1 0\\n1 1\\n\", \"1\\n4\\n2 2\\n1 1\\n1 2\\n3 4\\n\", \"1\\n4\\n1 0\\n1 2\\n2 3\\n3 0\\n\", \"1\\n4\\n2 1\\n1 1\\n2 0\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 0\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 100\\n1 2\\n1 1\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n2 100\\n1 2\\n1 1\\n\", \"1\\n4\\n2 2\\n1 1\\n3 2\\n3 4\\n\", \"1\\n4\\n1 0\\n1 1\\n2 4\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 3\\n1 1\\n1 1\\n3\\n2 100\\n1 0\\n2 1\\n\", \"1\\n4\\n2 1\\n1 1\\n1 2\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n2 2\\n1 1\\n1 1\\n3\\n2 100\\n1 0\\n2 1\\n\", \"1\\n4\\n1 0\\n1 4\\n2 3\\n3 0\\n\", \"1\\n4\\n1 0\\n1 1\\n2 4\\n3 1\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n2 2\\n1 1\\n1 1\\n3\\n2 101\\n1 0\\n2 1\\n\", \"1\\n4\\n1 0\\n1 1\\n1 4\\n3 1\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 2\\n1 2\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 0\\n\", \"1\\n4\\n1 1\\n1 0\\n2 2\\n3 4\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 2\\n1 1\\n1 1\\n3\\n1 100\\n1 1\\n1 2\\n\", \"5\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n1 1\\n1 1\\n1 1\\n3\\n2 1\\n1 1\\n1 1\\n3\\n1 100\\n1 2\\n1 1\\n\", \"5\\n3\\n1 6\\n1 7\\n1 5\\n2\\n1 4\\n1 3\\n3\\n1 10\\n3 5\\n2 3\\n3\\n1 15\\n2 4\\n1 10\\n1\\n1 100\\n\"], \"outputs\": [\"263\\n\", \"211\\n\", \"4\\n\", \"211\\n\", \"4\\n\", \"212\\n\", \"4\\n\", \"274\\n\", \"299\\n\", \"211\\n\", \"268\\n\", \"271\\n\", \"5\\n\", \"210\\n\", \"8\\n\", \"275\\n\", \"3\\n\", \"213\\n\", \"345\\n\", \"6\\n\", \"270\\n\", \"7\\n\", \"9\\n\", \"214\\n\", \"13\\n\", \"215\\n\", \"276\\n\", \"263\\n\", \"212\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"211\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"212\\n\", \"212\\n\", \"4\\n\", \"5\\n\", \"211\\n\", \"4\\n\", \"210\\n\", \"7\\n\", \"5\\n\", \"212\\n\", \"5\\n\", \"214\\n\", \"4\\n\", \"213\\n\", \"212\\n\", \"263\\n\"]}", "source": "primeintellect"} | You are playing a computer card game called Splay the Sire. Currently you are struggling to defeat the final boss of the game.
The boss battle consists of $n$ turns. During each turn, you will get several cards. Each card has two parameters: its cost $c_i$ and damage $d_i$. You may play some of your cards during each turn in some sequence (you choose the cards and the exact order they are played), as long as the total cost of the cards you play during the turn does not exceed $3$. After playing some (possibly zero) cards, you end your turn, and all cards you didn't play are discarded. Note that you can use each card at most once.
Your character has also found an artifact that boosts the damage of some of your actions: every $10$-th card you play deals double damage.
What is the maximum possible damage you can deal during $n$ turns?
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of turns.
Then $n$ blocks of input follow, the $i$-th block representing the cards you get during the $i$-th turn.
Each block begins with a line containing one integer $k_i$ ($1 \le k_i \le 2 \cdot 10^5$) — the number of cards you get during $i$-th turn. Then $k_i$ lines follow, each containing two integers $c_j$ and $d_j$ ($1 \le c_j \le 3$, $1 \le d_j \le 10^9$) — the parameters of the corresponding card.
It is guaranteed that $\sum \limits_{i = 1}^{n} k_i \le 2 \cdot 10^5$.
-----Output-----
Print one integer — the maximum damage you may deal.
-----Example-----
Input
5
3
1 6
1 7
1 5
2
1 4
1 3
3
1 10
3 5
2 3
3
1 15
2 4
1 10
1
1 100
Output
263
-----Note-----
In the example test the best course of action is as follows:
During the first turn, play all three cards in any order and deal $18$ damage.
During the second turn, play both cards and deal $7$ damage.
During the third turn, play the first and the third card and deal $13$ damage.
During the fourth turn, play the first and the third card and deal $25$ damage.
During the fifth turn, play the only card, which will deal double damage ($200$).
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[1], [2], [13], [19], [41], [93]], \"outputs\": [[[1]], [[3, 5]], [[157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181]], [[343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379]], [[1641, 1643, 1645, 1647, 1649, 1651, 1653, 1655, 1657, 1659, 1661, 1663, 1665, 1667, 1669, 1671, 1673, 1675, 1677, 1679, 1681, 1683, 1685, 1687, 1689, 1691, 1693, 1695, 1697, 1699, 1701, 1703, 1705, 1707, 1709, 1711, 1713, 1715, 1717, 1719, 1721]], [[8557, 8559, 8561, 8563, 8565, 8567, 8569, 8571, 8573, 8575, 8577, 8579, 8581, 8583, 8585, 8587, 8589, 8591, 8593, 8595, 8597, 8599, 8601, 8603, 8605, 8607, 8609, 8611, 8613, 8615, 8617, 8619, 8621, 8623, 8625, 8627, 8629, 8631, 8633, 8635, 8637, 8639, 8641, 8643, 8645, 8647, 8649, 8651, 8653, 8655, 8657, 8659, 8661, 8663, 8665, 8667, 8669, 8671, 8673, 8675, 8677, 8679, 8681, 8683, 8685, 8687, 8689, 8691, 8693, 8695, 8697, 8699, 8701, 8703, 8705, 8707, 8709, 8711, 8713, 8715, 8717, 8719, 8721, 8723, 8725, 8727, 8729, 8731, 8733, 8735, 8737, 8739, 8741]]]}", "source": "primeintellect"} | Given a triangle of consecutive odd numbers:
```
1
3 5
7 9 11
13 15 17 19
21 23 25 27 29
...
```
find the triangle's row knowing its index (the rows are 1-indexed), e.g.:
```
odd_row(1) == [1]
odd_row(2) == [3, 5]
odd_row(3) == [7, 9, 11]
```
**Note**: your code should be optimized to handle big inputs.
___
The idea for this kata was taken from this kata: [Sum of odd numbers](https://www.codewars.com/kata/sum-of-odd-numbers)
Write your solution by modifying this code:
```python
def odd_row(n):
```
Your solution should implemented in the function "odd_row". The i
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"bbabb\\nbababbbbab\\n\", \"ab\\nbbbba\\n\", \"xzzxxxzxzzzxzzzxxzzxzzxzxzxxzxxzxxzxzzxxzxxzxxxzxzxzxxzzxxxxzxzzzxxxzxzxxxzzxxzxxzxxzzxxzxxzxzxzzzxzzzzxzxxzzxzxxzxxzzxzxzx\\nzzx\\n\", \"a\\nb\\n\", \"zxzxzxzxzxzxzx\\nd\\n\", \"pfdempfohomnpgbeegikfmflnalbbajpnpgeacaicoehopgnabnklheepnlnflohjegcciflmfjhachnhekckfjgoffhkblncidn\\nidlhklpclcghngeggpjdgefccihndpoikojdjnbkdfjgaanoolfmnifnmbpeeghpicehjdiipnlfnjpglidpnnnjfmjfhbcogojkcfflmmfcgajbjbfaikhmjofbnjnaolbcdkelcieeodbfjcfiblhhmeelmpcmmcdhjcnnfklgedjjbaljndjonanlojclboeelkab\\n\", \"ababababab\\nababb\\n\", \"zxx\\nxzzxxxxzzzxxxzzxxxzxxxzzxxzxxxzzxzxxzxxzxxzxzxxzxxxxzzxxzzxzzxxzzxxzxzxzxxzxzxzxxxzxxzzxxzxxxxzzxxxzxxxzxzxzzxzzxxxxzzxxzxz\\n\", \"ababbabbab\\nababb\\n\", \"coderscontest\\ncodeforces\\n\", \"b\\nab\\n\", \"sbypoaavsbqxfiqvpbjyimhzotlxuramhdamvyobsgaehwhtfdvgvlxpophtvzrmvyxwyzeauyatzitsqvlabufbcefaivwzoccfvhrdbzlmzoofczqzbxoqioctzzxqksuorhnldrfavlhyfyobvnqsyegsbvlusxchixbddzbwwnvuulcarguxvnvzkdqcjxxdetll\\nlbawrainjjdgkdmwkqzxlwxhzjyrxbuwjhnvjlnmgfyrxdynsanvibfhngsioisbyldaplituqhebeicpsyerpiiqpjtnxvuotjv\\n\", \"ab\\na\\n\", \"abbbccbba\\nabcabc\\n\", \"baabb\\nbababbbbab\\n\", \"ab\\nbbbca\\n\", \"xzzxxxzxzzzxzzzxxzzxzzxzxzxxzxxzxxzxzzxxzxxzxxxzxzxzxxzzxxxxzxzzzxxxzxzxxxzzxxzxxzxxzzxxzxxzxzxzzzxzzzzxzxxzzxzxxzxxzzxzxzx\\nyzx\\n\", \"`\\nb\\n\", \"pfdempfohomnpgbfegikfmflnalbbajpnpgeacaicoehopgnabnklheepnlnflohjegcciflmfjhachnhekckfjgoffhkblncidn\\nidlhklpclcghngeggpjdgefccihndpoikojdjnbkdfjgaanoolfmnifnmbpeeghpicehjdiipnlfnjpglidpnnnjfmjfhbcogojkcfflmmfcgajbjbfaikhmjofbnjnaolbcdkelcieeodbfjcfiblhhmeelmpcmmcdhjcnnfklgedjjbaljndjonanlojclboeelkab\\n\", \"abababab`b\\nababb\\n\", \"zxx\\nxzzxxxxzzzxxxzzxxxzxxxzzxxzxxxzzxzxxzxxzxxzxzxxzxxxxzzxxzzxzzxxzzxxzxzxzxxzxzxyxxxzxxzzxxzxxxxzzxxxzxxxzxzxzzxzzxxxxzzxxzxz\\n\", \"abaababbab\\nababb\\n\", \"coderscontest\\ncodeforcds\\n\", \"b\\nba\\n\", \"lltedxxjcqdkzvnvxugracluuvnwwbzddbxihcxsulvbsgeysqnvboyfyhlvafrdlnhrouskqxzztcoiqoxbzqzcfoozmlzbdrhvfccozwviafecbfubalvqstiztayuaezywxyvmrzvthpopxlvgvdfthwheagsboyvmadhmaruxltozhmiyjbpvqifxqbsvaaopybs\\nlbawrainjjdgkdmwkqzxlwxhzjyrxbuwjhnvjlnmgfyrxdynsanvibfhngsioisbyldaplituqhebeicpsyerpiiqpjtnxvuotjv\\n\", \"abbbccbba\\nabbabc\\n\", \"codeforces\\nfosceofcode\\n\", \"a`\\naa\\n\", \"baabb\\nbbbabbbbaa\\n\", \"ab\\nacbbb\\n\", \"pfdempfohomnpgbfegikfmflnalbbajpnpgeacaicoehopgnabnklheepnlnflohjegcciflmfjhachnhekckfjgoffhkblncidn\\nidlhklpclcghngeggpjdgefccihndpoikojdjnbkdfjgaanoolfmnifnmbpeeghpicehjdiipnlfnjpglidpnnnjfmjfhbcogojkcfflmmfcgajbjbfaikhmjofbnjnaolbcdkelcieeodbfjcfiblhhmeelmpcmmcdhjcnnfklgedjjbaljndjonanlojclboeemkab\\n\", \"xxz\\nxzzxxxxzzzxxxzzxxxzxxxzzxxzxxxzzxzxxzxxzxxzxzxxzxxxxzzxxzzxzzxxzzxxzxzxzxxzxzxyxxxzxxzzxxzxxxxzzxxxzxxxzxzxzzxzzxxxxzzxxzxz\\n\", \"tsetnocsredoc\\ncodeforcds\\n\", \"lltedxxjcqdkzvnvxugracluuvnwwbzddbxihcxsulvbsgeysqnvboyfyhlvafrdlnhrouskqxzztcoiqoxbzqzcfoozmlzbdrhvfccozwviafecbfubalvqstiztayuaezywxyvmrzvthpopxlvgvdfthwheagsboyvmadhmaruxltozhmiyjbpvqifxqbsvaaopybs\\nlbawrainjjdgkdmwkqzxxwlhzjyrxbuwjhnvjlnmgfyrxdynsanvibfhngsioisbyldaplituqhebeicpsyerpiiqpjtnxvuotjv\\n\", \"bbbbccbaa\\nabbabc\\n\", \"codeforces\\nedocfoecsof\\n\", \"baabb\\naabbbbabbb\\n\", \"ab\\naccbb\\n\", \"xzzxyxzxzzzxzzzxxzzxzzxzxzxxzxxzxxzxzzxxzxxzxxxzxzxzxxzzxxxxzxzzzxxxzxzxxxzzxxzxxzxxzzxxzxxzxzxzzzxzzzzxzxxzzxzxxzxxzzxzxzx\\nxzy\\n\", \"pfdempfohomnpgbfegikfmflnalbbajphpgeacaicoenopgnabnklheepnlnflohjegcciflmfjhachnhekckfjgoffhkblncidn\\nidlhklpclcghngeggpjdgefccihndpoikojdjnbkdfjgaanoolfmnifnmbpeeghpicehjdiipnlfnjpglidpnnnjfmjfhbcogojkcfflmmfcgajbjbfaikhmjofbnjnaolbcdkelcieeodbfjcfiblhhmeelmpcmmcdhjcnnfklgedjjbaljndjonanlojclboeemkab\\n\", \"ababbbab`a\\nbbaba\\n\", \"xxz\\nxzzxxxxzzzxxxzzxxxzxxxzzxxzxxxzzxzxxzxxzxxzxzxxzxxxxzzxxzzxzzxxzzxxzxzxzxxzxzxyxxxzzxzzxxzxxxxzzxxxzxxxzxzxzzxzzxxxxzxxxzxz\\n\", \"bbaaaabbab\\nbbaba\\n\", \"tsetnocsreeoc\\ncodeforcds\\n\", \"lltedxxjcqdkzvnvxugracluuvnwwbzddbxihcxsulvbsgeysqnvboyfyhlvafrdlnhrouskqxzztcoiqoxbzqzcfoozmlzbdrhvfccozwviafecbfubalvqstiztayuaezywxyvmrzvthpopxlvgvdfthwheagsboyvmadhmaruxltozhmiyjbpvqifxqbsvaaopybs\\nlbawrainjjdgkdmwkqzxxwlhzjyrxbuwjhnvjlnmgfyrxdynsanvibfhngsioisbyldapliuuqhebeicpsyerpiiqpjtnxvuotjv\\n\", \"bbbbccbaa\\nabbabd\\n\", \"codeforbes\\nedocfoecsof\\n\", \"bbabb\\naabbbbabbb\\n\", \"pfdempfohomnpgbfegikfmflnalbbajphpgeacaicoenopgnabnklheepnlnflohjegcciflmfjhachnhekckfjgoffhkblncidn\\nidlgklpclcghngeggpjdgefccihndpoikojdjnbkdfjgaanoolfmnifnmbpeeghpicehjdiipnlfnjpglidpnnnjfmjfhbcogojkcfflmmfcgajbjbfaikhmjofbnjnaolbcdkelcieeodbfjcfiblhhmeelmpcmmcdhjcnnfklgedjjbaljndjonanlojclboeemkab\\n\", \"xx{\\nxzzxxxxzzzxxxzzxxxzxxxzzxxzxxxzzxzxxzxxzxxzxzxxzxxxxzzxxzzxzzxxzzxxzxzxzxxzxzxyxxxzzxzzxxzxxxxzzxxxzxxxzxzxzzxzzxxxxzxxxzxz\\n\", \"babbaaaabb\\nbbaba\\n\", \"tsetnocrreeoc\\ncodeforcds\\n\", \"lltedxxjcqdkzvnvxugracluuvnwwbzddbxihcxsulvbsgeysqnvboyfyhlvafrdlnhrouskqxzztcoiqoxbzqzcfoozmlzbdrhvfccozwviafecbfubalvqstiztayuaezywxyvmrzvthpopxlvgvdfthwheagsboyvmadhm`ruxltozhmiyjbpvqifxqbsvaaopybs\\nlbawrainjjdgkdmwkqzxxwlhzjyrxbuwjhnvjlnmgfyrxdynsanvibfhngsioisbyldapliuuqhebeicpsyerpiiqpjtnxvuotjv\\n\", \"bbbbccbaa\\nbbaabd\\n\", \"codoferbes\\nedocfoecsof\\n\", \"zxzxzxzxzxzxzx\\ne\\n\", \"`b\\na\\n\", \"xzzxxxzxzzzxzzzxxzzxzzxzxzxxzxxzxxzxzzxxzxxzxxxzxzxzxxzzxxxxzxzzzxxxzxzxxxzzxxzxxzxxzzxxzxxzxzxzzzxzzzzxzxxzzxzxxzxxzzxzxzx\\nxzy\\n\", \"`\\nc\\n\", \"zwzxzxzxzxzxzx\\nd\\n\", \"ababbbab`a\\nababb\\n\", \"abaababbab\\nbbaba\\n\", \"b\\naa\\n\", \"b`\\na\\n\", \"b`\\naa\\n\", \"_\\nb\\n\", \"zwzxzxzx{xzxzx\\nd\\n\", \"c\\naa\\n\", \"b_\\na\\n\", \"b`\\nba\\n\", \"ac\\naccbb\\n\", \"xzzxyxzxzzzxzzzxxzzxzzxzxzxxzxxzxxzxzzxxzxxzxxxzxzxzxxzzxxxxzxzzzxxxzxzxxxzzxxzxxzxzzzxxzxxzxzxzzzxzzzzxzxxzxxzxxzxxzzxzxzx\\nxzy\\n\", \"_\\na\\n\", \"zwzxyxzx{xzxzx\\nd\\n\", \"ababbbab`a\\n`babb\\n\", \"c\\nba\\n\", \"_b\\na\\n\", \"codeforces\\nforceofcode\\n\", \"aa\\naa\\n\"], \"outputs\": [\"222\\n\", \"5\\n\", \"291\\n\", \"0\\n\", \"0\\n\", \"26774278\\n\", \"74\\n\", \"46917\\n\", \"75\\n\", \"39\\n\", \"1\\n\", \"8095\\n\", \"1\\n\", \"33\\n\", \"136\\n\", \"4\\n\", \"161\\n\", \"0\\n\", \"29632099\\n\", \"61\\n\", \"46538\\n\", \"68\\n\", \"38\\n\", \"1\\n\", \"6889\\n\", \"50\\n\", \"43\\n\", \"2\\n\", \"91\\n\", \"7\\n\", \"27452886\\n\", \"49017\\n\", \"26\\n\", \"6888\\n\", \"42\\n\", \"34\\n\", \"157\\n\", \"5\\n\", \"162\\n\", \"27885006\\n\", \"54\\n\", \"46969\\n\", \"60\\n\", \"24\\n\", \"6757\\n\", \"33\\n\", \"30\\n\", \"205\\n\", \"28538247\\n\", \"2774\\n\", \"55\\n\", \"21\\n\", \"6586\\n\", \"37\\n\", \"35\\n\", \"0\\n\", \"0\\n\", \"161\\n\", \"0\\n\", \"0\\n\", \"61\\n\", \"61\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"5\\n\", \"162\\n\", \"0\\n\", \"0\\n\", \"42\\n\", \"0\\n\", \"0\\n\", \"60\\n\", \"5\\n\"]}", "source": "primeintellect"} | One day Polycarpus got hold of two non-empty strings s and t, consisting of lowercase Latin letters. Polycarpus is quite good with strings, so he immediately wondered, how many different pairs of "x y" are there, such that x is a substring of string s, y is a subsequence of string t, and the content of x and y is the same. Two pairs are considered different, if they contain different substrings of string s or different subsequences of string t. Read the whole statement to understand the definition of different substrings and subsequences.
The length of string s is the number of characters in it. If we denote the length of the string s as |s|, we can write the string as s = s1s2... s|s|.
A substring of s is a non-empty string x = s[a... b] = sasa + 1... sb (1 ≤ a ≤ b ≤ |s|). For example, "code" and "force" are substrings or "codeforces", while "coders" is not. Two substrings s[a... b] and s[c... d] are considered to be different if a ≠ c or b ≠ d. For example, if s="codeforces", s[2...2] and s[6...6] are different, though their content is the same.
A subsequence of s is a non-empty string y = s[p1p2... p|y|] = sp1sp2... sp|y| (1 ≤ p1 < p2 < ... < p|y| ≤ |s|). For example, "coders" is a subsequence of "codeforces". Two subsequences u = s[p1p2... p|u|] and v = s[q1q2... q|v|] are considered different if the sequences p and q are different.
Input
The input consists of two lines. The first of them contains s (1 ≤ |s| ≤ 5000), and the second one contains t (1 ≤ |t| ≤ 5000). Both strings consist of lowercase Latin letters.
Output
Print a single number — the number of different pairs "x y" such that x is a substring of string s, y is a subsequence of string t, and the content of x and y is the same. As the answer can be rather large, print it modulo 1000000007 (109 + 7).
Examples
Input
aa
aa
Output
5
Input
codeforces
forceofcode
Output
60
Note
Let's write down all pairs "x y" that form the answer in the first sample: "s[1...1] t[1]", "s[2...2] t[1]", "s[1...1] t[2]","s[2...2] t[2]", "s[1...2] t[1 2]".
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.25 |
{"tests": "{\"inputs\": [\"5 3 10\\n1 2 3 4 5\\nRGBRR\\n\", \"2 1 15\\n5 6\\nRG\\n\", \"6 1 21\\n4 2 3 5 1 6\\nRGBGRB\\n\", \"6 1 21\\n6 5 4 3 2 1\\nRGBRGB\\n\", \"1 1 10\\n10\\nR\\n\", \"2 1 10\\n5 5\\nRG\\n\", \"2 1 10\\n5 6\\nRR\\n\", \"5 3 10\\n1 2 3 4 5\\nRGBRG\\n\", \"9 1 6\\n1 1 1 3 3 3 2 2 2\\nRGGBRRGBB\\n\", \"50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 10 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 33 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"50 32 600\\n21 21 18 47 16 11 10 46 9 15 27 5 11 42 29 25 16 41 31 8 12 28 1 24 17 40 45 12 33 32 34 2 45 17 49 17 20 42 15 17 8 29 2 20 4 27 50 1 49 1\\nBBRBBGBGBBRBGRRGRGGGBGBRRBBBGGBBBBGBGBRBBGRRGGBRGR\\n\", \"50 37 500\\n25 43 15 16 29 23 46 18 15 21 33 26 38 25 2 17 48 50 33 31 3 45 40 12 42 29 37 42 7 11 47 16 44 17 27 46 32 23 14 7 27 25 13 32 43 33 36 39 35 7\\nGGBBRGBRRRRBBRGBRRRGGRGGRGGBRRRGBBRRGRGGRBGBGGRGBR\\n\", \"50 4 200\\n14 10 50 47 41 9 22 21 42 36 50 10 27 28 39 1 36 12 45 35 17 3 15 25 32 4 34 39 44 34 20 15 18 1 38 25 20 45 24 9 18 15 35 36 12 9 28 4 44 10\\nBGBRRBGBRRRGRGRBRGGGRBRRGBBGGRBRRGGRGGGBRRBRGGBGBG\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"30 28 208\\n3 42 42 47 46 44 5 28 35 28 35 44 25 44 47 3 3 35 28 5 3 42 3 46 25 25 5 47 46 3\\nBGBBGBBBBGRRGGGBRGRGRRGBBRRRRG\\n\", \"39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 20 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 3 17 12 4 28 25 14 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n\", \"48 25 323\\n39 37 32 4 4 32 18 44 49 4 12 12 12 22 22 37 38 32 24 45 44 37 18 39 45 22 24 22 45 39 4 22 24 22 12 49 4 29 18 38 29 29 38 44 12 12 49 4\\nRRRRRBRRGBBRGRGGBGGBGBBBRBRGGGGBBRGRBGGGRBRBBRBG\\n\", \"48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 37 49 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"30 28 208\\n3 42 42 47 46 44 5 28 35 28 35 44 25 44 47 3 3 35 28 5 3 42 3 46 25 25 5 47 46 3\\nBGBBGBBBBGRRGGGBRGRGRRGBBRRRRG\\n\", \"50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 10 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n\", \"50 32 600\\n21 21 18 47 16 11 10 46 9 15 27 5 11 42 29 25 16 41 31 8 12 28 1 24 17 40 45 12 33 32 34 2 45 17 49 17 20 42 15 17 8 29 2 20 4 27 50 1 49 1\\nBBRBBGBGBBRBGRRGRGGGBGBRRBBBGGBBBBGBGBRBBGRRGGBRGR\\n\", \"48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 3 17 12 4 28 25 14 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n\", \"1 1 10\\n10\\nR\\n\", \"9 1 6\\n1 1 1 3 3 3 2 2 2\\nRGGBRRGBB\\n\", \"5 3 10\\n1 2 3 4 5\\nRGBRG\\n\", \"6 1 21\\n6 5 4 3 2 1\\nRGBRGB\\n\", \"2 1 10\\n5 5\\nRG\\n\", \"2 1 10\\n5 6\\nRR\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 37 49 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n\", \"48 25 323\\n39 37 32 4 4 32 18 44 49 4 12 12 12 22 22 37 38 32 24 45 44 37 18 39 45 22 24 22 45 39 4 22 24 22 12 49 4 29 18 38 29 29 38 44 12 12 49 4\\nRRRRRBRRGBBRGRGGBGGBGBBBRBRGGGGBBRGRBGGGRBRBBRBG\\n\", \"39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 20 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 33 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"50 4 200\\n14 10 50 47 41 9 22 21 42 36 50 10 27 28 39 1 36 12 45 35 17 3 15 25 32 4 34 39 44 34 20 15 18 1 38 25 20 45 24 9 18 15 35 36 12 9 28 4 44 10\\nBGBRRBGBRRRGRGRBRGGGRBRRGBBGGRBRRGGRGGGBRRBRGGBGBG\\n\", \"6 1 21\\n4 2 3 5 1 6\\nRGBGRB\\n\", \"50 37 500\\n25 43 15 16 29 23 46 18 15 21 33 26 38 25 2 17 48 50 33 31 3 45 40 12 42 29 37 42 7 11 47 16 44 17 27 46 32 23 14 7 27 25 13 32 43 33 36 39 35 7\\nGGBBRGBRRRRBBRGBRRRGGRGGRGGBRRRGBBRRGRGGRBGBGGRGBR\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 1 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n\", \"48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 3 17 12 4 28 25 21 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n\", \"9 1 6\\n1 1 2 3 3 3 2 2 2\\nRGGBRRGBB\\n\", \"2 1 10\\n9 5\\nRG\\n\", \"48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 37 2 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n\", \"39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"50 37 500\\n25 43 15 16 29 23 46 18 15 21 33 26 38 25 2 17 48 50 33 31 3 23 40 12 42 29 37 42 7 11 47 16 44 17 27 46 32 23 14 7 27 25 13 32 43 33 36 39 35 7\\nGGBBRGBRRRRBBRGBRRRGGRGGRGGBRRRGBBRRGRGGRBGBGGRGBR\\n\", \"39 36 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"30 28 208\\n3 42 42 47 46 12 5 28 35 28 35 44 25 44 47 3 3 35 28 5 3 42 3 46 25 25 5 47 46 3\\nBGBBGBBBBGRRGGGBRGRGRRGBBRRRRG\\n\", \"9 1 6\\n1 1 1 3 3 6 2 2 2\\nRGGBRRGBB\\n\", \"5 3 10\\n1 2 4 4 5\\nRGBRG\\n\", \"39 21 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 20 44 21 34 36 39 30 34 21 20 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"50 4 200\\n14 10 50 47 41 9 22 21 42 36 50 10 27 28 39 1 36 12 45 35 17 3 15 25 32 4 34 39 44 34 20 15 18 1 38 25 20 3 24 9 18 15 35 36 12 9 28 4 44 10\\nBGBRRBGBRRRGRGRBRGGGRBRRGBBGGRBRRGGRGGGBRRBRGGBGBG\\n\", \"6 1 21\\n6 5 4 3 4 1\\nRGBRGB\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"6 1 21\\n4 2 3 5 1 6\\nRGBRGB\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"2 1 24\\n5 6\\nRG\\n\", \"48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 27 5 46 12 6 46 3 17 12 4 28 25 21 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n\", \"9 1 6\\n1 1 2 5 3 3 2 2 2\\nRGGBRRGBB\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 15 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"6 1 21\\n4 2 3 5 1 6\\nBGRBGR\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"9 1 6\\n1 1 1 5 3 3 2 2 2\\nRGGBRRGBB\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"39 36 282\\n13 39 20 29 30 14 29 29 30 29 16 39 50 13 16 45 36 36 13 10 29 21 34 36 39 30 34 21 21 14 16 45 21 45 29 34 50 50 14\\nGGGBRRGRBGBRRBRGRBRBBGBGBGRRRGGRBBRGBGB\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 29 49 23 15 14 25 46 43 7 47 28 50 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"6 1 21\\n5 2 3 5 1 6\\nBGRBGR\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGGGGGGGGGGGGGGGGGGGGGGGGGRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"9 1 6\\n1 1 1 5 3 1 2 2 2\\nRGGBRRGBB\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 24 17 23 48 20 44 46 44 13 4 40 49 23 15 14 25 46 43 7 47 28 50 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 17 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 11 44 42 40 38 36 34 32 44 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGGGGGGGGGGGGGGGGGGGGGGGGGRRRRRRRRRRRRRRRRRRRRRRRRR\\n\", \"9 1 6\\n1 1 1 5 3 1 4 2 2\\nRGGBRRGBB\\n\", \"50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 10 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 50 2000\\n1 3 7 7 9 11 13 15 32 19 21 32 25 10 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 46 36 34 32 30 28 26 24 22 20 18 16 14 12 10 1 10 6 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"50 39 2000\\n48 43 26 24 46 37 15 30 39 34 4 14 29 34 8 18 40 8 17 40 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 10 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n\", \"48 2 259\\n25 31 22 30 30 17 31 50 28 30 46 43 4 6 10 22 50 14 5 46 12 6 46 4 17 12 4 28 25 14 5 5 6 14 22 12 17 43 43 10 4 3 31 3 25 28 50 10\\nBBBBGGRRBRRBBRGGGBGGRGBRBGRGRGRBBRRBRRGBGBGGGRBR\\n\", \"1 1 20\\n10\\nR\\n\", \"2 1 16\\n5 5\\nRG\\n\", \"2 1 10\\n1 6\\nRR\\n\", \"50 50 2000\\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 7 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nGRGRGBBGGRGGRRRGGBGGGRRRBGRRBGBRGBBGGGGRRGGBBRRRRG\\n\", \"48 33 357\\n18 37 22 21 4 17 39 32 40 43 29 29 50 21 39 43 11 11 4 50 36 40 32 50 18 32 11 36 29 36 22 21 29 43 49 18 17 29 37 40 17 43 49 4 39 49 22 29\\nGRGGGGBRBRRGGRGBRGBBGRBRRGBBRRBBBGRBBBBGRGGRRBRG\\n\", \"50 49 1000\\n30 37 34 31 26 44 32 12 36 15 5 5 31 24 17 24 43 19 17 23 45 2 31 17 23 48 20 44 46 44 13 4 29 49 33 41 14 25 46 43 7 47 28 25 2 30 37 37 19 32\\nGBBBRBGRBRBRGRGRBBGBGRRBGGRBGRBRRRRRRRBRGRGGGGBRGG\\n\", \"6 1 21\\n4 2 3 2 1 6\\nRGBGRB\\n\", \"50 50 1250\\n1 3 5 7 9 11 13 15 17 19 21 1 25 27 29 31 33 35 37 39 41 43 45 47 49 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2\\nRRRRRRRRRRRRRRRRRRRRRRRRRGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"2 1 15\\n5 1\\nRG\\n\", \"50 39 2000\\n48 43 26 24 46 37 15 30 36 34 4 14 29 34 8 18 40 8 17 37 15 29 2 23 41 7 12 13 36 11 24 22 26 46 11 31 1 46 11 35 6 41 16 50 11 1 46 20 46 28\\nBGBBBBBBRGGBBBRRRRBBGRGGRBBRBBBRBBBBBRRGBGGRRRBBRB\\n\", \"2 1 15\\n5 6\\nRG\\n\", \"5 3 10\\n1 2 3 4 5\\nRGBRR\\n\"], \"outputs\": [\"4\\n\", \"-1\\n\", \"15\\n\", \"10\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"7\\n\", \"-1\\n\", \"-1\\n\", \"185\\n\", \"86\\n\", \"23\\n\", \"992\\n\", \"20\\n\", \"24\\n\", \"39\\n\", \"64\\n\", \"63\\n\", \"-1\\n\", \"20\\n\", \"-1\\n\", \"185\\n\", \"39\\n\", \"0\\n\", \"7\\n\", \"2\\n\", \"10\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"63\\n\", \"64\\n\", \"24\\n\", \"-1\\n\", \"23\\n\", \"15\\n\", \"86\\n\", \"992\", \"-1\\n\", \"39\\n\", \"3\\n\", \"2\\n\", \"63\\n\", \"24\\n\", \"86\\n\", \"31\\n\", \"20\\n\", \"5\\n\", \"4\\n\", \"28\\n\", \"23\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"39\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"3\\n\", \"-1\\n\", \"31\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"39\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"63\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4\\n\"]}", "source": "taco"} | There are $n$ candy boxes in front of Tania. The boxes are arranged in a row from left to right, numbered from $1$ to $n$. The $i$-th box contains $r_i$ candies, candies have the color $c_i$ (the color can take one of three values — red, green, or blue). All candies inside a single box have the same color (and it is equal to $c_i$).
Initially, Tanya is next to the box number $s$. Tanya can move to the neighbor box (that is, with a number that differs by one) or eat candies in the current box. Tanya eats candies instantly, but the movement takes one second.
If Tanya eats candies from the box, then the box itself remains in place, but there is no more candies in it. In other words, Tanya always eats all the candies from the box and candies in the boxes are not refilled.
It is known that Tanya cannot eat candies of the same color one after another (that is, the colors of candies in two consecutive boxes from which she eats candies are always different). In addition, Tanya's appetite is constantly growing, so in each next box from which she eats candies, there should be strictly more candies than in the previous one.
Note that for the first box from which Tanya will eat candies, there are no restrictions on the color and number of candies.
Tanya wants to eat at least $k$ candies. What is the minimum number of seconds she will need? Remember that she eats candies instantly, and time is spent only on movements.
-----Input-----
The first line contains three integers $n$, $s$ and $k$ ($1 \le n \le 50$, $1 \le s \le n$, $1 \le k \le 2000$) — number of the boxes, initial position of Tanya and lower bound on number of candies to eat. The following line contains $n$ integers $r_i$ ($1 \le r_i \le 50$) — numbers of candies in the boxes. The third line contains sequence of $n$ letters 'R', 'G' and 'B', meaning the colors of candies in the correspondent boxes ('R' for red, 'G' for green, 'B' for blue). Recall that each box contains candies of only one color. The third line contains no spaces.
-----Output-----
Print minimal number of seconds to eat at least $k$ candies. If solution doesn't exist, print "-1".
-----Examples-----
Input
5 3 10
1 2 3 4 5
RGBRR
Output
4
Input
2 1 15
5 6
RG
Output
-1
-----Note-----
The sequence of actions of Tanya for the first example:
move from the box $3$ to the box $2$; eat candies from the box $2$; move from the box $2$ to the box $3$; eat candy from the box $3$; move from the box $3$ to the box $4$; move from the box $4$ to the box $5$; eat candies from the box $5$.
Since Tanya eats candy instantly, the required time is four seconds.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"9714431\", \"16612328\", \"23422731\", \"754526\", \"955577\", \"75547\", \"2112\", \"799\", \"88\", \"32523857\", \"4787\", \"1859551\", \"135661\", \"3675\", \"156692\", \"167918384\", \"83994\", \"4837847\", \"14513597\", \"15282598\", \"12659326\", \"1468417\", \"6280\", \"115464\", \"52376853\", \"2315\", \"3641224\", \"97187\", \"836\", \"195884\", \"36250\", \"2427817\", \"17598762\", \"5744554\", \"9295\", \"129848\", \"3863342\", \"3743\", \"133862\", \"1237\", \"1625\", \"1179729\", \"12651\", \"3776912\", \"4829\", \"73\", \"2228\", \"2546\", \"3136\", \"138\", \"3380\", \"4828\", \"3652\", \"5667\", \"7275\", \"774\", \"9329\", \"279\", \"15119\", \"200\", \"2461\", \"19\", \"2258\", \"31\", \"1250\", \"1216\", \"1595\", \"271\", \"236\", \"187\", \"166\", \"123\", \"231272\", \"12342923\", \"16587352\", \"32887158\", \"42478456\", \"353843\", \"1884868\", \"148239\", \"54241537\", \"213811\", \"3614\", \"1003\", \"177127860\", \"54250\", \"1720310\", \"6415742\", \"12117\", \"1293\", \"5541389\", \"44936\", \"550\", \"43448\", \"664\", \"39426\", \"5003285\", \"73925\", \"4379155\", \"2270\", \"123125129\", \"119138\", \"11121314\"], \"outputs\": [\"8\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"4\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"5\\n\", \"4\\n\", \"8\\n\", \"8\\n\", \"6\\n\", \"5\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"7\\n\", \"8\\n\", \"5\\n\", \"6\\n\", \"4\\n\", \"5\\n\", \"8\\n\", \"5\\n\", \"8\\n\", \"6\\n\", \"7\\n\", \"8\\n\", \"3\\n\", \"3\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"8\\n\", \"5\\n\", \"8\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"7\\n\", \"6\\n\", \"2\\n\", \"5\\n\", \"8\\n\", \"6\\n\", \"2\\n\", \"5\\n\", \"4\\n\", \"8\\n\", \"6\\n\", \"4\\n\", \"7\\n\", \"5\\n\", \"2\\n\", \"6\\n\", \"8\\n\", \"7\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"7\\n\", \"8\\n\", \"6\\n\", \"7\\n\", \"5\\n\", \"3\\n\", \"8\\n\", \"5\\n\", \"7\\n\", \"6\\n\", \"5\\n\", \"8\\n\", \"8\\n\", \"6\\n\", \"5\\n\", \"5\\n\", \"2\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"8\\n\", \"7\\n\", \"6\", \"5\", \"3\"]}", "source": "taco"} | If you visit Aizu Akabeko shrine, you will find a unique paper fortune on which a number with more than one digit is written.
Each digit ranges from 1 to 9 (zero is avoided because it is considered a bad omen in this shrine). Using this string of numeric values, you can predict how many years it will take before your dream comes true. Cut up the string into more than one segment and compare their values. The difference between the largest and smallest value will give you the number of years before your wish will be fulfilled. Therefore, the result varies depending on the way you cut up the string. For example, if you are given a string 11121314 and divide it into segments, say, as 1,11,21,3,14, then the difference between the largest and smallest is 21 - 1 = 20. Another division 11,12,13,14 produces 3 (i.e. 14 - 11) years. Any random division produces a game of luck. However, you can search the minimum number of years using a program.
Given a string of numerical characters, write a program to search the minimum years before your wish will be fulfilled.
Input
The input is given in the following format.
n
An integer n is given. Its number of digits is from 2 to 100,000, and each digit ranges from 1 to 9.
Output
Output the minimum number of years before your wish will be fulfilled.
Examples
Input
11121314
Output
3
Input
123125129
Output
6
Input
119138
Output
5
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[\"foefet\", \"toffee\"], [\"Buckethead\", \"DeathCubeK\"], [\"Twoo\", \"WooT\"], [\"dumble\", \"bumble\"], [\"ound\", \"round\"], [\"apple\", \"pale\"]], \"outputs\": [[true], [true], [true], [false], [false], [false]]}", "source": "taco"} | An **anagram** is the result of rearranging the letters of a word to produce a new word.
**Note:** anagrams are case insensitive
Complete the function to return `true` if the two arguments given are anagrams of each other; return `false` otherwise.
## Examples
* `"foefet"` is an anagram of `"toffee"`
* `"Buckethead"` is an anagram of `"DeathCubeK"`
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.125 |
{"tests": "{\"inputs\": [\"3\\n0 1 1\\n\", \"4\\n0 0 1 2\\n\", \"2\\n0 0\\n\", \"4\\n0 1 1 0\\n\", \"3\\n0 1 0\\n\", \"2\\n0 1\\n\", \"8\\n0 0 2 0 3 0 3 2\\n\", \"3\\n0 1 2\\n\", \"10\\n0 0 2 2 3 2 3 3 1 3\\n\", \"6\\n0 0 0 2 0 1\\n\", \"10\\n0 1 2 0 4 5 3 6 0 5\\n\", \"4\\n0 0 1 1\\n\", \"3\\n0 0 0\\n\", \"9\\n0 1 0 1 1 4 0 4 8\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 23 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"3\\n0 0 1\\n\", \"5\\n0 1 0 3 1\\n\", \"4\\n0 1 0 3\\n\", \"7\\n0 1 1 3 0 0 6\\n\", \"1\\n0\\n\", \"3\\n0 0 2\\n\", \"4\\n0 1 1 1\\n\", \"10\\n0 0 1 2 3 2 3 3 1 3\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"5\\n0 1 0 3 0\\n\", \"7\\n0 1 2 3 0 0 6\\n\", \"5\\n0 1 2 0 2\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"7\\n0 0 1 3 0 0 6\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 30 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"10\\n0 0 2 2 1 2 3 3 1 3\\n\", \"10\\n0 1 2 0 4 0 3 6 0 5\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 23 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 11 43 4\\n\", \"10\\n0 0 1 2 3 2 3 0 1 3\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 16 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 0 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 21 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 30 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 69 45 43 4\\n\", \"10\\n0 1 2 0 4 0 3 6 1 5\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 71 37 37 38 39 28 0 2 23 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 11 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 16 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 0 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 0 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 30 31 31 31 0 3 15 31 13 33 6 35 35 35 36 36 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 8 28 0 2 26 41 9 9 0 6 25 41 41 12 42 20 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 21 14 8 15 15 15 19 25 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 30 0 5 8 28 29 48 31 31 31 0 3 3 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 69 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 71 37 37 38 39 28 0 2 23 41 9 5 0 6 25 41 41 12 42 43 43 36 44 51 11 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 9 12 16 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 8 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 39 28 0 0 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 10 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 8 28 0 2 26 41 9 9 0 6 25 41 41 12 42 20 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 21 14 8 15 15 15 19 25 7 17 17 18 19 9 10 5 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 30 0 5 8 28 29 48 31 31 31 0 3 3 31 8 33 6 35 35 35 36 0 37 37 38 39 28 0 2 26 41 9 9 0 0 25 41 41 12 42 43 43 36 44 69 45 43 4\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 14 5 3 28 29 30 31 31 31 0 3 15 31 8 33 6 35 35 35 36 71 37 37 38 39 28 0 2 23 41 9 5 0 6 25 41 41 12 42 43 43 36 44 51 11 43 4\\n\", \"4\\n0 1 0 2\\n\", \"4\\n0 1 0 0\\n\", \"6\\n0 0 0 1 0 1\\n\", \"4\\n0 0 1 0\\n\", \"4\\n0 1 1 3\\n\", \"5\\n0 1 1 1 2\\n\", \"5\\n0 1 2 1 4\\n\", \"6\\n0 1 1 3 0 2\\n\", \"4\\n0 1 2 1\\n\", \"5\\n0 1 0 1 0\\n\", \"100\\n0 1 2 2 3 0 1 5 6 6 0 0 8 7 1 9 9 4 10 11 12 2 12 12 12 12 9 13 14 8 15 15 15 19 15 7 17 17 18 19 9 10 21 0 22 9 2 24 24 4 24 7 25 0 5 8 28 29 48 31 31 31 0 3 15 31 8 33 6 35 35 35 36 36 37 37 38 8 28 0 2 26 41 9 9 0 6 25 41 41 12 42 43 43 36 44 51 45 43 4\\n\", \"6\\n0 0 0 1 1 1\\n\", \"5\\n0 1 2 0 4\\n\", \"6\\n0 0 1 3 0 2\\n\", \"4\\n0 0 2 1\\n\", \"5\\n0 1 1 1 0\\n\", \"10\\n0 1 1 0 4 0 3 6 1 5\\n\", \"6\\n0 0 1 3 0 3\\n\", \"4\\n0 0 2 0\\n\", \"5\\n0 1 1 2 0\\n\", \"10\\n0 1 1 1 4 0 3 6 1 5\\n\", \"6\\n0 0 0 3 0 3\\n\", \"5\\n0 1 1 2 2\\n\", \"5\\n0 1 2 1 2\\n\", \"6\\n0 1 0 3 0 2\\n\"], \"outputs\": [\"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"7\\n\", \"0\\n\", \"4\\n\", \"4\\n\", \"12\\n\", \"0\\n\", \"0\\n\", \"17\\n\", \"761\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"10\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"3\\n\", \"758\\n\", \"5\\n\", \"9\\n\", \"2\\n\", \"772\\n\", \"11\\n\", \"1479\\n\", \"1515\\n\", \"1510\\n\", \"4\\n\", \"16\\n\", \"795\\n\", \"6\\n\", \"774\\n\", \"773\\n\", \"1549\\n\", \"1771\\n\", \"15\\n\", \"2658\\n\", \"776\\n\", \"768\\n\", \"1533\\n\", \"1543\\n\", \"1783\\n\", \"2662\\n\", \"779\\n\", \"1528\\n\", \"1559\\n\", \"1789\\n\", \"2667\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"2\\n\", \"1510\\n\", \"0\\n\", \"3\\n\", \"6\\n\", \"2\\n\", \"1\\n\", \"16\\n\", \"5\\n\", \"3\\n\", \"2\\n\", \"15\\n\", \"6\\n\", \"0\\n\", \"1\\n\", \"6\\n\"]}", "source": "taco"} | Arkady decides to observe a river for n consecutive days. The river's water level on each day is equal to some real value.
Arkady goes to the riverside each day and makes a mark on the side of the channel at the height of the water level, but if it coincides with a mark made before, no new mark is created. The water does not wash the marks away. Arkady writes down the number of marks strictly above the water level each day, on the i-th day this value is equal to mi.
Define di as the number of marks strictly under the water level on the i-th day. You are to find out the minimum possible sum of di over all days. There are no marks on the channel before the first day.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of days.
The second line contains n space-separated integers m1, m2, ..., mn (0 ≤ mi < i) — the number of marks strictly above the water on each day.
Output
Output one single integer — the minimum possible sum of the number of marks strictly below the water level among all days.
Examples
Input
6
0 1 0 3 0 2
Output
6
Input
5
0 1 2 1 2
Output
1
Input
5
0 1 1 2 2
Output
0
Note
In the first example, the following figure shows an optimal case.
<image>
Note that on day 3, a new mark should be created because if not, there cannot be 3 marks above water on day 4. The total number of marks underwater is 0 + 0 + 2 + 0 + 3 + 1 = 6.
In the second example, the following figure shows an optimal case.
<image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1 2 1\\n2 4 4\\n0 2 1\\n7 6 7\\n5 2 3\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n2 7 5\\n2 16 12\\n17 7 7\\n13 2 13\\n12 18 3\\n16 15 19\\n5 6 2\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n2 7 5\\n2 16 12\\n17 7 7\\n13 2 13\\n12 18 3\\n22 15 19\\n5 6 2\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n7953 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n2 7 5\\n2 16 12\\n17 7 7\\n13 2 3\\n12 18 3\\n22 15 19\\n5 6 2\", \"1 2 1\\n2 4 4\\n1 2 1\\n7 6 2\\n5 3 3\", \"3 3 2\\n16 17 1\\n2 7 5\\n2 16 12\\n17 7 7\\n13 2 3\\n12 13 3\\n22 15 19\\n5 6 2\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 7236 141577431\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 12598 141577431\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n61732 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 53151 327161251\\n58589 12598 141577431\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n61732 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 53151 327161251\\n58589 12598 141577431\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 53151 327161251\\n84495 18431 141577431\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 53151 327161251\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 1573 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289910583\\n50598 35195 478112689\\n8201 1573 103962455\\n9712 69657 699253752\\n74454 98144 468443709\\n2332 29437 87287886\\n18946 19060 845062869\\n60126 62114 382963164\", \"1 2 1\\n2 4 7\\n3 2 2\\n7 6 7\\n5 4 3\", \"3 3 2\\n16 17 1\\n2 7 2\\n2 0 12\\n17 7 7\\n13 2 10\\n12 18 3\\n16 15 26\\n5 6 2\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 261301742\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n42489 135203 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 115476935\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 11501 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n7953 69657 699253752\\n42489 36004 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n66232 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 85321 394223083\\n8801 53151 218424419\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 1573 103962455\\n9712 69657 699253752\\n74454 98144 468443709\\n2332 42580 87287886\\n39752 19060 845062869\\n60126 62114 570675168\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n110501 17565 289910583\\n50598 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n44255 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n105264 91167 245001003\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 261301742\\n58589 4337 796697686\\n66854 17565 289910583\\n5650 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n42489 135203 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 115476935\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n44701 35195 478112689\\n13919 1573 111724159\\n9712 69657 699253752\\n69352 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n104581 7236 796697686\\n57317 17565 289910583\\n69438 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 37860 845062869\\n60126 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 500599301\\n8801 53151 632227322\\n58589 12598 141577431\\n66854 17565 130159932\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n61732 98144 468443709\\n2332 42580 1492635034\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 53151 327161251\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 37174 468443709\\n2332 7005 752437097\\n39752 19060 845062869\\n40358 15102 382963164\", \"6 2 4\\n33189 159130 277349742\\n25568 46764 394223083\\n8801 53151 327161251\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 1573 103962455\\n9712 69657 699253752\\n74454 98144 468443709\\n2332 29437 87287886\\n18946 19060 715215246\\n60126 62114 124089072\", \"3 3 2\\n0 17 1\\n2 7 5\\n2 21 12\\n27 2 7\\n13 2 3\\n12 18 3\\n31 15 19\\n5 6 2\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n44701 35195 478112689\\n13919 1573 111724159\\n9712 69657 699253752\\n69352 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n72164 74101 382963164\", \"6 2 4\\n33189 87907 179450675\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 10425 199827665\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 1041467256\\n42489 98144 468443709\\n2332 42580 997425647\\n39752 19060 845062869\\n60126 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 7236 78600873\\n66854 17565 289910583\\n43805 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 36869 752437097\\n39752 27851 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 85321 394223083\\n8801 53151 3205876\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 1573 103962455\\n9712 69657 699253752\\n74454 98144 496532349\\n2332 42580 87287886\\n39752 19060 845062869\\n60126 62114 570675168\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n110501 17565 289910583\\n50598 35195 478112689\\n13919 118109 103962455\\n7953 69657 699253752\\n44255 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n105264 135743 245001003\", \"6 2 4\\n33189 88609 25397593\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 136264683\\n7953 69657 699253752\\n71858 98144 468443709\\n2332 27840 752437097\\n39752 19060 845062869\\n60126 80230 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 74934 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n44701 35195 478112689\\n13919 1573 111724159\\n9712 69657 699253752\\n69352 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n72164 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n104581 7236 886275317\\n57317 17565 289910583\\n69438 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 65491 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n0 3 5\\n2 20 12\\n17 7 7\\n13 2 3\\n12 13 2\\n22 15 22\\n9 6 1\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 656167279\\n8801 53151 624602328\\n58589 12598 214222412\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1283 103962455\\n9712 69657 699253752\\n59705 98144 468443709\\n2332 42580 752437097\\n7996 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 500599301\\n8801 53151 632227322\\n58589 12598 141577431\\n66854 17565 130159932\\n50598 35195 478112689\\n16833 1573 103962455\\n9712 69657 699253752\\n71970 98144 468443709\\n2332 42580 1492635034\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 102169 277349742\\n33905 46764 394223083\\n9873 53151 327161251\\n58589 12598 118670620\\n66854 17565 173583719\\n50598 35195 478112689\\n13919 1573 42293659\\n17814 69657 699253752\\n74454 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 657407748\\n6440 53151 213255275\\n84495 18431 141577431\\n66854 17565 100595605\\n50598 56534 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 107411 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8801 15308 327161251\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 37174 468443709\\n2332 7005 752437097\\n39752 19060 845062869\\n40358 25029 382963164\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n110501 17565 289910583\\n50598 35195 478112689\\n13919 53191 103962455\\n7953 69657 699253752\\n44255 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n105264 135743 245001003\", \"6 2 4\\n33189 88609 25397593\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 136264683\\n7953 69657 699253752\\n71858 132580 468443709\\n2332 27840 752437097\\n39752 19060 845062869\\n60126 80230 382963164\", \"3 3 2\\n16 17 1\\n2 7 5\\n3 12 12\\n17 9 7\\n13 2 13\\n12 18 0\\n22 15 2\\n6 6 0\", \"6 2 4\\n33189 60740 277349742\\n33905 46764 575306520\\n8801 53151 327161251\\n104581 7236 886275317\\n57317 17565 289910583\\n69438 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n39752 65491 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n0 3 5\\n2 20 12\\n17 7 7\\n13 2 3\\n12 17 2\\n22 15 22\\n9 6 1\", \"6 2 4\\n33189 148451 277349742\\n33905 46764 656167279\\n8801 53151 624602328\\n58589 12598 214222412\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1283 103962455\\n9712 69657 699253752\\n59705 98144 468443709\\n2332 42580 752437097\\n7996 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 500599301\\n8801 53151 632227322\\n58589 12598 141577431\\n66854 17565 130159932\\n50598 35195 478112689\\n16833 1573 103962455\\n9712 69657 699253752\\n71970 98144 468443709\\n2332 42580 1492635034\\n39752 19060 48797902\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 657407748\\n6440 53151 213255275\\n84495 18431 141577431\\n66854 17565 100595605\\n50598 56534 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 168808 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 394223083\\n8490 15308 327161251\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 37174 468443709\\n2332 7005 752437097\\n39752 19060 845062869\\n40358 25029 382963164\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 261301742\\n58589 4337 796697686\\n66854 17565 4018814\\n5650 35195 478112689\\n13919 88414 103962455\\n7953 69657 674703161\\n42489 135203 468443709\\n2332 42580 752437097\\n39752 34092 845062869\\n60126 21442 115476935\", \"6 2 4\\n33189 147435 25397593\\n33905 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 136264683\\n7953 69657 699253752\\n71858 132580 468443709\\n2332 27840 752437097\\n39752 19060 845062869\\n60126 80230 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n11508 53151 327161251\\n58589 1173 78600873\\n66854 17565 289910583\\n43805 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 36869 752437097\\n39752 26806 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 74934 327161251\\n38899 4337 796697686\\n66854 17565 289910583\\n44701 35195 478112689\\n16051 1573 111724159\\n9712 69657 699253752\\n69352 98144 468443709\\n2332 42580 752437097\\n21769 19060 845062869\\n72164 74101 382963164\", \"6 2 4\\n33189 148451 277349742\\n33905 30594 656167279\\n8801 53151 624602328\\n58589 12598 214222412\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 1283 103962455\\n9712 69657 699253752\\n59705 98144 468443709\\n2332 42580 1311285814\\n7996 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 57442 277349742\\n33905 46764 657407748\\n6440 53151 213255275\\n84495 18431 141577431\\n66854 17565 100595605\\n50598 56534 499531067\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 168808 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 39844 394223083\\n9170 53151 327161251\\n129926 526 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 2368 134806813\\n9712 69657 699253752\\n74454 98144 468443709\\n2144 42580 752437097\\n39752 19060 845062869\\n60126 62114 262490364\", \"3 3 2\\n29 17 2\\n2 7 5\\n3 12 12\\n21 9 7\\n13 2 13\\n12 18 0\\n22 15 2\\n6 6 0\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 45986694\\n58589 5487 305429394\\n66854 11501 289910583\\n50598 35195 478112689\\n13919 2504 103962455\\n7953 69657 699253752\\n42489 36004 343885277\\n1315 40284 752437097\\n39752 19060 845062869\\n66232 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 74934 327161251\\n38899 4337 796697686\\n66854 17565 289910583\\n44701 35195 478112689\\n25447 1573 111724159\\n9712 69657 699253752\\n69352 98144 468443709\\n2332 42580 752437097\\n21769 19060 845062869\\n72164 74101 382963164\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n11508 53151 327161251\\n58589 1173 78600873\\n66854 17565 289910583\\n43805 58381 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 36869 752437097\\n39752 26806 845062869\\n75132 62114 382963164\", \"6 2 4\\n33189 148451 277349742\\n33905 30594 656167279\\n8801 53151 624602328\\n58589 12598 214222412\\n66854 17565 289910583\\n50598 35195 478112689\\n26829 1283 103962455\\n9712 69657 699253752\\n59705 98144 468443709\\n2332 42580 1311285814\\n7996 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 102169 344107733\\n33905 46764 394223083\\n9873 53151 327161251\\n58589 12598 20784962\\n66854 34525 173583719\\n50598 35195 478112689\\n13919 1573 42293659\\n17814 69657 699253752\\n74454 98144 468443709\\n2332 42580 752437097\\n39752 19060 1438466979\\n60126 62114 382963164\", \"6 2 4\\n33189 57442 277349742\\n33905 46764 657407748\\n6440 53151 213255275\\n84495 18431 141577431\\n66854 17565 100595605\\n50598 56534 499531067\\n13919 1573 103962455\\n9712 69657 699253752\\n74454 266085 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 261301742\\n58589 4337 796697686\\n66854 17565 4018814\\n5650 35195 478112689\\n13919 88414 103962455\\n6505 69657 721009150\\n42275 135203 468443709\\n2332 42580 752437097\\n39752 34092 845062869\\n60126 21442 115476935\", \"3 3 2\\n29 17 2\\n2 7 5\\n3 12 12\\n21 9 7\\n13 2 15\\n12 18 0\\n22 15 2\\n6 6 0\", \"3 3 2\\n1 17 1\\n2 7 5\\n2 21 0\\n27 1 7\\n13 2 3\\n12 26 3\\n31 1 19\\n5 6 2\", \"6 2 4\\n33189 60740 277349742\\n33905 29724 575306520\\n8801 53151 327161251\\n104581 7236 886275317\\n68908 15379 289910583\\n69438 35195 478112689\\n13919 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 42580 752437097\\n63908 65491 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n0 3 5\\n0 20 12\\n17 7 7\\n5 2 2\\n12 17 2\\n22 15 22\\n14 6 1\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n11508 53151 327161251\\n58589 1173 78600873\\n66854 17565 289910583\\n43805 58381 478112689\\n9339 1573 103962455\\n9712 69657 699253752\\n42489 98144 468443709\\n2332 36869 752437097\\n39752 26806 845062869\\n75132 62114 382963164\", \"6 2 4\\n33189 87907 402986692\\n21176 46764 500599301\\n8801 53151 1210998588\\n58589 12598 141577431\\n66854 17565 130159932\\n50598 35195 478112689\\n16833 1573 103962455\\n9712 69657 699253752\\n71970 98144 468443709\\n1018 42580 1492635034\\n39752 19060 48797902\\n60126 62114 382963164\", \"6 2 4\\n33189 87907 530443197\\n33905 85321 394223083\\n8801 27804 4040527\\n84495 18431 141577431\\n66854 32775 289910583\\n50598 35195 478112689\\n8201 1573 103962455\\n9712 69657 699253752\\n119260 98144 496532349\\n2332 42580 74611723\\n39752 22945 845062869\\n60126 62114 570675168\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n12506 53151 261301742\\n58589 4337 796697686\\n66854 17565 4018814\\n5650 35195 478112689\\n13919 88414 103962455\\n6505 69657 721009150\\n42275 135203 468443709\\n2332 42580 752437097\\n39752 34092 845062869\\n60126 21442 115476935\", \"6 2 4\\n33189 87907 277349742\\n33905 46764 575306520\\n8801 53151 45986694\\n58589 5487 305429394\\n66854 11501 289910583\\n50598 35195 478112689\\n13919 2504 103962455\\n7953 69657 699253752\\n42489 36004 275737389\\n1315 40284 143834229\\n39752 19060 845062869\\n66232 74101 382963164\", \"3 3 2\\n1 17 1\\n2 7 5\\n2 21 0\\n27 1 7\\n23 2 3\\n12 26 3\\n31 1 19\\n5 6 2\", \"1 2 1\\n2 4 4\\n3 2 1\\n7 6 7\\n5 2 3\", \"6 2 4\\n33189 87907 277349742\\n71616 46764 575306520\\n8801 53151 327161251\\n58589 4337 796697686\\n66854 17565 289910583\\n50598 35195 478112689\\n13919 88414 103962455\\n7953 69657 699253752\\n44255 98144 468443709\\n2332 42580 752437097\\n39752 19060 845062869\\n60126 74101 382963164\", \"3 3 2\\n16 17 1\\n2 7 5\\n2 16 12\\n17 7 7\\n13 2 10\\n12 18 3\\n16 15 19\\n5 6 2\"], \"outputs\": [\"18\\n\", \"3093929146\\n\", \"111\\n\", \"3093891435\\n\", \"113\\n\", \"3093871658\\n\", \"110\\n\", \"17\\n\", \"105\\n\", \"2872505176\\n\", \"2872513114\\n\", \"2775302590\\n\", \"2775315312\\n\", \"2775341218\\n\", \"2775335500\\n\", \"2491269990\\n\", \"2491261653\\n\", \"3093929975\\n\", \"108\\n\", \"19\\n\", \"22\\n\", \"3093877764\\n\", \"119\\n\", \"16\\n\", \"3093863555\\n\", \"109\\n\", \"3214718680\\n\", \"2872514554\\n\", \"2929451082\\n\", \"3093975113\\n\", \"23\\n\", \"124\\n\", \"3093879113\\n\", \"106\\n\", \"3093862121\\n\", \"2953373873\\n\", \"2958089934\\n\", \"2491277056\\n\", \"2491332876\\n\", \"20\\n\", \"115\\n\", \"3093966205\\n\", \"3093866459\\n\", \"2593522843\\n\", \"3094018760\\n\", \"3093921257\\n\", \"3093881319\\n\", \"3093880961\\n\", \"3669649019\\n\", \"2775321450\\n\", \"2361485253\\n\", \"134\\n\", \"3093893357\\n\", \"3459707230\\n\", \"2872498383\\n\", \"2611918647\\n\", \"3094048455\\n\", \"3093920569\\n\", \"3093915140\\n\", \"3183458592\\n\", \"116\\n\", \"2953371846\\n\", \"3669651933\\n\", \"2775329574\\n\", \"2954652970\\n\", \"2775289959\\n\", \"3093998154\\n\", \"3093925871\\n\", \"112\\n\", \"3183448224\\n\", \"120\\n\", \"2953432390\\n\", \"3325194212\\n\", \"2954700613\\n\", \"2775289648\\n\", \"3069370666\\n\", \"3093979395\\n\", \"2872501090\\n\", \"3093917272\\n\", \"3512281107\\n\", \"2954692606\\n\", \"2775380931\\n\", \"128\\n\", \"2872499977\\n\", \"3093926668\\n\", \"2872516096\\n\", \"3512294017\\n\", \"3368733684\\n\", \"2954789883\\n\", \"3115676655\\n\", \"130\\n\", \"142\\n\", \"3183459815\\n\", \"117\\n\", \"2872511516\\n\", \"3903965478\\n\", \"2645901096\\n\", \"3115680360\\n\", \"2598126286\\n\", \"152\\n\", \"18\", \"3093929975\", \"110\"]}", "source": "taco"} | There are X+Y+Z people, conveniently numbered 1 through X+Y+Z. Person i has A_i gold coins, B_i silver coins and C_i bronze coins.
Snuke is thinking of getting gold coins from X of those people, silver coins from Y of the people and bronze coins from Z of the people. It is not possible to get two or more different colors of coins from a single person. On the other hand, a person will give all of his/her coins of the color specified by Snuke.
Snuke would like to maximize the total number of coins of all colors he gets. Find the maximum possible number of coins.
Constraints
* 1 \leq X
* 1 \leq Y
* 1 \leq Z
* X+Y+Z \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* 1 \leq C_i \leq 10^9
Input
Input is given from Standard Input in the following format:
X Y Z
A_1 B_1 C_1
A_2 B_2 C_2
:
A_{X+Y+Z} B_{X+Y+Z} C_{X+Y+Z}
Output
Print the maximum possible total number of coins of all colors he gets.
Examples
Input
1 2 1
2 4 4
3 2 1
7 6 7
5 2 3
Output
18
Input
3 3 2
16 17 1
2 7 5
2 16 12
17 7 7
13 2 10
12 18 3
16 15 19
5 6 2
Output
110
Input
6 2 4
33189 87907 277349742
71616 46764 575306520
8801 53151 327161251
58589 4337 796697686
66854 17565 289910583
50598 35195 478112689
13919 88414 103962455
7953 69657 699253752
44255 98144 468443709
2332 42580 752437097
39752 19060 845062869
60126 74101 382963164
Output
3093929975
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"7 6\\nAlena\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\nMariana\\nAlena John\\nAlena Alice\\nOlya John\\nOlya Alice\\nVanya John\\nVanya Alice\\n\", \"7 6\\nj\\nZ\\nPZNeTyY\\nm\\na\\nUj\\nsuaaSiKcK\\nUj PZNeTyY\\na j\\nPZNeTyY Z\\nPZNeTyY j\\nm PZNeTyY\\nm j\\n\", \"15 3\\na\\nYclKFJoaIA\\nhalYcB\\nbLOlPzAeQ\\ntckjt\\noDFijpx\\nb\\npz\\nVDLb\\nlCEHPibt\\noF\\npzJD\\nMC\\nqklsX\\nTAU\\npzJD tckjt\\nqklsX oF\\nMC pzJD\\n\", \"8 6\\nU\\nC\\nPEElYwaxf\\nVubTXNI\\nJ\\nIxZUHV\\nhLNFnzmqFE\\nDPPvwuWvmA\\nhLNFnzmqFE IxZUHV\\nIxZUHV C\\nJ PEElYwaxf\\nIxZUHV PEElYwaxf\\nPEElYwaxf C\\nJ VubTXNI\\n\", \"2 0\\nAndrey\\nTaras\\n\", \"4 2\\nadQx\\nrJGeodBycK\\ntgPYZk\\ncz\\ncz tgPYZk\\nrJGeodBycK adQx\\n\", \"16 37\\ntIWi\\nq\\nIEAYCq\\nXozwkum\\nCC\\niPwfd\\nS\\nXEf\\nWqEiwkH\\nWX\\ne\\nltmruh\\nKGx\\nauTUYZRC\\nmeJa\\nM\\nmeJa q\\nKGx e\\nXEf Xozwkum\\ne q\\nauTUYZRC KGx\\ne CC\\nM CC\\nM meJa\\nWX CC\\nWqEiwkH IEAYCq\\nauTUYZRC WqEiwkH\\nKGx WX\\nmeJa KGx\\nXEf q\\nauTUYZRC XEf\\nauTUYZRC IEAYCq\\nWX XEf\\nM XEf\\nWqEiwkH q\\nM KGx\\nKGx CC\\nM e\\nWqEiwkH Xozwkum\\nCC q\\nS Xozwkum\\nKGx tIWi\\nWX q\\nXEf S\\nauTUYZRC S\\nCC IEAYCq\\nKGx IEAYCq\\ne WqEiwkH\\nM S\\nauTUYZRC q\\nS tIWi\\nM ltmruh\\nM iPwfd\\n\", \"16 11\\ntulhZxeKgo\\nbrAXY\\nyQUkaihDAg\\nmwjlDVaktK\\nweVtBIP\\nzRwb\\nds\\nhXPfJrL\\nAdIfP\\nazQeXn\\nB\\nJlmscIUOxO\\nZuxr\\nV\\nOfyLIUO\\nuaMl\\nhXPfJrL yQUkaihDAg\\nweVtBIP yQUkaihDAg\\nazQeXn hXPfJrL\\nV tulhZxeKgo\\nzRwb yQUkaihDAg\\nds mwjlDVaktK\\nzRwb brAXY\\nyQUkaihDAg brAXY\\nB yQUkaihDAg\\nAdIfP mwjlDVaktK\\nbrAXY tulhZxeKgo\\n\", \"6 1\\nuPVIuLBuYM\\nVejWyKCtbN\\nqqjgF\\nulBD\\nDRNzxJU\\nCOzbXWOt\\nulBD qqjgF\\n\", \"5 1\\nWEYUdpYmZp\\nfhNmMpjr\\nydARivBg\\ncilTtE\\nyeXxkhPzB\\nyeXxkhPzB cilTtE\\n\", \"16 8\\nJIo\\nINanHVnP\\nKaxyCBWt\\nkVfnsz\\nRAwFYCrSvI\\nF\\nvIEWWIvh\\nTGF\\nFeuhJJwJ\\nTngcmS\\nSqI\\nRmcaVngp\\neGwhme\\nlwaFfXzM\\noabGmpvVH\\nTMT\\nFeuhJJwJ F\\neGwhme FeuhJJwJ\\nRmcaVngp SqI\\nINanHVnP JIo\\nSqI FeuhJJwJ\\nF kVfnsz\\nTGF F\\nTMT TGF\\n\", \"15 8\\ncXeOANpvBF\\nbkeDfi\\nnsEUAKNxQI\\noSIb\\naU\\nXYXYVo\\nduZQ\\naPkr\\nPVrHpL\\nmVgmv\\nhHhukllwbf\\nGkNPGYVxjY\\nbgBjA\\nslNKCLIlOv\\nmPILXy\\nbgBjA cXeOANpvBF\\nGkNPGYVxjY cXeOANpvBF\\nslNKCLIlOv GkNPGYVxjY\\nGkNPGYVxjY mVgmv\\nXYXYVo cXeOANpvBF\\nslNKCLIlOv bkeDfi\\nmVgmv aPkr\\nslNKCLIlOv nsEUAKNxQI\\n\", \"8 12\\nBkgxqAF\\nKhq\\nNpIfk\\nkheqUyDVG\\niRBkHlRpp\\nZDaQY\\nNG\\nqN\\nqN BkgxqAF\\nNpIfk BkgxqAF\\niRBkHlRpp BkgxqAF\\niRBkHlRpp NpIfk\\nNG Khq\\niRBkHlRpp Khq\\nNG ZDaQY\\nNG iRBkHlRpp\\nNG NpIfk\\nqN Khq\\nZDaQY kheqUyDVG\\nNpIfk Khq\\n\", \"7 12\\nPasha\\nLesha\\nVanya\\nTaras\\nNikita\\nSergey\\nAndrey\\nPasha Taras\\nPasha Nikita\\nPasha Andrey\\nPasha Sergey\\nLesha Taras\\nLesha Nikita\\nLesha Andrey\\nLesha Sergey\\nVanya Taras\\nVanya Nikita\\nVanya Andrey\\nVanya Sergey\\n\", \"3 0\\nr\\nyVwqs\\nsdTDerOyhp\\n\", \"7 14\\nFXCT\\nn\\no\\nS\\nMdFuonu\\nmszv\\nbqScOCw\\nS o\\nbqScOCw FXCT\\nMdFuonu o\\no n\\nbqScOCw n\\nmszv S\\nbqScOCw MdFuonu\\nmszv n\\nS FXCT\\nbqScOCw o\\no FXCT\\nmszv MdFuonu\\nmszv FXCT\\nbqScOCw mszv\\n\", \"9 6\\nfLfek\\nEQPcotnrp\\nCaAlbwoIL\\nVG\\nNAZKIBiKT\\noFy\\njFluh\\nKqHXRNya\\nQSwgobA\\noFy EQPcotnrp\\nKqHXRNya jFluh\\noFy NAZKIBiKT\\njFluh oFy\\njFluh fLfek\\noFy fLfek\\n\", \"16 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nAlena\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\n\", \"9 5\\nRFiow\\naxgvtiBGbx\\ngGBVZtI\\nVWAxrqx\\nmnASVEQI\\ntZHzWGAvXc\\nBeaCYhIRLy\\nhTdUL\\nFJd\\nhTdUL RFiow\\nhTdUL gGBVZtI\\nFJd axgvtiBGbx\\nFJd BeaCYhIRLy\\nhTdUL axgvtiBGbx\\n\", \"5 2\\niBrgNFlNXd\\nlnGPIV\\nnb\\nB\\nVgqRcEOG\\nlnGPIV iBrgNFlNXd\\nB iBrgNFlNXd\\n\", \"2 1\\ncLWdg\\nGoWegdDRp\\nGoWegdDRp cLWdg\\n\", \"9 14\\nmoRNeufngu\\nBSKI\\nzXl\\ngwmIDluW\\nYFn\\nHvasEgl\\nXcAC\\neVP\\nAiOm\\neVP BSKI\\neVP YFn\\nHvasEgl YFn\\neVP XcAC\\nAiOm HvasEgl\\nXcAC YFn\\nzXl moRNeufngu\\neVP zXl\\nHvasEgl BSKI\\nXcAC gwmIDluW\\nXcAC HvasEgl\\nYFn moRNeufngu\\nzXl BSKI\\nHvasEgl gwmIDluW\\n\", \"12 12\\njWuGgOjV\\nWs\\njTZQMyH\\nULp\\nUfsnPRt\\nk\\nbPKrnP\\nW\\nJOaQdgglDG\\nAodc\\ncpRjAUyYIW\\nMrjB\\nbPKrnP ULp\\nk Ws\\ncpRjAUyYIW k\\nULp jTZQMyH\\nbPKrnP jWuGgOjV\\ncpRjAUyYIW jTZQMyH\\nW ULp\\nk jTZQMyH\\nk ULp\\nMrjB ULp\\ncpRjAUyYIW Aodc\\nW k\\n\", \"16 25\\nbBZ\\nEr\\nZ\\nrYJmfZLgmx\\nPaJNrF\\naHtRqSxOO\\nD\\nhsagsG\\nMDuBOXrmWH\\nSgjMQZ\\nYXgWq\\nxDwpppG\\nSDY\\nJwZWx\\ncOzrgrBaE\\nFJYX\\nYXgWq SgjMQZ\\nSDY PaJNrF\\nFJYX rYJmfZLgmx\\nhsagsG Er\\nxDwpppG rYJmfZLgmx\\naHtRqSxOO rYJmfZLgmx\\nhsagsG bBZ\\nJwZWx hsagsG\\nFJYX cOzrgrBaE\\nSDY YXgWq\\nFJYX Z\\nJwZWx rYJmfZLgmx\\nD rYJmfZLgmx\\nYXgWq Z\\nrYJmfZLgmx Z\\naHtRqSxOO bBZ\\nSDY rYJmfZLgmx\\ncOzrgrBaE D\\nYXgWq hsagsG\\nSDY aHtRqSxOO\\ncOzrgrBaE xDwpppG\\nSDY bBZ\\nSDY Er\\nJwZWx xDwpppG\\nFJYX JwZWx\\n\", \"9 13\\nYiUXqlBUx\\nQNgYuX\\ndPtyZ\\nITtwRJCv\\nLJ\\nrAG\\nOgxNq\\nsitechE\\nvVAAz\\nOgxNq QNgYuX\\nOgxNq dPtyZ\\nsitechE rAG\\nLJ QNgYuX\\nQNgYuX YiUXqlBUx\\nOgxNq LJ\\nvVAAz OgxNq\\nrAG dPtyZ\\nvVAAz LJ\\nvVAAz ITtwRJCv\\nsitechE LJ\\nrAG YiUXqlBUx\\nsitechE QNgYuX\\n\", \"3 3\\nvRVatwL\\nWmkUGiYEn\\nuvvsXKXcJ\\nWmkUGiYEn vRVatwL\\nuvvsXKXcJ vRVatwL\\nuvvsXKXcJ WmkUGiYEn\\n\", \"11 13\\ncZAMfd\\nSWQnweM\\nKlQW\\nWRsnNZT\\nix\\nUC\\nLWqsVHcWec\\nfeb\\ncBy\\ntvk\\nRXDlX\\nfeb SWQnweM\\ncBy WRsnNZT\\nLWqsVHcWec KlQW\\nRXDlX feb\\nLWqsVHcWec cZAMfd\\ncBy UC\\nWRsnNZT SWQnweM\\nRXDlX cBy\\ntvk UC\\ncBy SWQnweM\\nUC KlQW\\nRXDlX KlQW\\nUC WRsnNZT\\n\", \"2 0\\nNgzlPJgFgz\\nQfpagVpWz\\n\", \"16 11\\njA\\nkyRNTE\\neY\\nToLcqN\\nbnenhMxiK\\nzlkOe\\nXCKZ\\neaQrds\\nqUdInpi\\nKgPQA\\nmQIl\\ninOCWEZHxy\\nyA\\nPIZRMOu\\nXtueKFM\\nfRNwNn\\ninOCWEZHxy qUdInpi\\nKgPQA zlkOe\\ninOCWEZHxy KgPQA\\nfRNwNn XCKZ\\ninOCWEZHxy eY\\nyA mQIl\\ninOCWEZHxy ToLcqN\\nyA KgPQA\\nqUdInpi ToLcqN\\nqUdInpi eaQrds\\nPIZRMOu eY\\n\", \"4 2\\noVemoZhjW\\nHspFEry\\nhFO\\njxt\\nhFO HspFEry\\njxt oVemoZhjW\\n\", \"5 10\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nTaras Romka\\nTaras Nikita\\nTaras Sergey\\nTaras Andrey\\nRomka Nikita\\nRomka Sergey\\nRomka Andrey\\nNikita Sergey\\nNikita Andrey\\nSergey Andrey\\n\", \"6 6\\nAlena\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\nAlena John\\nAlena Alice\\nOlya John\\nOlya Alice\\nVanya John\\nVanya Alice\\n\", \"1 0\\nPetr\\n\", \"6 9\\noySkmhCD\\nUIKWj\\nmHolKkBx\\nQBikssqz\\nZ\\nzoFUJYa\\nZ UIKWj\\nQBikssqz oySkmhCD\\nQBikssqz UIKWj\\nZ oySkmhCD\\nzoFUJYa UIKWj\\nzoFUJYa Z\\nzoFUJYa mHolKkBx\\nzoFUJYa QBikssqz\\nQBikssqz mHolKkBx\\n\", \"11 17\\njFTNgFBO\\ntZDgmdF\\nIjeDjoj\\nBEMAaYkNb\\nRZRQl\\ntK\\nlNHWt\\nIdG\\nLAbVLYiY\\notOBsWqJuo\\nUoTy\\ntK BEMAaYkNb\\nBEMAaYkNb jFTNgFBO\\nIjeDjoj tZDgmdF\\nRZRQl jFTNgFBO\\nlNHWt tZDgmdF\\nRZRQl tZDgmdF\\nUoTy LAbVLYiY\\nBEMAaYkNb IjeDjoj\\nIdG BEMAaYkNb\\nLAbVLYiY tK\\nLAbVLYiY jFTNgFBO\\nUoTy IjeDjoj\\nlNHWt jFTNgFBO\\nlNHWt BEMAaYkNb\\ntK IjeDjoj\\nUoTy RZRQl\\nBEMAaYkNb tZDgmdF\\n\", \"15 3\\na\\nYcJKFloaIA\\nhalYcB\\nbLOlPzAeQ\\ntckjt\\noDFijpx\\nb\\npz\\nVDLb\\nlCEHPibt\\noF\\npzJD\\nMC\\nqklsX\\nTAU\\npzJD tckjt\\nqklsX oF\\nMC pzJD\\n\", \"2 0\\nAndrey\\nTar`s\\n\", \"16 8\\nJIo\\nINanHVnP\\nKaxyCBWt\\nkVfnsz\\nRAwFYCrSvI\\nF\\nvIEWWIvh\\nTGF\\nFeuhJJwJ\\nSmcgnT\\nSqI\\nRmcaVngp\\neGwhme\\nlwaFfXzM\\noabGmpvVH\\nTMT\\nFeuhJJwJ F\\neGwhme FeuhJJwJ\\nRmcaVngp SqI\\nINanHVnP JIo\\nSqI FeuhJJwJ\\nF kVfnsz\\nTGF F\\nTMT TGF\\n\", \"3 0\\nr\\nyVwqs\\nphyOreDTds\\n\", \"9 6\\nfLfek\\nEQPcotnrp\\nCaAlbwoIL\\nGV\\nNAZKIBiKT\\noFy\\njFluh\\nKqHXRNya\\nQSwgobA\\noFy EQPcotnrp\\nKqHXRNya jFluh\\noFy NAZKIBiKT\\njFluh oFy\\njFluh fLfek\\noFy fLfek\\n\", \"16 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nanelA\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\n\", \"9 5\\nRFiow\\naxgvtiBGbx\\ngGBVZtI\\nVWAxrqx\\nAnmSVEQI\\ntZHzWGAvXc\\nBeaCYhIRLy\\nhTdUL\\nFJd\\nhTdUL RFiow\\nhTdUL gGBVZtI\\nFJd axgvtiBGbx\\nFJd BeaCYhIRLy\\nhTdUL axgvtiBGbx\\n\", \"2 0\\nNgzlPJzFgg\\nQfpagVpWz\\n\", \"1 0\\nePtr\\n\", \"2 0\\nAodrey\\nTar`s\\n\", \"3 0\\nr\\nzVwqs\\nsdTDerOyhp\\n\", \"1 0\\nrPte\\n\", \"3 0\\ns\\nzVwqs\\nsdTDerOyhp\\n\", \"3 0\\ns\\nzVqws\\nsdTDerOyhp\\n\", \"3 0\\ns\\nzVqws\\nrdTDesOyhp\\n\", \"2 0\\nAnerey\\nTaras\\n\", \"6 1\\nuPVIuLBuYM\\nVejWyKCtbN\\nqqjgF\\nulBD\\nDRNzxJU\\nCOzbXXOt\\nulBD qqjgF\\n\", \"3 0\\ns\\nyVwqs\\nsdTDerOyhp\\n\", \"16 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\n\", \"9 5\\nRFiow\\naxgvtiBGbx\\ngGBVZtI\\nVWBxrqx\\nmnASVEQI\\ntZHzWGAvXc\\nBeaCYhIRLy\\nhTdUL\\nFJd\\nhTdUL RFiow\\nhTdUL gGBVZtI\\nFJd axgvtiBGbx\\nFJd BeaCYhIRLy\\nhTdUL axgvtiBGbx\\n\", \"3 2\\nvRVatwL\\nWmkUGiYEn\\nuvvsXKXcJ\\nWmkUGiYEn vRVatwL\\nuvvsXKXcJ vRVatwL\\nuvvsXKXcJ WmkUGiYEn\\n\", \"6 6\\nAlena\\nOlya\\nVanya\\nBrvs\\nJohn\\nAlice\\nAlena John\\nAlena Alice\\nOlya John\\nOlya Alice\\nVanya John\\nVanya Alice\\n\", \"1 0\\nPdtr\\n\", \"11 17\\njFTNgFBO\\ntZDgmdF\\nIjeDjoj\\nBEMAaYkNb\\nRZRQl\\ntK\\nlNHWt\\nIdG\\nLAbVLYiY\\notOBsWqJvo\\nUoTy\\ntK BEMAaYkNb\\nBEMAaYkNb jFTNgFBO\\nIjeDjoj tZDgmdF\\nRZRQl jFTNgFBO\\nlNHWt tZDgmdF\\nRZRQl tZDgmdF\\nUoTy LAbVLYiY\\nBEMAaYkNb IjeDjoj\\nIdG BEMAaYkNb\\nLAbVLYiY tK\\nLAbVLYiY jFTNgFBO\\nUoTy IjeDjoj\\nlNHWt jFTNgFBO\\nlNHWt BEMAaYkNb\\ntK IjeDjoj\\nUoTy RZRQl\\nBEMAaYkNb tZDgmdF\\n\", \"3 0\\nPasha\\nLeshb\\nVanya\\n\", \"3 0\\nr\\nyVxqs\\nphyOreDTds\\n\", \"3 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nanelA\\nOlya\\nVanya\\nBrus\\nJohn\\nAlice\\n\", \"1 0\\nrtPe\\n\", \"2 0\\nAodsey\\nTar`s\\n\", \"3 0\\nr\\nzVwqs\\nphyOreDTds\\n\", \"1 0\\nrOte\\n\", \"3 0\\nt\\nzVwqs\\nsdTDerOyhp\\n\", \"2 0\\ns\\nzVqws\\nrdTDesOyhp\\n\", \"2 0\\nAnerey\\nTarar\\n\", \"6 1\\nuPVIuLBuYM\\nVejWyKCtbN\\nqqjgF\\nulBD\\nDRNzxJU\\nCOzbWXOt\\nulBD qqjgF\\n\", \"16 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nnaVya\\nBrus\\nJohn\\nAlice\\n\", \"1 0\\nPdts\\n\", \"3 0\\nPasha\\nbhseL\\nVanya\\n\", \"3 0\\nr\\nyVqxs\\nphyOreDTds\\n\", \"1 0\\nrtPd\\n\", \"3 0\\nr\\nzVwqs\\nseTDdrOyhp\\n\", \"1 0\\nAnerey\\nTarar\\n\", \"16 0\\nTaras\\nNikita\\nSergey\\nyndreA\\nRomka\\nAlexey\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nnaVya\\nBrus\\nJohn\\nAlice\\n\", \"1 0\\nPdss\\n\", \"1 0\\nPasha\\nbhseL\\nVanya\\n\", \"3 0\\nTar`s\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nanelA\\nOlya\\naynaV\\nBrus\\nJohn\\nAlice\\n\", \"3 0\\nq\\nzVwqs\\nseTDdrOyhp\\n\", \"16 0\\nTaras\\nNikita\\nSerfey\\nyndreA\\nRomka\\nAlexey\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nnaVya\\nBrus\\nJohn\\nAlice\\n\", \"1 0\\nPssd\\n\", \"16 0\\nTaras\\nNikita\\nSerfey\\nyndreA\\nRomka\\nyexelA\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nnaVya\\nBrus\\nJohn\\nAlice\\n\", \"1 0\\nsaPha\\nbhseL\\naynaV\\n\", \"16 0\\nTaras\\nNikita\\nSerfey\\nAerdny\\nRomka\\nyexelA\\nUra\\nsineD\\nEgor\\nVadim\\nAlena\\nOlya\\nnaVya\\nBrus\\nJohn\\nAlice\\n\", \"3 0\\nTaras\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nanelA\\nOlya\\naynaV\\nBrus\\nJohn\\nAlice\\n\", \"2 0\\ns\\nzVqws\\nTdrDesOyhp\\n\", \"1 0\\nPasha\\nbhseL\\naynaV\\n\", \"3 0\\nTar`s\\nNikita\\nSergey\\nAndrey\\nRomka\\nAlexey\\nUra\\nDenis\\nEgor\\nVadim\\nanelA\\nOlya\\naynaV\\nBrut\\nJohn\\nAlice\\n\", \"3 0\\nPasha\\nLesha\\nVanya\\n\", \"3 1\\nPetya\\nVasya\\nMasha\\nPetya Vasya\\n\"], \"outputs\": [\"5\\nAlena\\nBrus\\nMariana\\nOlya\\nVanya\\n\", \"5\\nUj\\nZ\\na\\nm\\nsuaaSiKcK\\n\", \"13\\nMC\\nTAU\\nVDLb\\nYclKFJoaIA\\na\\nb\\nbLOlPzAeQ\\nhalYcB\\nlCEHPibt\\noDFijpx\\noF\\npz\\ntckjt\\n\", \"5\\nC\\nDPPvwuWvmA\\nU\\nVubTXNI\\nhLNFnzmqFE\\n\", \"2\\nAndrey\\nTaras\\n\", \"2\\nadQx\\ntgPYZk\\n\", \"8\\nIEAYCq\\nWX\\nXozwkum\\ne\\niPwfd\\nltmruh\\nmeJa\\ntIWi\\n\", \"11\\nAdIfP\\nB\\nJlmscIUOxO\\nOfyLIUO\\nZuxr\\nds\\nhXPfJrL\\ntulhZxeKgo\\nuaMl\\nweVtBIP\\nzRwb\\n\", \"5\\nCOzbXWOt\\nDRNzxJU\\nVejWyKCtbN\\nqqjgF\\nuPVIuLBuYM\\n\", \"4\\nWEYUdpYmZp\\ncilTtE\\nfhNmMpjr\\nydARivBg\\n\", \"11\\nFeuhJJwJ\\nJIo\\nKaxyCBWt\\nRAwFYCrSvI\\nRmcaVngp\\nTGF\\nTngcmS\\nkVfnsz\\nlwaFfXzM\\noabGmpvVH\\nvIEWWIvh\\n\", \"12\\nGkNPGYVxjY\\nPVrHpL\\nXYXYVo\\naPkr\\naU\\nbgBjA\\nbkeDfi\\nduZQ\\nhHhukllwbf\\nmPILXy\\nnsEUAKNxQI\\noSIb\\n\", \"3\\nBkgxqAF\\nKhq\\nkheqUyDVG\\n\", \"4\\nAndrey\\nNikita\\nSergey\\nTaras\\n\", \"3\\nr\\nsdTDerOyhp\\nyVwqs\\n\", \"3\\nFXCT\\nMdFuonu\\nn\\n\", \"7\\nCaAlbwoIL\\nEQPcotnrp\\nKqHXRNya\\nNAZKIBiKT\\nQSwgobA\\nVG\\nfLfek\\n\", \"16\\nAlena\\nAlexey\\nAlice\\nAndrey\\nBrus\\nDenis\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSergey\\nTaras\\nUra\\nVadim\\nVanya\\n\", \"7\\nBeaCYhIRLy\\nRFiow\\nVWAxrqx\\naxgvtiBGbx\\ngGBVZtI\\nmnASVEQI\\ntZHzWGAvXc\\n\", \"4\\nB\\nVgqRcEOG\\nlnGPIV\\nnb\\n\", \"1\\ncLWdg\\n\", \"4\\nAiOm\\nBSKI\\ngwmIDluW\\nmoRNeufngu\\n\", \"8\\nAodc\\nJOaQdgglDG\\nMrjB\\nUfsnPRt\\nW\\nWs\\njTZQMyH\\njWuGgOjV\\n\", \"8\\nD\\nEr\\nMDuBOXrmWH\\nPaJNrF\\nSgjMQZ\\nZ\\nbBZ\\nxDwpppG\\n\", \"4\\nITtwRJCv\\nLJ\\nYiUXqlBUx\\ndPtyZ\\n\", \"1\\nvRVatwL\\n\", \"6\\nKlQW\\nWRsnNZT\\ncZAMfd\\nfeb\\nix\\ntvk\\n\", \"2\\nNgzlPJgFgz\\nQfpagVpWz\\n\", \"10\\nToLcqN\\nXCKZ\\nXtueKFM\\nbnenhMxiK\\neY\\neaQrds\\njA\\nkyRNTE\\nmQIl\\nzlkOe\\n\", \"2\\nHspFEry\\noVemoZhjW\\n\", \"1\\nTaras\\n\", \"4\\nAlena\\nBrus\\nOlya\\nVanya\\n\", \"1\\nPetr\\n\", \"3\\nUIKWj\\nmHolKkBx\\noySkmhCD\\n\", \"6\\nIdG\\nIjeDjoj\\nLAbVLYiY\\nRZRQl\\nlNHWt\\notOBsWqJuo\\n\", \"13\\nMC\\nTAU\\nVDLb\\nYcJKFloaIA\\na\\nb\\nbLOlPzAeQ\\nhalYcB\\nlCEHPibt\\noDFijpx\\noF\\npz\\ntckjt\\n\", \"2\\nAndrey\\nTar`s\\n\", \"11\\nFeuhJJwJ\\nJIo\\nKaxyCBWt\\nRAwFYCrSvI\\nRmcaVngp\\nSmcgnT\\nTGF\\nkVfnsz\\nlwaFfXzM\\noabGmpvVH\\nvIEWWIvh\\n\", \"3\\nphyOreDTds\\nr\\nyVwqs\\n\", \"7\\nCaAlbwoIL\\nEQPcotnrp\\nGV\\nKqHXRNya\\nNAZKIBiKT\\nQSwgobA\\nfLfek\\n\", \"16\\nAlexey\\nAlice\\nAndrey\\nBrus\\nDenis\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSergey\\nTaras\\nUra\\nVadim\\nVanya\\nanelA\\n\", \"7\\nAnmSVEQI\\nBeaCYhIRLy\\nRFiow\\nVWAxrqx\\naxgvtiBGbx\\ngGBVZtI\\ntZHzWGAvXc\\n\", \"2\\nNgzlPJzFgg\\nQfpagVpWz\\n\", \"1\\nePtr\\n\", \"2\\nAodrey\\nTar`s\\n\", \"3\\nr\\nsdTDerOyhp\\nzVwqs\\n\", \"1\\nrPte\\n\", \"3\\ns\\nsdTDerOyhp\\nzVwqs\\n\", \"3\\ns\\nsdTDerOyhp\\nzVqws\\n\", \"3\\nrdTDesOyhp\\ns\\nzVqws\\n\", \"2\\nAnerey\\nTaras\\n\", \"5\\nCOzbXXOt\\nDRNzxJU\\nVejWyKCtbN\\nqqjgF\\nuPVIuLBuYM\\n\", \"3\\ns\\nsdTDerOyhp\\nyVwqs\\n\", \"16\\nAlena\\nAlexey\\nAlice\\nAndrey\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSergey\\nTaras\\nUra\\nVadim\\nVanya\\nsineD\\n\", \"7\\nBeaCYhIRLy\\nRFiow\\nVWBxrqx\\naxgvtiBGbx\\ngGBVZtI\\nmnASVEQI\\ntZHzWGAvXc\\n\", \"2\\nWmkUGiYEn\\nuvvsXKXcJ\\n\", \"4\\nAlena\\nBrvs\\nOlya\\nVanya\\n\", \"1\\nPdtr\\n\", \"6\\nIdG\\nIjeDjoj\\nLAbVLYiY\\nRZRQl\\nlNHWt\\notOBsWqJvo\\n\", \"3\\nLeshb\\nPasha\\nVanya\\n\", \"3\\nphyOreDTds\\nr\\nyVxqs\\n\", \"3\\nNikita\\nSergey\\nTaras\\n\", \"1\\nrtPe\\n\", \"2\\nAodsey\\nTar`s\\n\", \"3\\nphyOreDTds\\nr\\nzVwqs\\n\", \"1\\nrOte\\n\", \"3\\nsdTDerOyhp\\nt\\nzVwqs\\n\", \"2\\ns\\nzVqws\\n\", \"2\\nAnerey\\nTarar\\n\", \"5\\nCOzbWXOt\\nDRNzxJU\\nVejWyKCtbN\\nqqjgF\\nuPVIuLBuYM\\n\", \"16\\nAlena\\nAlexey\\nAlice\\nAndrey\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSergey\\nTaras\\nUra\\nVadim\\nnaVya\\nsineD\\n\", \"1\\nPdts\\n\", \"3\\nPasha\\nVanya\\nbhseL\\n\", \"3\\nphyOreDTds\\nr\\nyVqxs\\n\", \"1\\nrtPd\\n\", \"3\\nr\\nseTDdrOyhp\\nzVwqs\\n\", \"1\\nAnerey\\n\", \"16\\nAlena\\nAlexey\\nAlice\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSergey\\nTaras\\nUra\\nVadim\\nnaVya\\nsineD\\nyndreA\\n\", \"1\\nPdss\\n\", \"1\\nPasha\\n\", \"3\\nNikita\\nSergey\\nTar`s\\n\", \"3\\nq\\nseTDdrOyhp\\nzVwqs\\n\", \"16\\nAlena\\nAlexey\\nAlice\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSerfey\\nTaras\\nUra\\nVadim\\nnaVya\\nsineD\\nyndreA\\n\", \"1\\nPssd\\n\", \"16\\nAlena\\nAlice\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSerfey\\nTaras\\nUra\\nVadim\\nnaVya\\nsineD\\nyexelA\\nyndreA\\n\", \"1\\nsaPha\\n\", \"16\\nAerdny\\nAlena\\nAlice\\nBrus\\nEgor\\nJohn\\nNikita\\nOlya\\nRomka\\nSerfey\\nTaras\\nUra\\nVadim\\nnaVya\\nsineD\\nyexelA\\n\", \"3\\nNikita\\nSergey\\nTaras\\n\", \"2\\ns\\nzVqws\\n\", \"1\\nPasha\\n\", \"3\\nNikita\\nSergey\\nTar`s\\n\", \"3\\nLesha\\nPasha\\nVanya\\n\", \"2\\nMasha\\nPetya\\n\"]}", "source": "taco"} | When little Petya grew up and entered the university, he started to take part in АСМ contests. Later he realized that he doesn't like how the АСМ contests are organised: the team could only have three members (and he couldn't take all his friends to the competitions and distribute the tasks between the team members efficiently), so he decided to organize his own contests PFAST Inc. — Petr and Friends Are Solving Tasks Corporation. PFAST Inc. rules allow a team to have unlimited number of members.
To make this format of contests popular he organised his own tournament. To create the team he will prepare for the contest organised by the PFAST Inc. rules, he chose several volunteers (up to 16 people) and decided to compile a team from them. Petya understands perfectly that if a team has two people that don't get on well, then the team will perform poorly. Put together a team with as many players as possible given that all players should get on well with each other.
Input
The first line contains two integer numbers n (1 ≤ n ≤ 16) — the number of volunteers, and m (<image>) — the number of pairs that do not get on. Next n lines contain the volunteers' names (each name is a non-empty string consisting of no more than 10 uppercase and/or lowercase Latin letters). Next m lines contain two names — the names of the volunteers who do not get on. The names in pair are separated with a single space. Each pair of volunteers who do not get on occurs exactly once. The strings are case-sensitive. All n names are distinct.
Output
The first output line should contain the single number k — the number of people in the sought team. Next k lines should contain the names of the sought team's participants in the lexicographical order. If there are several variants to solve the problem, print any of them. Petya might not be a member of the sought team.
Examples
Input
3 1
Petya
Vasya
Masha
Petya Vasya
Output
2
Masha
Petya
Input
3 0
Pasha
Lesha
Vanya
Output
3
Lesha
Pasha
Vanya
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.625 |
{"tests": "{\"inputs\": [[\"x - 5 = 20\"], [\"5 * x + 5 = 30\"], [\"20 = 5 * x - 5\"], [\"24 = 4 + 5 * x\"], [\"x = 5\"], [\"x * 100 = 700\"], [\"2 * x + 5 = 105\"], [\"2 * x = 198\"], [\"x - 100 + 2 - 50 = 52\"], [\"x / 3 = 33\"], [\"x + 80 = 20\"], [\"x + 20 = -60\"], [\"5 * x + 20 - x = 60\"], [\"x + x + 6 = 10\"], [\"5 * x = x + 8\"], [\"x = x / 2 + 25\"], [\"(5 - 3) * x = x + 2\"], [\"(x - 30) * 2 = x\"]], \"outputs\": [[25], [5], [5], [4], [5], [7], [50], [99], [200], [99], [-60], [-80], [10], [2], [2], [50], [2], [60]]}", "source": "taco"} | # Solve For X
You will be given an equation as a string and you will need to [solve for X](https://www.mathplacementreview.com/algebra/basic-algebra.php#solve-for-a-variable) and return x's value. For example:
```python
solve_for_x('x - 5 = 20') # should return 25
solve_for_x('20 = 5 * x - 5') # should return 5
solve_for_x('5 * x = x + 8') # should return 2
solve_for_x('(5 - 3) * x = x + 2') # should return 2
```
NOTES:
* All numbers will be whole numbers
* Don't forget about the [order of operations](https://www.mathplacementreview.com/algebra/basic-algebra.php#order-of-operations).
* If the random tests don't pass the first time, just run them again.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n1 2\\n1 3\\n\", \"2\\n1 2\\n\", \"5\\n1 2\\n2 3\\n3 4\\n3 5\\n\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n3 6\\n6 7\\n6 8\\n\", \"5\\n1 2\\n1 3\\n3 4\\n3 5\", \"5\\n1 2\\n1 4\\n3 4\\n3 5\", \"5\\n1 2\\n1 4\\n5 4\\n3 5\", \"3\\n2 3\\n1 3\", \"5\\n1 2\\n2 3\\n2 4\\n3 5\", \"5\\n1 2\\n1 5\\n3 4\\n3 5\", \"5\\n1 2\\n1 5\\n5 4\\n3 5\", \"5\\n1 2\\n2 3\\n1 4\\n3 5\", \"5\\n1 2\\n1 5\\n2 4\\n3 5\", \"5\\n1 3\\n2 3\\n1 4\\n3 5\", \"5\\n1 3\\n2 3\\n1 4\\n1 5\", \"5\\n1 2\\n1 4\\n5 2\\n3 5\", \"5\\n1 3\\n2 5\\n3 4\\n3 5\", \"5\\n1 4\\n1 5\\n2 4\\n3 5\", \"5\\n1 2\\n2 4\\n5 2\\n3 5\", \"8\\n1 2\\n2 3\\n6 4\\n3 5\\n3 6\\n6 7\\n6 8\", \"5\\n1 4\\n1 3\\n2 4\\n3 5\", \"3\\n1 2\\n2 3\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n3 6\\n6 7\\n1 8\", \"5\\n1 2\\n2 5\\n3 4\\n3 5\", \"8\\n1 2\\n2 3\\n6 4\\n3 5\\n3 6\\n3 7\\n6 8\", \"5\\n1 2\\n4 3\\n1 4\\n4 5\", \"2\\n2 1\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n3 6\\n6 7\\n6 8\", \"5\\n1 2\\n1 5\\n2 4\\n3 2\", \"5\\n1 3\\n2 3\\n1 4\\n2 5\", \"5\\n1 2\\n2 4\\n5 4\\n3 5\", \"5\\n1 3\\n2 4\\n3 2\\n3 5\", \"5\\n1 2\\n2 3\\n3 4\\n4 5\", \"5\\n1 3\\n2 5\\n1 4\\n3 5\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n3 6\\n6 7\\n1 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n3 6\\n3 7\\n6 8\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n3 6\\n3 7\\n6 8\", \"5\\n1 2\\n2 3\\n1 4\\n4 5\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n1 6\\n6 7\\n1 8\", \"5\\n1 4\\n2 3\\n2 4\\n3 5\", \"5\\n1 3\\n2 5\\n3 4\\n4 5\", \"5\\n1 4\\n1 5\\n2 1\\n3 5\", \"5\\n1 2\\n2 5\\n3 4\\n3 1\", \"5\\n1 2\\n2 5\\n2 4\\n3 2\", \"5\\n1 5\\n2 4\\n3 2\\n3 5\", \"8\\n1 2\\n1 3\\n2 4\\n3 5\\n3 6\\n6 7\\n1 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n3 6\\n3 7\\n1 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n1 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n3 6\\n6 7\\n5 8\", \"5\\n1 2\\n1 3\\n1 4\\n3 5\", \"5\\n1 2\\n2 4\\n3 4\\n3 5\", \"8\\n1 2\\n2 3\\n6 4\\n3 5\\n3 6\\n3 7\\n2 8\", \"5\\n1 3\\n2 3\\n2 4\\n2 5\", \"5\\n1 3\\n2 3\\n3 4\\n4 5\", \"8\\n1 2\\n1 3\\n2 4\\n3 5\\n5 6\\n6 7\\n1 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n3 6\\n4 7\\n1 8\", \"8\\n1 2\\n2 3\\n3 4\\n3 8\\n3 6\\n6 7\\n5 8\", \"8\\n1 2\\n2 3\\n5 4\\n3 5\\n3 6\\n3 7\\n2 8\", \"8\\n1 3\\n2 3\\n3 4\\n3 5\\n3 6\\n6 7\\n6 8\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n4 6\\n6 7\\n6 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n5 6\\n3 7\\n6 8\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n2 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n2 6\\n6 7\\n5 8\", \"8\\n1 2\\n2 3\\n6 4\\n3 5\\n5 6\\n3 7\\n2 8\", \"5\\n1 4\\n2 3\\n2 4\\n2 5\", \"5\\n1 3\\n2 3\\n3 4\\n3 5\", \"8\\n1 3\\n2 3\\n5 4\\n3 5\\n3 6\\n3 7\\n2 8\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n4 6\\n6 7\\n2 8\", \"5\\n1 3\\n2 4\\n1 4\\n4 5\", \"8\\n1 2\\n2 4\\n3 4\\n3 5\\n2 6\\n6 7\\n5 8\", \"8\\n1 2\\n1 3\\n6 4\\n3 5\\n5 6\\n3 7\\n2 8\", \"5\\n1 3\\n2 3\\n3 4\\n1 5\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n8 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 4\\n3 4\\n4 5\\n2 6\\n6 7\\n5 8\", \"8\\n1 2\\n2 3\\n1 4\\n2 5\\n8 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 3\\n3 4\\n4 5\\n3 6\\n6 7\\n6 8\", \"8\\n1 4\\n2 3\\n6 4\\n3 5\\n3 6\\n6 7\\n6 8\", \"5\\n1 4\\n1 3\\n2 4\\n2 5\", \"5\\n1 5\\n2 3\\n1 4\\n2 5\", \"5\\n1 4\\n2 3\\n2 4\\n4 5\", \"8\\n1 2\\n2 3\\n2 4\\n3 5\\n1 6\\n6 7\\n4 8\", \"5\\n1 3\\n2 4\\n3 4\\n3 5\", \"8\\n1 2\\n4 3\\n2 4\\n3 5\\n3 6\\n4 7\\n1 8\", \"8\\n1 3\\n2 3\\n5 4\\n3 5\\n3 6\\n3 7\\n3 8\", \"8\\n1 4\\n2 4\\n3 4\\n3 5\\n2 6\\n6 7\\n5 8\", \"8\\n1 2\\n1 3\\n6 4\\n3 5\\n3 6\\n3 7\\n2 8\", \"8\\n1 2\\n2 4\\n3 4\\n4 8\\n2 6\\n6 7\\n5 8\", \"5\\n1 3\\n2 5\\n3 4\\n3 2\", \"8\\n1 2\\n2 6\\n3 4\\n3 5\\n3 6\\n6 7\\n1 8\", \"8\\n1 2\\n1 3\\n1 4\\n3 5\\n3 6\\n3 7\\n6 8\", \"5\\n1 3\\n2 5\\n3 4\\n1 5\", \"8\\n1 3\\n2 3\\n2 4\\n3 5\\n1 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n3 6\\n5 7\\n5 8\", \"8\\n1 2\\n2 3\\n6 4\\n3 8\\n3 6\\n6 7\\n5 8\", \"5\\n1 2\\n2 3\\n5 4\\n2 5\", \"5\\n1 2\\n2 5\\n2 4\\n3 4\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n1 6\\n6 7\\n5 8\", \"8\\n1 2\\n2 3\\n6 4\\n1 5\\n5 6\\n3 7\\n2 8\", \"8\\n1 3\\n2 3\\n5 4\\n1 5\\n3 6\\n3 7\\n2 8\", \"5\\n1 5\\n2 3\\n3 4\\n2 5\", \"8\\n1 2\\n2 3\\n1 4\\n3 5\\n5 6\\n6 7\\n2 8\", \"8\\n1 2\\n2 4\\n3 4\\n2 5\\n2 6\\n6 7\\n5 8\", \"5\\n1 3\\n1 5\\n2 4\\n3 4\", \"5\\n1 4\\n2 4\\n3 4\\n3 5\", \"3\\n1 2\\n1 3\", \"2\\n1 2\", \"5\\n1 2\\n2 3\\n3 4\\n3 5\", \"8\\n1 2\\n2 3\\n3 4\\n3 5\\n3 6\\n6 7\\n6 8\"], \"outputs\": [\"2\\n1\\n1\\n\", \"1\\n1\\n\", \"2\\n8\\n12\\n3\\n3\\n\", \"40\\n280\\n840\\n120\\n120\\n504\\n72\\n72\\n\", \"8\\n2\\n12\\n3\\n3\\n\", \"4\\n1\\n4\\n6\\n1\\n\", \"4\\n1\\n1\\n6\\n4\\n\", \"1\\n1\\n2\\n\", \"3\\n12\\n8\\n3\\n2\\n\", \"4\\n1\\n4\\n1\\n6\\n\", \"8\\n2\\n3\\n3\\n12\\n\", \"4\\n6\\n4\\n1\\n1\\n\", \"6\\n4\\n1\\n1\\n4\\n\", \"8\\n3\\n12\\n2\\n3\\n\", \"12\\n2\\n8\\n3\\n3\\n\", \"4\\n6\\n1\\n1\\n4\\n\", \"3\\n2\\n12\\n3\\n8\\n\", \"6\\n1\\n1\\n4\\n4\\n\", \"3\\n12\\n2\\n3\\n8\\n\", \"30\\n210\\n630\\n90\\n90\\n630\\n90\\n90\\n\", \"6\\n1\\n4\\n4\\n1\\n\", \"1\\n2\\n1\\n\", \"84\\n252\\n420\\n60\\n60\\n140\\n20\\n12\\n\", \"1\\n4\\n4\\n1\\n6\\n\", \"40\\n280\\n840\\n72\\n120\\n504\\n120\\n72\\n\", \"8\\n2\\n3\\n12\\n3\\n\", \"1\\n1\\n\", \"56\\n168\\n280\\n8\\n40\\n168\\n24\\n24\\n\", \"8\\n12\\n3\\n3\\n2\\n\", \"4\\n4\\n6\\n1\\n1\\n\", \"1\\n4\\n1\\n6\\n4\\n\", \"3\\n8\\n12\\n2\\n3\\n\", \"1\\n4\\n6\\n4\\n1\\n\", \"4\\n1\\n6\\n1\\n4\\n\", \"105\\n315\\n315\\n45\\n45\\n105\\n15\\n15\\n\", \"72\\n504\\n840\\n72\\n120\\n280\\n120\\n40\\n\", \"84\\n252\\n420\\n12\\n60\\n140\\n60\\n20\\n\", \"6\\n4\\n1\\n4\\n1\\n\", \"315\\n315\\n105\\n45\\n15\\n105\\n15\\n45\\n\", \"1\\n6\\n4\\n4\\n1\\n\", \"1\\n1\\n4\\n6\\n4\\n\", \"12\\n3\\n2\\n3\\n8\\n\", \"6\\n4\\n4\\n1\\n1\\n\", \"6\\n24\\n6\\n6\\n6\\n\", \"1\\n4\\n6\\n1\\n4\\n\", \"315\\n105\\n315\\n15\\n45\\n105\\n15\\n45\\n\", \"210\\n630\\n630\\n90\\n90\\n90\\n90\\n30\\n\", \"252\\n420\\n140\\n60\\n20\\n84\\n12\\n60\\n\", \"30\\n210\\n630\\n90\\n210\\n210\\n30\\n30\\n\", \"12\\n3\\n8\\n3\\n2\\n\", \"1\\n4\\n4\\n6\\n1\\n\", \"72\\n504\\n840\\n40\\n120\\n280\\n120\\n72\\n\", \"2\\n12\\n8\\n3\\n3\\n\", \"3\\n3\\n12\\n8\\n2\\n\", \"105\\n35\\n105\\n5\\n63\\n21\\n3\\n15\\n\", \"140\\n420\\n252\\n140\\n36\\n36\\n20\\n20\\n\", \"30\\n210\\n630\\n90\\n30\\n210\\n30\\n210\\n\", \"72\\n504\\n840\\n40\\n280\\n120\\n120\\n72\\n\", \"240\\n240\\n1680\\n240\\n240\\n1008\\n144\\n144\\n\", \"70\\n42\\n14\\n70\\n2\\n42\\n6\\n6\\n\", \"24\\n168\\n280\\n24\\n168\\n56\\n40\\n8\\n\", \"180\\n1260\\n420\\n180\\n60\\n420\\n60\\n180\\n\", \"45\\n315\\n315\\n45\\n105\\n105\\n15\\n15\\n\", \"24\\n168\\n280\\n8\\n168\\n56\\n40\\n24\\n\", \"2\\n12\\n3\\n8\\n3\\n\", \"6\\n6\\n24\\n6\\n6\\n\", \"180\\n420\\n1260\\n60\\n420\\n180\\n180\\n60\\n\", \"105\\n105\\n35\\n63\\n5\\n21\\n3\\n15\\n\", \"8\\n3\\n2\\n12\\n3\\n\", \"15\\n105\\n63\\n105\\n21\\n35\\n5\\n3\\n\", \"84\\n28\\n140\\n4\\n84\\n28\\n20\\n4\\n\", \"8\\n3\\n12\\n3\\n2\\n\", \"70\\n210\\n70\\n10\\n10\\n42\\n6\\n126\\n\", \"45\\n315\\n45\\n315\\n105\\n105\\n15\\n15\\n\", \"140\\n420\\n60\\n20\\n60\\n84\\n12\\n252\\n\", \"20\\n140\\n420\\n140\\n20\\n252\\n36\\n36\\n\", \"40\\n72\\n504\\n280\\n72\\n840\\n120\\n120\\n\", \"4\\n4\\n1\\n6\\n1\\n\", \"4\\n4\\n1\\n1\\n6\\n\", \"3\\n8\\n2\\n12\\n3\\n\", \"126\\n210\\n70\\n70\\n10\\n42\\n6\\n10\\n\", \"3\\n2\\n12\\n8\\n3\\n\", \"56\\n168\\n168\\n280\\n24\\n24\\n40\\n8\\n\", \"360\\n360\\n2520\\n120\\n840\\n360\\n360\\n360\\n\", \"20\\n84\\n84\\n140\\n28\\n28\\n4\\n4\\n\", \"252\\n84\\n420\\n20\\n60\\n140\\n60\\n12\\n\", \"45\\n315\\n45\\n315\\n15\\n105\\n15\\n105\\n\", \"3\\n8\\n12\\n3\\n2\\n\", \"56\\n168\\n168\\n24\\n24\\n280\\n40\\n8\\n\", \"504\\n72\\n840\\n72\\n120\\n280\\n120\\n40\\n\", \"6\\n1\\n4\\n1\\n4\\n\", \"168\\n168\\n280\\n24\\n40\\n56\\n8\\n24\\n\", \"40\\n280\\n840\\n120\\n504\\n120\\n72\\n72\\n\", \"20\\n140\\n420\\n36\\n20\\n252\\n36\\n140\\n\", \"3\\n12\\n3\\n2\\n8\\n\", \"3\\n12\\n2\\n8\\n3\\n\", \"63\\n105\\n105\\n15\\n35\\n21\\n3\\n5\\n\", \"105\\n105\\n35\\n3\\n63\\n21\\n5\\n15\\n\", \"252\\n140\\n420\\n12\\n84\\n60\\n60\\n20\\n\", \"1\\n6\\n4\\n1\\n4\\n\", \"35\\n105\\n105\\n5\\n63\\n21\\n3\\n15\\n\", \"90\\n630\\n30\\n210\\n210\\n210\\n30\\n30\\n\", \"4\\n1\\n6\\n4\\n1\\n\", \"3\\n3\\n8\\n12\\n2\\n\", \"2\\n1\\n1\", \"1\\n1\", \"2\\n8\\n12\\n3\\n3\", \"40\\n280\\n840\\n120\\n120\\n504\\n72\\n72\"]}", "source": "taco"} | We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.
For each k=1, ..., N, solve the problem below:
- Consider writing a number on each vertex in the tree in the following manner:
- First, write 1 on Vertex k.
- Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:
- Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.
- Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).
-----Constraints-----
- 2 \leq N \leq 2 \times 10^5
- 1 \leq a_i,b_i \leq N
- The given graph is a tree.
-----Input-----
Input is given from Standard Input in the following format:
N
a_1 b_1
:
a_{N-1} b_{N-1}
-----Output-----
For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.
-----Sample Input-----
3
1 2
1 3
-----Sample Output-----
2
1
1
The graph in this input is as follows:
For k=1, there are two ways in which we can write the numbers on the vertices, as follows:
- Writing 1, 2, 3 on Vertex 1, 2, 3, respectively
- Writing 1, 3, 2 on Vertex 1, 2, 3, respectively
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5 5 5 5 5 5\\n\", \"4 4 4 4 2 2\\n\", \"1 1 2 2 3 4\\n\", \"1 3 3 3 4 5\\n\", \"4 4 5 6 7 8\\n\", \"4 4 4 4 4 5\\n\", \"5 5 5 6 6 6\\n\", \"4 4 2 2 2 2\\n\", \"1 1 3 3 3 5\\n\", \"1 8 9 1 1 1\\n\", \"9 9 9 1 9 9\\n\", \"4 4 4 4 4 2\\n\", \"1 1 2 2 2 2\\n\", \"1 1 1 1 1 2\\n\", \"4 4 4 4 4 3\\n\", \"1 1 1 1 1 1\\n\", \"2 2 4 4 4 4\\n\", \"2 2 3 3 4 4\\n\", \"9 9 9 9 9 9\\n\", \"1 1 1 2 3 5\\n\", \"1 2 5 5 5 5\\n\", \"1 2 2 3 3 3\\n\", \"1 2 3 8 9 7\\n\", \"5 1 1 1 1 1\\n\", \"1 2 2 2 2 2\\n\", \"1 1 1 1 2 2\\n\", \"5 7 5 5 5 5\\n\", \"4 4 2 2 1 2\\n\", \"1 1 5 5 5 5\\n\", \"3 4 4 4 4 2\\n\", \"4 4 4 4 7 5\\n\", \"1 8 9 2 1 1\\n\", \"8 9 9 1 9 9\\n\", \"4 4 8 4 4 2\\n\", \"1 1 1 2 2 2\\n\", \"1 4 4 4 4 3\\n\", \"2 1 1 1 1 1\\n\", \"2 2 4 4 4 1\\n\", \"1 2 2 3 2 3\\n\", \"1 2 3 5 9 7\\n\", \"1 2 2 2 2 3\\n\", \"1 1 3 4 5 6\\n\", \"4 4 7 4 4 5\\n\", \"4 2 1 4 4 4\\n\", \"5 7 5 4 5 5\\n\", \"4 4 4 4 3 5\\n\", \"4 4 2 2 1 3\\n\", \"1 2 9 1 1 1\\n\", \"4 4 1 4 4 2\\n\", \"1 1 1 2 1 2\\n\", \"1 4 4 4 2 3\\n\", \"2 1 1 1 1 2\\n\", \"2 2 4 4 8 1\\n\", \"1 2 2 5 9 7\\n\", \"1 2 2 2 4 3\\n\", \"4 3 1 4 4 4\\n\", \"4 4 4 5 3 5\\n\", \"4 4 2 2 1 6\\n\", \"1 1 9 1 1 1\\n\", \"3 4 1 4 4 2\\n\", \"1 2 1 2 1 2\\n\", \"1 4 4 4 2 4\\n\", \"1 2 2 5 9 4\\n\", \"4 4 6 5 3 5\\n\", \"1 1 9 1 1 2\\n\", \"1 2 1 2 2 2\\n\", \"2 2 2 5 9 4\\n\", \"4 4 6 5 5 5\\n\", \"1 3 1 2 2 2\\n\", \"2 2 2 5 2 4\\n\", \"4 1 6 5 5 5\\n\", \"5 8 5 5 5 5\\n\", \"4 4 6 4 2 2\\n\", \"4 3 5 6 7 8\\n\", \"4 4 4 4 2 5\\n\", \"5 5 9 6 6 6\\n\", \"2 1 3 3 3 5\\n\", \"1 8 9 1 2 1\\n\", \"4 4 6 4 4 3\\n\", \"1 2 1 1 1 1\\n\", \"4 4 7 4 4 3\\n\", \"1 1 2 1 1 1\\n\", \"2 2 4 4 6 4\\n\", \"1 2 2 3 3 4\\n\", \"1 4 3 8 9 7\\n\", \"1 2 4 2 2 2\\n\", \"1 1 2 1 2 3\\n\", \"1 2 4 4 5 6\\n\", \"8 4 5 4 4 5\\n\", \"4 2 5 4 3 4\\n\", \"5 7 5 5 5 6\\n\", \"3 4 4 7 4 2\\n\", \"4 6 4 4 7 5\\n\", \"4 4 2 4 1 2\\n\", \"1 8 6 2 1 1\\n\", \"2 1 1 2 2 2\\n\", \"1 4 4 4 7 3\\n\", \"4 2 4 4 4 1\\n\", \"1 1 6 5 5 5\\n\", \"1 2 2 3 2 1\\n\", \"1 2 5 5 9 7\\n\", \"4 4 7 4 2 5\\n\", \"4 2 1 4 4 3\\n\", \"5 7 1 4 5 5\\n\", \"4 2 4 4 3 5\\n\", \"1 2 3 4 5 6\\n\", \"4 4 5 4 4 5\\n\", \"4 2 5 4 4 4\\n\"], \"outputs\": [\"Elephant\\n\", \"Elephant\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Elephant\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Bear\\n\", \"Elephant\\n\", \"Bear\\n\", \"Bear\\n\", \"Elephant\\n\", \"Elephant\\n\", \"Alien\\n\", \"Elephant\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Elephant\\n\", \"Bear\\n\", \"Alien\\n\", \"Elephant\\n\", \"Bear\\n\", \"Bear\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Bear\\n\", \"Bear\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Elephant\\n\", \"Alien\\n\", \"Elephant\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Elephant\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Bear\\n\", \"Bear\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Elephant\\n\", \"Alien\\n\", \"Bear\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Alien\\n\", \"Elephant\\n\", \"Bear\\n\"]}", "source": "taco"} | Two polar bears Menshykov and Uslada from the St.Petersburg zoo and elephant Horace from the Kiev zoo got six sticks to play with and assess the animals' creativity. Menshykov, Uslada and Horace decided to make either an elephant or a bear from those sticks. They can make an animal from sticks in the following way:
* Four sticks represent the animal's legs, these sticks should have the same length.
* Two remaining sticks represent the animal's head and body. The bear's head stick must be shorter than the body stick. The elephant, however, has a long trunk, so his head stick must be as long as the body stick. Note that there are no limits on the relations between the leg sticks and the head and body sticks.
Your task is to find out which animal can be made from the given stick set. The zoo keeper wants the sticks back after the game, so they must never be broken, even bears understand it.
Input
The single line contains six space-separated integers li (1 ≤ li ≤ 9) — the lengths of the six sticks. It is guaranteed that the input is such that you cannot make both animals from the sticks.
Output
If you can make a bear from the given set, print string "Bear" (without the quotes). If you can make an elephant, print string "Elephant" (wıthout the quotes). If you can make neither a bear nor an elephant, print string "Alien" (without the quotes).
Examples
Input
4 2 5 4 4 4
Output
Bear
Input
4 4 5 4 4 5
Output
Elephant
Input
1 2 3 4 5 6
Output
Alien
Note
If you're out of creative ideas, see instructions below which show how to make a bear and an elephant in the first two samples. The stick of length 2 is in red, the sticks of length 4 are in green, the sticks of length 5 are in blue.
<image>
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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442 1804 67 434 483 719 565 20 355\", \"2\\n5 2 1 2\", \"4\\n261 780 219 20 796 875 48 442 1804 67 161 483 719 565 20 355\", \"2\\n2 2 1 2\", \"4\\n261 780 219 20 796 875 21 442 1804 67 161 483 719 565 20 355\", \"2\\n2 2 1 1\", \"4\\n346 780 219 20 796 875 21 442 1804 67 161 483 719 565 20 355\", \"2\\n2 2 2 1\", \"4\\n346 780 219 3 796 875 21 442 1804 67 161 483 719 565 20 355\", \"2\\n2 2 2 2\", \"4\\n346 780 219 3 796 875 21 442 1804 67 161 483 484 565 20 355\", \"2\\n3 2 2 2\", \"4\\n346 780 219 3 796 875 21 797 1804 67 161 483 484 565 20 355\", \"2\\n3 2 2 4\", \"4\\n346 780 219 3 796 875 21 797 1804 67 161 483 484 565 22 355\", \"4\\n346 780 219 3 796 875 21 797 1804 67 161 483 484 565 22 87\", \"2\\n2 2 0 4\", \"4\\n346 780 219 3 796 875 7 797 1804 67 161 483 484 565 22 87\", \"2\\n2 3 0 4\", \"4\\n346 780 219 3 796 875 7 797 1804 67 161 483 484 565 22 150\", \"2\\n2 1 0 4\", \"4\\n346 780 219 3 796 875 7 797 1804 67 161 483 484 565 22 186\", \"2\\n2 2 0 1\", \"4\\n346 780 219 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| Snuke found a random number generator. It generates an integer between 0 and 2^N-1 (inclusive). An integer sequence A_0, A_1, \cdots, A_{2^N-1} represents the probability that each of these integers is generated. The integer i (0 \leq i \leq 2^N-1) is generated with probability A_i / S, where S = \sum_{i=0}^{2^N-1} A_i. The process of generating an integer is done independently each time the generator is executed.
Snuke has an integer X, which is now 0. He can perform the following operation any number of times:
* Generate an integer v with the generator and replace X with X \oplus v, where \oplus denotes the bitwise XOR.
For each integer i (0 \leq i \leq 2^N-1), find the expected number of operations until X becomes i, and print it modulo 998244353. More formally, represent the expected number of operations as an irreducible fraction P/Q. Then, there exists a unique integer R such that R \times Q \equiv P \mod 998244353,\ 0 \leq R < 998244353, so print this R.
We can prove that, for every i, the expected number of operations until X becomes i is a finite rational number, and its integer representation modulo 998244353 can be defined.
Constraints
* 1 \leq N \leq 18
* 1 \leq A_i \leq 1000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_0 A_1 \cdots A_{2^N-1}
Output
Print 2^N lines. The (i+1)-th line (0 \leq i \leq 2^N-1) should contain the expected number of operations until X becomes i, modulo 998244353.
Examples
Input
2
1 1 1 1
Output
0
4
4
4
Input
2
1 2 1 2
Output
0
499122180
4
499122180
Input
4
337 780 799 10 796 875 331 223 941 67 148 483 390 565 116 355
Output
0
468683018
635850749
96019779
657074071
24757563
745107950
665159588
551278361
143136064
557841197
185790407
988018173
247117461
129098626
789682908
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"8\\n4 5\\n1 2\\n6 3\\n2 3\\n2 8\\n4 7\\n2 4\\n\", \"7\\n2 7\\n2 6\\n4 7\\n7 3\\n7 5\\n1 7\\n\", \"3\\n1 2\\n3 2\\n\", \"2\\n2 1\\n\", \"10\\n5 4\\n5 2\\n3 7\\n9 3\\n3 2\\n3 1\\n3 8\\n9 10\\n1 6\\n\", \"6\\n2 1\\n3 2\\n4 1\\n5 4\\n1 6\\n\", \"5\\n3 5\\n4 3\\n2 4\\n1 2\\n\", \"6\\n4 6\\n1 5\\n5 4\\n5 3\\n2 4\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 6\\n4 1\\n3 6\\n8 1\\n1 9\\n\", \"8\\n4 5\\n1 2\\n6 3\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"6\\n2 1\\n3 4\\n4 1\\n5 4\\n1 6\\n\", \"4\\n1 2\\n2 3\\n2 4\\n\", \"4\\n1 2\\n1 3\\n3 4\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 8\\n4 1\\n3 6\\n8 1\\n1 9\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 8\\n4 1\\n3 6\\n8 2\\n1 9\\n\", \"6\\n2 1\\n3 4\\n5 1\\n5 4\\n1 6\\n\", \"6\\n2 1\\n3 4\\n5 1\\n5 4\\n2 6\\n\", \"8\\n4 5\\n1 2\\n6 3\\n2 3\\n3 8\\n4 7\\n2 4\\n\", \"3\\n1 2\\n3 1\\n\", \"10\\n5 4\\n5 2\\n3 7\\n9 3\\n3 2\\n4 1\\n3 8\\n9 10\\n1 6\\n\", \"8\\n4 5\\n1 2\\n6 3\\n2 3\\n4 8\\n1 7\\n2 4\\n\", \"6\\n2 1\\n3 4\\n4 1\\n5 1\\n1 6\\n\", \"8\\n2 5\\n1 2\\n6 3\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"8\\n4 5\\n1 2\\n6 3\\n2 3\\n4 8\\n1 7\\n2 8\\n\", \"8\\n4 5\\n1 2\\n6 3\\n2 3\\n4 8\\n4 7\\n2 4\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 8\\n4 2\\n1 6\\n8 1\\n1 9\\n\", \"8\\n4 5\\n1 4\\n6 3\\n2 3\\n7 8\\n1 7\\n2 8\\n\", \"8\\n8 5\\n1 2\\n6 2\\n2 3\\n4 8\\n2 7\\n2 8\\n\", \"8\\n6 5\\n1 2\\n6 3\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"4\\n1 2\\n1 4\\n3 4\\n\", \"9\\n5 4\\n1 3\\n2 3\\n7 8\\n4 1\\n3 6\\n8 2\\n1 9\\n\", \"6\\n2 1\\n3 4\\n4 2\\n5 1\\n1 6\\n\", \"8\\n2 5\\n1 2\\n6 3\\n2 6\\n2 8\\n1 7\\n2 4\\n\", \"4\\n1 3\\n2 3\\n3 4\\n\", \"9\\n5 4\\n1 3\\n2 3\\n7 8\\n4 1\\n3 6\\n8 2\\n2 9\\n\", \"6\\n4 6\\n1 5\\n5 4\\n6 3\\n2 4\\n\", \"4\\n1 2\\n2 3\\n1 4\\n\", \"6\\n2 1\\n3 4\\n4 2\\n5 4\\n1 6\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 8\\n4 2\\n3 6\\n8 1\\n1 9\\n\", \"10\\n7 4\\n5 2\\n3 7\\n9 3\\n3 2\\n4 1\\n3 8\\n9 10\\n1 6\\n\", \"4\\n1 2\\n1 4\\n3 1\\n\", \"8\\n4 5\\n1 4\\n6 3\\n2 3\\n4 8\\n1 7\\n2 8\\n\", \"8\\n1 5\\n1 2\\n6 3\\n2 3\\n2 8\\n4 7\\n2 4\\n\", \"9\\n5 6\\n1 3\\n2 3\\n7 8\\n4 2\\n3 6\\n8 2\\n1 9\\n\", \"9\\n5 4\\n1 3\\n2 6\\n7 8\\n4 1\\n3 6\\n8 2\\n1 9\\n\", \"8\\n1 5\\n1 3\\n6 3\\n2 3\\n2 8\\n4 7\\n2 4\\n\", \"8\\n1 5\\n1 3\\n6 3\\n2 5\\n2 8\\n4 7\\n2 4\\n\", \"8\\n1 5\\n1 3\\n6 4\\n2 5\\n2 8\\n4 7\\n2 4\\n\", \"4\\n1 2\\n4 3\\n2 4\\n\", \"8\\n6 5\\n1 2\\n6 1\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"8\\n4 5\\n1 2\\n6 2\\n2 3\\n4 8\\n1 7\\n2 8\\n\", \"4\\n1 2\\n1 4\\n3 2\\n\", \"8\\n7 5\\n1 2\\n6 1\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"8\\n4 5\\n1 2\\n6 2\\n2 3\\n4 8\\n2 7\\n2 8\\n\", \"8\\n8 5\\n1 2\\n6 2\\n2 3\\n4 3\\n2 7\\n2 8\\n\", \"4\\n1 4\\n2 3\\n2 4\\n\", \"8\\n6 5\\n1 2\\n6 4\\n2 3\\n2 8\\n1 7\\n2 4\\n\", \"8\\n2 5\\n1 2\\n6 3\\n4 6\\n2 8\\n1 7\\n2 4\\n\", \"6\\n2 1\\n3 4\\n4 2\\n5 2\\n1 6\\n\", \"9\\n5 6\\n1 2\\n2 3\\n7 8\\n4 2\\n3 6\\n8 1\\n1 9\\n\", \"8\\n2 5\\n1 2\\n6 3\\n2 3\\n2 8\\n4 7\\n2 4\\n\", \"8\\n1 7\\n1 3\\n6 3\\n2 5\\n2 8\\n4 7\\n2 4\\n\", \"4\\n1 2\\n1 3\\n1 4\\n\", \"4\\n1 2\\n1 3\\n2 4\\n\"], \"outputs\": [\"2304\\n\", \"1680\\n\", \"6\\n\", \"2\\n\", \"19200\\n\", \"144\\n\", \"40\\n\", \"216\\n\", \"7776\\n\", \"1536\\n\", \"216\\n\", \"24\\n\", \"16\\n\", \"5184\\n\", \"2592\\n\", \"144\\n\", \"96\\n\", \"1728\\n\", \"6\\n\", \"7680\\n\", \"1152\\n\", \"288\\n\", \"3840\\n\", \"768\\n\", \"2304\\n\", \"3456\\n\", \"512\\n\", \"5760\\n\", \"1536\\n\", \"16\\n\", \"2592\\n\", \"144\\n\", \"3840\\n\", \"24\\n\", \"2592\\n\", \"144\\n\", \"16\\n\", \"144\\n\", \"2592\\n\", \"7680\\n\", \"24\\n\", \"768\\n\", \"1536\\n\", \"2592\\n\", \"1728\\n\", \"1152\\n\", \"768\\n\", \"1152\\n\", \"16\\n\", \"2304\\n\", \"1536\\n\", \"16\\n\", \"2304\\n\", \"3840\\n\", \"3840\\n\", \"16\\n\", \"1536\\n\", \"1536\\n\", \"144\\n\", \"2592\\n\", \"3840\\n\", \"768\\n\", \"24\\n\", \"16\\n\"]}", "source": "taco"} | Nauuo is a girl who loves drawing circles.
One day she has drawn a circle and wanted to draw a tree on it.
The tree is a connected undirected graph consisting of n nodes and n-1 edges. The nodes are numbered from 1 to n.
Nauuo wants to draw a tree on the circle, the nodes of the tree should be in n distinct points on the circle, and the edges should be straight without crossing each other.
"Without crossing each other" means that every two edges have no common point or the only common point is an endpoint of both edges.
Nauuo wants to draw the tree using a permutation of n elements. A permutation of n elements is a sequence of integers p_1,p_2,…,p_n in which every integer from 1 to n appears exactly once.
After a permutation is chosen Nauuo draws the i-th node in the p_i-th point on the circle, then draws the edges connecting the nodes.
The tree is given, Nauuo wants to know how many permutations are there so that the tree drawn satisfies the rule (the edges are straight without crossing each other). She only wants to know the answer modulo 998244353, can you help her?
It is obvious that whether a permutation is valid or not does not depend on which n points on the circle are chosen.
Input
The first line contains a single integer n (2≤ n≤ 2⋅ 10^5) — the number of nodes in the tree.
Each of the next n-1 lines contains two integers u and v (1≤ u,v≤ n), denoting there is an edge between u and v.
It is guaranteed that the given edges form a tree.
Output
The output contains a single integer — the number of permutations suitable to draw the given tree on a circle satisfying the rule, modulo 998244353.
Examples
Input
4
1 2
1 3
2 4
Output
16
Input
4
1 2
1 3
1 4
Output
24
Note
Example 1
All valid permutations and their spanning trees are as follows.
<image>
Here is an example of invalid permutation: the edges (1,3) and (2,4) are crossed.
<image>
Example 2
Every permutation leads to a valid tree, so the answer is 4! = 24.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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240\\n\", \"29 634 982\\n60 1351\\n54 640\\n1 253\\n72 24\\n40 529\\n52 339\\n73 21\\n34 1284\\n32 1264\\n76 1346\\n92 320\\n11 1441\\n67 1215\\n45 1524\\n77 1672\\n83 412\\n48 241\\n25 894\\n91 1474\\n18 1743\\n98 1944\\n48 1506\\n77 860\\n31 629\\n91 1042\\n36 1116\\n41 1162\\n63 129\\n15 1920\\n\", \"5 1652 591\\n92 762\\n59 255\\n15 285\\n53 1016\\n10 527\\n\", \"20 1000 100\\n49 26\\n46 36\\n1 114\\n80 4\\n80 125\\n100 3\\n6 184\\n100 20\\n41 60\\n47 92\\n57 20\\n44 50\\n3 15\\n10 192\\n6 13\\n60 3\\n63 102\\n78 17\\n0 124\\n31 100\\n\", \"10 100 5\\n61 3\\n55 2\\n12 9\\n19 5\\n25 10\\n39 7\\n16 1\\n10 1\\n70 5\\n100 7\\n\", \"4 1164 722\\n67 360\\n96 778\\n6 441\\n62 395\\n\", \"35 999 199\\n95 80\\n79 279\\n14 291\\n110 88\\n64 55\\n100 209\\n85 4\\n14 237\\n75 126\\n41 260\\n81 67\\n99 313\\n71 220\\n98 312\\n53 213\\n55 377\\n78 374\\n79 308\\n34 40\\n92 281\\n53 119\\n96 170\\n90 7\\n87 176\\n27 50\\n78 95\\n31 327\\n56 138\\n91 221\\n7 144\\n100 335\\n29 139\\n61 244\\n38 203\\n100 242\\n\", \"2 337 283\\n25 510\\n52 34\\n\", \"70 1000 1\\n91 2\\n43 1\\n100 1\\n79 2\\n26 1\\n68 2\\n4 2\\n64 2\\n100 1\\n80 2\\n20 2\\n70 1\\n25 1\\n99 1\\n64 1\\n35 2\\n60 1\\n63 2\\n93 1\\n40 2\\n100 1\\n54 1\\n100 1\\n15 2\\n72 1\\n28 1\\n5 1\\n93 1\\n100 2\\n39 2\\n54 2\\n100 1\\n55 1\\n43 1\\n20 1\\n28 2\\n21 1\\n100 2\\n98 1\\n35 1\\n12 2\\n50 2\\n7 2\\n7 2\\n12 2\\n100 2\\n44 1\\n40 2\\n56 2\\n5 1\\n100 1\\n94 2\\n100 2\\n74 1\\n83 2\\n100 2\\n81 2\\n37 2\\n29 1\\n100 2\\n99 1\\n39 2\\n83 2\\n96 2\\n30 2\\n3 1\\n38 1\\n51 1\\n21 1\\n100 2\\n\", \"5 328 249\\n25 265\\n32 271\\n72 237\\n28 99\\n25 61\\n\", \"4 337 1185\\n62 81\\n87 942\\n39 1134\\n45 708\\n\", \"5 494 183\\n16 229\\n36 221\\n81 359\\n87 253\\n5 240\\n\", \"2 100 10\\n100 11\\n90 9\\n\", \"2 10 3\\n100 3\\n99 1\\n\"], \"outputs\": [\"NO\\n\", \"NO\\n\", \"YES\\n1001 2\\n0 1\\n1 2\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n509 10\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n\", \"YES\\n12 11\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n6 7\\n7 8\\n8 9\\n9 10\\n10 11\\n\", \"YES\\n102 3\\n0 2\\n1 1\\n101 3\\n\", \"YES\\n51 2\\n0 1\\n1 2\\n\", \"YES\\n102 3\\n0 1\\n1 2\\n2 3\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n148 6\\n0 1\\n1 2\\n2 3\\n3 4\\n4 5\\n5 6\\n\", \"YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 2\\n6 4\\n\", \"NO\\n\", \"YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n\", \"NO\\n\", \"YES\\n8 8\\n0 11\\n1 41\\n2 32\\n3 46\\n4 19\\n5 13\\n6 34\\n7 43\\n\", \"NO\\n\", \"YES\\n3 3\\n0 31\\n1 14\\n2 16\\n\", \"NO\\n\", \"YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 12\\n23 31\\n24 42\\n25 49\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n\", \"NO\\n\", \"YES\\n501 2\\n0 2\\n1 1\\n\", \"YES\\n82 6\\n0 3\\n1 1\\n2 2\\n3 4\\n4 5\\n5 6\\n\", \"YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 2\\n6 4\\n\", \"YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n\", \"YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 13\\n\", \"YES\\n3 3\\n0 31\\n1 14\\n2 16\\n\", \"YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n\", \"YES\\n35 3\\n0 2\\n1 1\\n2 3\\n\", \"YES\\n338 5\\n0 3\\n1 2\\n2 4\\n3 5\\n4 6\\n\", \"YES\\n3 3\\n0 31\\n1 12\\n2 16\\n\", \"YES\\n52 3\\n0 2\\n1 1\\n2 3\\n\", \"YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 16\\n6 4\\n\", \"YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 25\\n\", \"YES\\n334 2\\n0 2\\n1 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n501 2\\n0 2\\n1 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n7 7\\n0 18\\n1 15\\n2 20\\n3 5\\n4 6\\n5 2\\n6 4\\n\", \"NO\\n\", \"YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n\", \"NO\\n\", \"YES\\n8 8\\n0 19\\n1 11\\n2 32\\n3 46\\n4 41\\n5 34\\n6 43\\n7 13\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n501 2\\n0 2\\n1 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n21 6\\n0 10\\n15 9\\n17 1\\n18 2\\n19 6\\n20 5\\n\", \"NO\\n\", \"YES\\n3 3\\n0 31\\n1 12\\n2 16\\n\", \"NO\\n\", \"YES\\n34 34\\n0 29\\n1 38\\n2 46\\n3 53\\n4 56\\n5 60\\n6 70\\n7 64\\n8 52\\n9 3\\n10 1\\n11 9\\n12 14\\n13 19\\n14 55\\n15 4\\n16 10\\n17 57\\n18 63\\n19 6\\n20 8\\n21 18\\n22 49\\n23 31\\n24 42\\n25 2\\n26 20\\n27 16\\n28 30\\n29 36\\n30 11\\n31 24\\n32 41\\n33 7\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n19 2\\n0 1\\n10 2\\n\", \"NO\\n\"]}", "source": "taco"} | Vasya’s elder brother Petya loves playing computer games. In one of his favourite computer games Petya reached the final level where a fight with the boss take place.
While playing the game Petya found spell scrolls and now he is about to use them. Let’s describe the way fighting goes on this level:
1) The boss has two parameters: max — the initial amount of health and reg — regeneration rate per second.
2) Every scroll also has two parameters: powi — spell power measured in percents — the maximal amount of health counted off the initial one, which allows to use the scroll (i.e. if the boss has more than powi percent of health the scroll cannot be used); and dmgi the damage per second inflicted upon the boss if the scroll is used. As soon as a scroll is used it disappears and another spell is cast upon the boss that inflicts dmgi of damage per second upon him until the end of the game.
During the battle the actions per second are performed in the following order: first the boss gets the damage from all the spells cast upon him, then he regenerates reg of health (at the same time he can’t have more than max of health), then the player may use another scroll (no more than one per second).
The boss is considered to be defeated if at the end of a second he has nonpositive ( ≤ 0) amount of health.
Help Petya to determine whether he can win with the set of scrolls available to him and if he can, determine the minimal number of seconds he needs to do it.
Input
The first line contains three integers N, max and reg (1 ≤ N, max, reg ≤ 1000) –– the amount of scrolls and the parameters of the boss. The next N lines contain two integers powi and dmgi each — the parameters of the i-th scroll (0 ≤ powi ≤ 100, 1 ≤ dmgi ≤ 2000).
Output
In case Petya can’t complete this level, output in the single line NO.
Otherwise, output on the first line YES. On the second line output the minimal time after which the boss can be defeated and the number of used scrolls. In the next lines for each used scroll output space-separated number of seconds passed from the start of the battle to the moment the scroll was used and the number of the scroll. Scrolls are numbered starting from 1 in the input order. The first scroll is considered to be available to be used after 0 seconds.
Output scrolls in the order they were used. It is not allowed to use scrolls after the boss is defeated.
Examples
Input
2 10 3
100 3
99 1
Output
NO
Input
2 100 10
100 11
90 9
Output
YES
19 2
0 1
10 2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1071 1029\\n5 3\\n0 0\", \"1251 1029\\n5 3\\n0 0\", \"1251 1802\\n5 3\\n0 0\", \"1071 446\\n5 3\\n0 0\", \"1071 2\\n5 3\\n0 0\", \"1071 1029\\n2 3\\n0 0\", \"1251 3458\\n5 3\\n0 0\", \"826 2\\n5 3\\n0 0\", \"1251 3458\\n10 3\\n0 0\", \"1164 1029\\n4 3\\n0 0\", \"1251 3458\\n10 6\\n0 0\", \"835 2\\n5 2\\n0 0\", \"584 1029\\n4 3\\n0 0\", \"1893 3458\\n10 6\\n0 0\", \"584 556\\n4 3\\n0 0\", \"1893 2905\\n10 6\\n0 0\", \"13 2\\n5 1\\n0 0\", \"443 1029\\n5 3\\n0 0\", \"1071 1\\n5 3\\n0 0\", \"1071 1825\\n4 3\\n0 0\", \"1164 1001\\n4 3\\n0 0\", \"1251 5715\\n10 6\\n0 0\", \"1893 3458\\n10 3\\n0 0\", \"968 556\\n4 3\\n0 0\", \"1251 1070\\n1 3\\n0 0\", \"1071 1\\n5 1\\n0 0\", \"1251 5715\\n10 10\\n0 0\", \"1893 3458\\n10 4\\n0 0\", \"858 556\\n4 3\\n0 0\", \"83 170\\n5 3\\n0 0\", \"15 1070\\n1 3\\n0 0\", \"1971 3458\\n7 2\\n0 0\", \"1164 1001\\n5 5\\n0 0\", \"1251 3144\\n10 10\\n0 0\", \"1893 3845\\n10 4\\n0 0\", \"1251 3144\\n10 7\\n0 0\", \"858 556\\n2 2\\n0 0\", \"6 882\\n5 5\\n0 0\", \"1971 2659\\n7 4\\n0 0\", \"1492 3144\\n10 7\\n0 0\", \"1492 3254\\n10 7\\n0 0\", \"1492 6388\\n10 7\\n0 0\", \"1492 6388\\n10 3\\n0 0\", \"653 3184\\n7 1\\n0 0\", \"1071 2050\\n5 5\\n0 0\", \"1251 249\\n5 3\\n0 0\", \"1548 446\\n5 3\\n0 0\", \"1164 1029\\n3 3\\n0 0\", \"584 1250\\n4 3\\n0 0\", \"1893 1185\\n10 6\\n0 0\", \"1893 2905\\n11 6\\n0 0\", \"249 1029\\n5 3\\n0 0\", \"340 1825\\n4 3\\n0 0\", \"1164 0001\\n5 5\\n0 0\", \"858 651\\n4 3\\n0 0\", \"2 1070\\n1 3\\n0 0\", \"1810 3845\\n10 4\\n0 0\", \"2444 3144\\n10 7\\n0 0\", \"809 556\\n2 2\\n0 0\", \"1492 3144\\n12 7\\n0 0\", \"1492 3254\\n10 5\\n0 0\", \"1456 6388\\n10 3\\n0 0\", \"424 11977\\n7 3\\n0 0\", \"653 5883\\n7 1\\n0 0\", \"1071 2050\\n3 5\\n0 0\", \"2020 1029\\n5 5\\n0 0\", \"999 851\\n5 3\\n0 0\", \"1548 208\\n5 3\\n0 0\", \"974 2\\n5 6\\n0 0\", \"1664 1029\\n4 3\\n0 0\", \"1545 3458\\n6 3\\n0 0\", \"835 4\\n5 4\\n0 0\", \"1164 1029\\n1 3\\n0 0\", \"584 588\\n4 3\\n0 0\", \"1893 1185\\n14 6\\n0 0\", \"1810 3998\\n10 4\\n0 0\", \"2444 5098\\n10 7\\n0 0\", \"70 6388\\n10 6\\n0 0\", \"653 3184\\n6 2\\n0 0\", \"2020 1791\\n5 5\\n0 0\", \"999 851\\n6 3\\n0 0\", \"1548 21\\n5 3\\n0 0\", \"1664 372\\n4 3\\n0 0\", \"1545 444\\n6 3\\n0 0\", \"584 588\\n4 2\\n0 0\", \"1893 1185\\n3 6\\n0 0\", \"1810 3998\\n10 6\\n0 0\", \"2444 5098\\n1 7\\n0 0\", \"653 8852\\n4 1\\n0 0\", \"763 1952\\n2 2\\n0 0\", \"1664 174\\n4 3\\n0 0\", \"2180 444\\n6 3\\n0 0\", \"835 4\\n9 1\\n0 0\", \"1577 2\\n2 4\\n0 0\", \"1519 1185\\n3 6\\n0 0\", \"1810 3998\\n12 6\\n0 0\", \"1971 2126\\n4 4\\n0 0\", \"1971 2126\\n2 4\\n0 0\", \"68 6388\\n11 6\\n0 0\", \"653 2469\\n4 1\\n0 0\", \"1071 1029\\n5 5\\n0 0\"], \"outputs\": [\"21 3\\n1 3\\n\", \"3 8\\n1 3\\n\", \"1 9\\n1 3\\n\", \"1 5\\n1 3\\n\", \"1 2\\n1 3\\n\", \"21 3\\n1 2\\n\", \"1 7\\n1 3\\n\", \"2 1\\n1 3\\n\", \"1 7\\n1 2\\n\", \"3 8\\n1 2\\n\", \"1 7\\n2 3\\n\", \"1 2\\n1 2\\n\", \"1 6\\n1 2\\n\", \"1 9\\n2 3\\n\", \"4 4\\n1 2\\n\", \"1 11\\n2 3\\n\", \"1 2\\n1 1\\n\", \"1 6\\n1 3\\n\", \"1 1\\n1 3\\n\", \"1 11\\n1 2\\n\", \"1 5\\n1 2\\n\", \"9 6\\n2 3\\n\", \"1 9\\n1 2\\n\", \"4 6\\n1 2\\n\", \"1 6\\n1 1\\n\", \"1 1\\n1 1\\n\", \"9 6\\n10 1\\n\", \"1 9\\n2 2\\n\", \"2 7\\n1 2\\n\", \"1 4\\n1 3\\n\", \"5 2\\n1 1\\n\", \"1 8\\n1 2\\n\", \"1 5\\n5 1\\n\", \"3 6\\n10 1\\n\", \"1 5\\n2 2\\n\", \"3 6\\n1 3\\n\", \"2 7\\n2 1\\n\", \"6 1\\n5 1\\n\", \"1 8\\n1 3\\n\", \"4 4\\n1 3\\n\", \"2 6\\n1 3\\n\", \"4 8\\n1 3\\n\", \"4 8\\n1 2\\n\", \"1 5\\n1 1\\n\", \"1 10\\n5 1\\n\", \"3 3\\n1 3\\n\", \"2 4\\n1 3\\n\", \"3 8\\n3 1\\n\", \"2 4\\n1 2\\n\", \"3 7\\n2 3\\n\", \"1 11\\n1 3\\n\", \"3 5\\n1 3\\n\", \"5 7\\n1 2\\n\", \"1 1\\n5 1\\n\", \"3 5\\n1 2\\n\", \"2 1\\n1 1\\n\", \"5 4\\n2 2\\n\", \"4 6\\n1 3\\n\", \"1 6\\n2 1\\n\", \"4 4\\n1 4\\n\", \"2 6\\n5 1\\n\", \"4 9\\n1 2\\n\", \"1 4\\n1 2\\n\", \"1 4\\n1 1\\n\", \"1 10\\n1 3\\n\", \"1 6\\n5 1\\n\", \"37 4\\n1 3\\n\", \"4 5\\n1 3\\n\", \"2 1\\n1 2\\n\", \"1 12\\n1 2\\n\", \"1 5\\n3 1\\n\", \"1 3\\n1 2\\n\", \"3 8\\n1 1\\n\", \"4 2\\n1 2\\n\", \"3 7\\n2 2\\n\", \"2 10\\n2 2\\n\", \"2 8\\n1 3\\n\", \"2 4\\n2 3\\n\", \"1 5\\n2 1\\n\", \"1 9\\n5 1\\n\", \"37 4\\n3 1\\n\", \"3 4\\n1 3\\n\", \"4 5\\n1 2\\n\", \"3 5\\n3 1\\n\", \"4 2\\n2 1\\n\", \"3 7\\n3 1\\n\", \"2 10\\n2 3\\n\", \"2 8\\n1 1\\n\", \"1 7\\n1 1\\n\", \"1 9\\n2 1\\n\", \"2 6\\n1 2\\n\", \"4 4\\n3 1\\n\", \"1 3\\n1 1\\n\", \"1 2\\n2 1\\n\", \"1 10\\n3 1\\n\", \"2 10\\n6 1\\n\", \"1 8\\n4 1\\n\", \"1 8\\n2 1\\n\", \"4 3\\n1 3\\n\", \"1 9\\n1 1\\n\", \"21 3\\n5 1\"]}", "source": "taco"} | The greatest common divisor is an indispensable element in mathematics handled on a computer. Using the greatest common divisor can make a big difference in the efficiency of the calculation. One of the algorithms to find the greatest common divisor is "Euclidean algorithm". The flow of the process is shown below.
<image>
For example, for 1071 and 1029, substitute 1071 for X and 1029 for Y,
The remainder of 1071 ÷ 1029 is 42, and 42 is substituted for X to replace X and Y. (1 step)
The remainder of 1029 ÷ 42 is 21, and 21 is substituted for X to replace X and Y. (2 steps)
The remainder of 42 ÷ 21 is 0, and 0 is substituted for X to replace X and Y. (3 steps)
Since Y has become 0, X at this time is the greatest common divisor. Therefore, the greatest common divisor is 21.
In this way, we were able to find the greatest common divisor of 1071 and 1029 in just three steps. The Euclidean algorithm produces results overwhelmingly faster than the method of comparing divisors.
Create a program that takes two integers as inputs, finds the greatest common divisor using the Euclidean algorithm, and outputs the greatest common divisor and the number of steps required for the calculation.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two lines of zeros. Two integers a, b (2 ≤ a, b ≤ 231-1) are given on one line for each dataset.
The number of datasets does not exceed 1000.
Output
For each data set, the greatest common divisor of the two input integers and the number of steps of the Euclidean algorithm for calculation are output on one line separated by blanks.
Example
Input
1071 1029
5 5
0 0
Output
21 3
5 1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3 3 3 2\\n1 1\\n2 1\\n3 1\\n2 3\\n\", \"3 5 3 2\\n1 2\\n2 3\\n3 1\\n1 5\\n\", \"3 6 3 2\\n1 6\\n2 2\\n3 4\\n1 6\\n\", \"2 2 2 2\\n1 1\\n1 2\\n1 2\\n\", \"5 5 10 3\\n3 1\\n3 2\\n3 5\\n1 5\\n2 1\\n2 5\\n1 2\\n1 4\\n3 3\\n2 4\\n2 1 5\\n\", \"5 3 10 3\\n5 3\\n1 1\\n2 2\\n1 3\\n3 2\\n5 2\\n2 3\\n2 1\\n3 1\\n5 1\\n1 2 3\\n\", \"3 3 8 2\\n2 2\\n1 2\\n2 1\\n2 3\\n3 2\\n1 3\\n3 1\\n3 3\\n3 2\\n\", \"200000 200000 2 2\\n104889 58569\\n855 142967\\n125218 47859\\n\", \"2 2 3 2\\n2 2\\n2 1\\n1 1\\n1 2\\n\", \"2 3 2 3\\n1 1\\n1 2\\n2 1 3\\n\", \"3 2 4 2\\n3 2\\n2 1\\n2 2\\n3 1\\n2 1\\n\", \"11 2 4 2\\n5 1\\n4 1\\n8 2\\n5 2\\n1 2\\n\", \"2 11 7 6\\n1 1\\n1 5\\n1 2\\n1 4\\n1 11\\n1 8\\n1 3\\n3 6 5 10 2 7\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 4\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 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\"6 6 3 2\\n1 6\\n2 2\\n3 2\\n1 6\\n\", \"2 2 2 2\\n1 1\\n1 1\\n1 2\\n\", \"3 3 8 2\\n2 2\\n1 2\\n2 1\\n2 3\\n3 2\\n1 3\\n3 1\\n3 3\\n3 1\\n\", \"2 3 2 3\\n1 1\\n1 3\\n2 1 3\\n\", \"2 3 2 3\\n2 1\\n1 3\\n2 1 3\\n\", \"3 5 3 2\\n2 3\\n2 3\\n3 2\\n1 5\\n\", \"2 4 2 2\\n1 1\\n1 2\\n1 2\\n\", \"200000 200000 2 2\\n104889 58569\\n855 189083\\n125218 47859\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 4\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 10\\n2 12\\n2 3\\n3 3\\n3 39\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"5 3 10 3\\n5 3\\n1 1\\n2 2\\n1 3\\n3 2\\n2 2\\n2 3\\n2 1\\n3 1\\n5 1\\n1 2 3\\n\", \"21 3 61 3\\n18 3\\n21 3\\n11 3\\n13 2\\n5 2\\n14 2\\n10 3\\n9 3\\n12 1\\n1 2\\n7 2\\n20 1\\n16 3\\n18 2\\n9 1\\n20 3\\n17 3\\n6 1\\n4 2\\n1 1\\n3 1\\n4 1\\n6 3\\n6 2\\n2 1\\n13 3\\n5 3\\n3 2\\n13 1\\n10 1\\n11 1\\n18 1\\n11 2\\n5 1\\n19 2\\n20 2\\n16 1\\n12 3\\n2 2\\n3 3\\n19 3\\n8 2\\n15 3\\n8 1\\n14 1\\n17 1\\n21 1\\n19 1\\n21 2\\n12 2\\n2 3\\n8 3\\n1 3\\n16 2\\n17 2\\n7 1\\n10 2\\n18 2\\n7 3\\n4 3\\n14 3\\n2 3 1\\n\", \"3 6 3 2\\n1 6\\n3 2\\n3 4\\n1 6\\n\", \"3 5 3 2\\n2 2\\n2 1\\n3 2\\n1 2\\n\", \"3 3 8 2\\n2 2\\n1 2\\n2 1\\n2 3\\n1 2\\n1 3\\n3 1\\n3 3\\n3 2\\n\", \"5 5 10 3\\n3 1\\n3 2\\n3 10\\n1 5\\n3 1\\n2 5\\n1 2\\n1 4\\n3 3\\n2 4\\n2 1 5\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 16\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"3 5 3 2\\n2 2\\n2 3\\n3 1\\n1 2\\n\", \"5 6 10 3\\n3 1\\n3 2\\n3 10\\n1 5\\n3 1\\n2 5\\n1 2\\n1 4\\n3 3\\n2 4\\n2 1 5\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 8\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 16\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"3 5 3 2\\n2 2\\n2 1\\n3 1\\n1 2\\n\", \"1 11 7 6\\n1 1\\n1 5\\n1 2\\n1 4\\n1 11\\n1 8\\n1 3\\n3 6 5 10 2 7\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 4\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 4\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 10\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"3 5 3 2\\n1 1\\n2 1\\n3 1\\n2 3\\n\", \"3 5 3 2\\n1 3\\n2 3\\n3 1\\n1 5\\n\", \"5 5 10 3\\n3 1\\n3 2\\n3 10\\n1 5\\n2 1\\n2 5\\n1 2\\n1 4\\n3 4\\n2 4\\n2 1 5\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n2 12\\n3 1\\n2 13\\n3 18\\n2 10\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"3 3 4 2\\n3 2\\n2 1\\n2 2\\n3 1\\n2 2\\n\", \"6 6 3 2\\n1 6\\n2 2\\n3 2\\n1 5\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 8\\n3 13\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 8\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 16\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"3 5 3 2\\n1 1\\n2 1\\n3 1\\n2 2\\n\", \"3 5 3 2\\n2 3\\n2 3\\n3 1\\n1 5\\n\", \"3 5 3 2\\n2 3\\n2 3\\n3 4\\n1 5\\n\", \"2 11 7 6\\n1 1\\n1 1\\n1 2\\n1 4\\n1 11\\n1 8\\n1 3\\n3 6 5 10 2 7\\n\", \"11 2 4 2\\n4 1\\n4 1\\n8 2\\n5 2\\n1 2\\n\", \"2 2 3 2\\n2 2\\n2 2\\n1 1\\n1 2\\n\", \"3 3 8 2\\n2 2\\n1 2\\n2 1\\n2 3\\n1 2\\n1 3\\n3 1\\n3 3\\n3 0\\n\", \"6 11 3 2\\n1 6\\n2 2\\n3 4\\n1 6\\n\", \"3 5 3 2\\n1 2\\n1 3\\n3 1\\n1 2\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 16\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 2 18 2 12 11 21\\n\", \"6 6 3 2\\n1 6\\n2 2\\n3 2\\n1 2\\n\", \"3 5 3 2\\n2 2\\n1 3\\n3 1\\n1 2\\n\", \"1 11 7 6\\n1 1\\n1 7\\n1 2\\n1 4\\n1 11\\n1 8\\n1 3\\n3 6 5 10 2 7\\n\", \"2 2 2 2\\n1 1\\n1 1\\n1 0\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 4\\n3 6\\n2 4\\n3 10\\n2 19\\n3 15\\n3 13\\n3 2\\n3 12\\n3 4\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n1 12\\n3 1\\n2 13\\n3 18\\n2 10\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"2 3 2 3\\n1 1\\n1 3\\n2 1 2\\n\", \"3 5 3 2\\n1 1\\n2 1\\n3 1\\n4 3\\n\", \"5 5 10 3\\n3 1\\n3 2\\n3 10\\n1 5\\n3 1\\n2 5\\n1 2\\n1 4\\n3 4\\n2 4\\n2 1 5\\n\", \"3 21 49 11\\n3 5\\n1 14\\n2 17\\n3 17\\n3 9\\n1 9\\n3 20\\n2 9\\n3 11\\n2 4\\n3 16\\n2 7\\n1 2\\n3 7\\n3 8\\n2 15\\n2 2\\n3 6\\n2 5\\n3 10\\n2 19\\n3 15\\n3 4\\n3 2\\n3 12\\n3 3\\n2 20\\n2 8\\n3 14\\n2 6\\n2 1\\n1 16\\n2 18\\n2 21\\n3 19\\n2 16\\n2 11\\n1 3\\n2 14\\n1 6\\n2 12\\n3 1\\n2 13\\n3 18\\n2 10\\n2 12\\n2 3\\n3 3\\n3 21\\n14 8 20 6 4 10 18 2 12 11 21\\n\", \"6 8 3 2\\n1 6\\n2 2\\n3 2\\n1 5\\n\", \"3 6 3 2\\n1 6\\n2 2\\n3 4\\n1 6\\n\", \"3 3 3 2\\n1 1\\n2 1\\n3 1\\n2 3\\n\", \"3 5 3 2\\n1 2\\n2 3\\n3 1\\n1 5\\n\"], \"outputs\": [\"6\", \"8\", \"15\", \"1\", \"14\", \"12\", \"10\", \"332252\", \"2\", \"1\", \"4\", \"8\", \"10\", \"64\", \"62\", \"10\\n\", \"1\\n\", \"332252\\n\", \"14\\n\", \"64\\n\", \"12\\n\", \"4\\n\", \"8\\n\", \"2\\n\", \"10\\n\", \"62\\n\", \"1\\n\", \"10\\n\", \"19\\n\", \"64\\n\", \"4\\n\", \"60\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"0\\n\", \"8\\n\", \"2\\n\", \"5\\n\", \"7\\n\", \"1\\n\", \"424484\\n\", \"82\\n\", \"12\\n\", \"62\\n\", \"11\\n\", \"3\\n\", \"10\\n\", \"19\\n\", \"64\\n\", \"6\\n\", \"19\\n\", \"64\\n\", \"4\\n\", \"10\\n\", \"64\\n\", \"6\\n\", \"10\\n\", \"19\\n\", \"64\\n\", \"6\\n\", \"13\\n\", \"64\\n\", \"6\\n\", \"6\\n\", \"7\\n\", \"10\\n\", \"8\\n\", \"2\\n\", \"10\\n\", \"15\\n\", \"6\\n\", \"64\\n\", \"11\\n\", \"6\\n\", \"10\\n\", \"0\\n\", \"64\\n\", \"2\\n\", \"10\\n\", \"19\\n\", \"64\\n\", \"13\\n\", \"15\\n\", \"6\\n\", \"8\\n\"]}", "source": "taco"} | You are on the island which can be represented as a $n \times m$ table. The rows are numbered from $1$ to $n$ and the columns are numbered from $1$ to $m$. There are $k$ treasures on the island, the $i$-th of them is located at the position $(r_i, c_i)$.
Initially you stand at the lower left corner of the island, at the position $(1, 1)$. If at any moment you are at the cell with a treasure, you can pick it up without any extra time. In one move you can move up (from $(r, c)$ to $(r+1, c)$), left (from $(r, c)$ to $(r, c-1)$), or right (from position $(r, c)$ to $(r, c+1)$). Because of the traps, you can't move down.
However, moving up is also risky. You can move up only if you are in a safe column. There are $q$ safe columns: $b_1, b_2, \ldots, b_q$. You want to collect all the treasures as fast as possible. Count the minimum number of moves required to collect all the treasures.
-----Input-----
The first line contains integers $n$, $m$, $k$ and $q$ ($2 \le n, \, m, \, k, \, q \le 2 \cdot 10^5$, $q \le m$) — the number of rows, the number of columns, the number of treasures in the island and the number of safe columns.
Each of the next $k$ lines contains two integers $r_i, c_i$, ($1 \le r_i \le n$, $1 \le c_i \le m$) — the coordinates of the cell with a treasure. All treasures are located in distinct cells.
The last line contains $q$ distinct integers $b_1, b_2, \ldots, b_q$ ($1 \le b_i \le m$) — the indices of safe columns.
-----Output-----
Print the minimum number of moves required to collect all the treasures.
-----Examples-----
Input
3 3 3 2
1 1
2 1
3 1
2 3
Output
6
Input
3 5 3 2
1 2
2 3
3 1
1 5
Output
8
Input
3 6 3 2
1 6
2 2
3 4
1 6
Output
15
-----Note-----
In the first example you should use the second column to go up, collecting in each row treasures from the first column. [Image]
In the second example, it is optimal to use the first column to go up. [Image]
In the third example, it is optimal to collect the treasure at cell $(1;6)$, go up to row $2$ at column $6$, then collect the treasure at cell $(2;2)$, go up to the top row at column $1$ and collect the last treasure at cell $(3;4)$. That's a total of $15$ moves. [Image]
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[1221], [110011], [1456009006541], [123322], [1], [152], [9999], [\"ACCDDCCA\"], [\"@14AbC\"], [\"1221\"], [-450]], \"outputs\": [[true], [true], [true], [false], [true], [false], [true], [\"Not valid\"], [\"Not valid\"], [\"Not valid\"], [\"Not valid\"]]}", "source": "taco"} | A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are:
2332
110011
54322345
For a given number `num`, write a function to test if it's a numerical palindrome or not and return a boolean (true if it is and false if not).
```if-not:haskell
Return "Not valid" if the input is not an integer or less than `0`.
```
```if:haskell
Return `Nothing` if the input is less than `0` and `Just True` or `Just False` otherwise.
```
Other Kata in this Series:
Numerical Palindrome #1
Numerical Palindrome #1.5
Numerical Palindrome #2
Numerical Palindrome #3
Numerical Palindrome #3.5
Numerical Palindrome #4
Numerical Palindrome #5
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n4 5 7\\n\", \"2\\n1 1\\n\", \"10\\n38282 53699 38282 38282 38282 38282 38282 38282 38282 38282\\n\", \"10\\n50165 50165 50165 50165 50165 50165 50165 50165 50165 50165\\n\", \"10\\n83176 83176 83176 23495 83176 8196 83176 23495 83176 83176\\n\", \"10\\n32093 36846 32093 32093 36846 36846 36846 36846 36846 36846\\n\", \"3\\n1 2 3\\n\", \"4\\n2 3 4 5\\n\", \"10\\n30757 30757 33046 41744 39918 39914 41744 39914 33046 33046\\n\", \"10\\n50096 50096 50096 50096 50096 50096 28505 50096 50096 50096\\n\", \"10\\n54842 54842 54842 54842 57983 54842 54842 57983 57983 54842\\n\", \"10\\n87900 87900 5761 87900 87900 87900 5761 87900 87900 87900\\n\", \"10\\n53335 35239 26741 35239 35239 26741 35239 35239 53335 35239\\n\", \"10\\n75994 64716 75994 64716 75994 75994 56304 64716 56304 64716\\n\", \"1\\n1\\n\", \"5\\n2 2 1 1 1\\n\", \"5\\n1 4 4 5 5\\n\", \"3\\n1 3 3\\n\", \"3\\n2 2 2\\n\", \"5\\n1 1 1 2 2\\n\", \"4\\n1 2 1 2\\n\", \"7\\n7 7 7 7 6 6 6\\n\", \"3\\n2 3 3\\n\", \"3\\n1 1 100000\\n\", \"1\\n100000\\n\", \"5\\n3 3 3 4 4\\n\", \"3\\n1 2 2\\n\", \"3\\n4 4 5\\n\", \"1\\n2\\n\", \"3\\n97 97 100\\n\", \"5\\n100000 100000 100000 1 1\\n\", \"7\\n7 7 6 6 5 5 4\\n\", \"5\\n100000 100000 100000 2 2\\n\", \"4\\n3 3 2 1\\n\", \"1\\n485\\n\", \"3\\n4 4 100000\\n\", \"3\\n1 1 2\\n\", \"3\\n1 1 1\\n\", \"5\\n1 1 2 2 2\\n\", \"5\\n1 4 4 5 5\\n\", \"4\\n3 3 2 1\\n\", \"1\\n100000\\n\", \"10\\n50096 50096 50096 50096 50096 50096 28505 50096 50096 50096\\n\", \"3\\n4 4 100000\\n\", \"1\\n2\\n\", \"10\\n87900 87900 5761 87900 87900 87900 5761 87900 87900 87900\\n\", \"7\\n7 7 7 7 6 6 6\\n\", \"7\\n7 7 6 6 5 5 4\\n\", \"10\\n53335 35239 26741 35239 35239 26741 35239 35239 53335 35239\\n\", \"10\\n30757 30757 33046 41744 39918 39914 41744 39914 33046 33046\\n\", \"3\\n1 1 2\\n\", \"3\\n4 4 5\\n\", \"3\\n1 3 3\\n\", \"4\\n1 2 1 2\\n\", \"5\\n1 1 1 2 2\\n\", \"3\\n2 3 3\\n\", \"5\\n100000 100000 100000 2 2\\n\", \"5\\n2 2 1 1 1\\n\", \"4\\n2 3 4 5\\n\", \"10\\n75994 64716 75994 64716 75994 75994 56304 64716 56304 64716\\n\", \"3\\n1 2 2\\n\", \"1\\n485\\n\", \"10\\n54842 54842 54842 54842 57983 54842 54842 57983 57983 54842\\n\", \"10\\n38282 53699 38282 38282 38282 38282 38282 38282 38282 38282\\n\", \"5\\n1 1 2 2 2\\n\", \"10\\n32093 36846 32093 32093 36846 36846 36846 36846 36846 36846\\n\", \"5\\n3 3 3 4 4\\n\", \"3\\n2 2 2\\n\", \"3\\n1 1 100000\\n\", \"10\\n50165 50165 50165 50165 50165 50165 50165 50165 50165 50165\\n\", \"3\\n1 1 1\\n\", \"3\\n97 97 100\\n\", \"1\\n1\\n\", \"3\\n1 2 3\\n\", \"10\\n83176 83176 83176 23495 83176 8196 83176 23495 83176 83176\\n\", \"5\\n100000 100000 100000 1 1\\n\", \"4\\n3 2 2 1\\n\", \"4\\n0 2 0 2\\n\", \"10\\n50096 50096 50096 50096 50096 50096 55337 50096 50096 50096\\n\", \"10\\n87900 87900 5761 59670 87900 87900 5761 87900 87900 87900\\n\", \"7\\n7 7 6 6 5 7 4\\n\", \"10\\n53335 35239 26741 28797 35239 26741 35239 35239 53335 35239\\n\", \"10\\n30757 30757 5314 41744 39918 39914 41744 39914 33046 33046\\n\", \"3\\n4 6 5\\n\", \"3\\n2 6 3\\n\", \"4\\n0 2 1 2\\n\", \"5\\n1 1 1 1 2\\n\", \"3\\n2 3 5\\n\", \"5\\n2 2 1 2 1\\n\", \"4\\n2 3 5 5\\n\", \"3\\n1 2 0\\n\", \"1\\n147\\n\", \"10\\n38282 53699 38282 69689 38282 38282 38282 38282 38282 38282\\n\", \"5\\n1 1 2 2 1\\n\", \"10\\n32093 51620 32093 32093 36846 36846 36846 36846 36846 36846\\n\", \"5\\n3 4 3 4 4\\n\", \"3\\n2 2 3\\n\", \"3\\n0 1 100000\\n\", \"10\\n50165 50165 50165 50165 50165 50165 50165 50165 50165 66719\\n\", \"3\\n1 0 2\\n\", \"3\\n150 97 100\\n\", \"1\\n4\\n\", \"3\\n2 2 4\\n\", \"3\\n4 2 7\\n\", \"2\\n0 1\\n\", \"4\\n3 4 2 1\\n\", \"10\\n50096 50096 50096 83009 50096 50096 55337 50096 50096 50096\\n\", \"7\\n7 5 6 6 5 7 4\\n\", \"10\\n53335 35239 36302 28797 35239 26741 35239 35239 53335 35239\\n\", \"10\\n30757 49832 5314 41744 39918 39914 41744 39914 33046 33046\\n\", \"3\\n4 1 5\\n\", \"3\\n2 6 5\\n\", \"5\\n1 0 1 1 2\\n\", \"3\\n2 3 4\\n\", \"5\\n2 2 1 2 2\\n\", \"4\\n2 6 5 5\\n\", \"3\\n1 2 1\\n\", \"1\\n225\\n\", \"10\\n38282 53699 38282 69689 38282 38282 38282 8227 38282 38282\\n\", \"5\\n1 1 3 2 1\\n\", \"10\\n32093 51620 32093 32093 36846 36846 36846 36846 36846 65962\\n\", \"3\\n4 2 3\\n\", \"10\\n50165 50165 50165 50165 50165 50165 50855 50165 50165 66719\\n\", \"3\\n1 0 0\\n\", \"3\\n240 97 100\\n\", \"3\\n3 2 4\\n\", \"3\\n4 2 1\\n\", \"2\\n0 2\\n\", \"4\\n3 1 2 1\\n\", \"7\\n7 5 6 6 5 5 4\\n\", \"10\\n53335 35239 36302 28797 35239 26741 63400 35239 53335 35239\\n\", \"10\\n30757 49832 5314 41744 39918 39914 41744 52593 33046 33046\\n\", \"3\\n5 1 5\\n\", \"3\\n2 6 2\\n\", \"4\\n1 2 0 2\\n\", \"5\\n1 0 1 1 0\\n\", \"3\\n2 0 4\\n\", \"4\\n2 12 5 5\\n\", \"1\\n280\\n\", \"10\\n38282 53699 38282 69689 63357 38282 38282 8227 38282 38282\\n\", \"5\\n2 1 3 2 1\\n\", \"10\\n32093 51620 32093 32093 36846 36846 36846 36846 36846 76231\\n\", \"3\\n4 2 4\\n\", \"10\\n50165 50165 10543 50165 50165 50165 50855 50165 50165 66719\\n\", \"3\\n2 0 0\\n\", \"3\\n94 97 100\\n\", \"3\\n3 3 4\\n\", \"3\\n6 2 1\\n\", \"2\\n1 0\\n\", \"4\\n3 0 2 1\\n\", \"7\\n7 5 6 6 5 0 4\\n\", \"10\\n84715 35239 36302 28797 35239 26741 63400 35239 53335 35239\\n\", \"10\\n30757 49832 5314 41744 39918 39914 41744 52593 33046 42822\\n\", \"3\\n5 1 8\\n\", \"3\\n2 6 1\\n\", \"4\\n1 0 0 2\\n\", \"3\\n1 0 4\\n\", \"4\\n3 12 5 5\\n\", \"1\\n16\\n\", \"10\\n38282 53699 38282 69689 63357 38282 38282 8227 38282 50884\\n\", \"5\\n2 1 2 2 1\\n\", \"10\\n32093 51620 32093 32093 36846 36846 36846 36846 8485 76231\\n\", \"3\\n6 2 4\\n\", \"10\\n50165 50165 10543 50165 14278 50165 50855 50165 50165 66719\\n\", \"3\\n2 1 0\\n\", \"3\\n94 97 000\\n\", \"3\\n4 5 7\\n\", \"2\\n1 1\\n\"], \"outputs\": [\"Conan\\n\", \"Agasa\\n\", \"Conan\\n\", \"Agasa\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Agasa\\n\", \"Agasa\\n\", \"Agasa\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Agasa\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Agasa\", \"Conan\", \"Conan\", \"Agasa\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Agasa\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Agasa\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Agasa\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\", \"Conan\\n\", \"Agasa\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\\n\", \"Conan\", \"Agasa\"]}", "source": "taco"} | Edogawa Conan got tired of solving cases, and invited his friend, Professor Agasa, over. They decided to play a game of cards. Conan has n cards, and the i-th card has a number a_{i} written on it.
They take turns playing, starting with Conan. In each turn, the player chooses a card and removes it. Also, he removes all cards having a number strictly lesser than the number on the chosen card. Formally, if the player chooses the i-th card, he removes that card and removes the j-th card for all j such that a_{j} < a_{i}.
A player loses if he cannot make a move on his turn, that is, he loses if there are no cards left. Predict the outcome of the game, assuming both players play optimally.
-----Input-----
The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of cards Conan has.
The next line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^5), where a_{i} is the number on the i-th card.
-----Output-----
If Conan wins, print "Conan" (without quotes), otherwise print "Agasa" (without quotes).
-----Examples-----
Input
3
4 5 7
Output
Conan
Input
2
1 1
Output
Agasa
-----Note-----
In the first example, Conan can just choose the card having number 7 on it and hence remove all the cards. After that, there are no cards left on Agasa's turn.
In the second example, no matter which card Conan chooses, there will be one one card left, which Agasa can choose. After that, there are no cards left when it becomes Conan's turn again.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 1\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 1\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 16 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 1\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 16 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n16 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 17 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 16 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 17 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n2 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 16 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 17 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 2 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 1\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 5 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 13 7 20 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 1\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 16 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 18\\n20 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 9 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 17 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 4 5\\n5 5\\n2 5 3 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 5\\n0 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 16 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 17 20 20 4\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 1 2 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 13 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 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3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 16 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n16 20 20 20 7 20 20 20 20\\n0 0\", \"5 5\\n1 2 3 4 5\\n1 2 3 4 5\\n5 5\\n2 5 4 1 3\\n4 1 5 3 2\\n5 5\\n1 2 3 4 5\\n3 3 3 4 5\\n3 3\\n7 7 7\\n7 7 7\\n3 3\\n4 4 4\\n4 3 4\\n4 3\\n4 2 2 4\\n4 2 1\\n4 4\\n2 8 8 8\\n2 3 8 3\\n10 10\\n9 9 9 9 9 9 9 9 9 9\\n9 9 9 9 9 9 9 9 9 9\\n10 9\\n20 1 20 20 20 20 20 18 20 20\\n20 20 20 20 7 20 20 20 20\\n0 0\"], \"outputs\": [\"16\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n90\\n186\\n\", \"16\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n190\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n40\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n40\\n90\\n202\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n32\\n90\\n190\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n32\\n90\\n207\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n32\\n106\\n207\\n\", \"16\\n15\\n22\\n21\\n15\\n14\\n32\\n106\\n207\\n\", \"18\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n203\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n40\\n90\\n204\\n\", \"16\\n15\\n21\\n30\\n15\\n14\\n32\\n90\\n207\\n\", \"16\\n18\\n21\\n21\\n15\\n14\\n32\\n106\\n207\\n\", \"18\\n15\\n21\\n34\\n15\\n13\\n32\\n90\\n186\\n\", \"16\\n16\\n20\\n21\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n15\\n21\\n21\\n15\\n13\\n34\\n90\\n203\\n\", \"16\\n18\\n21\\n21\\n12\\n14\\n32\\n106\\n207\\n\", \"18\\n15\\n21\\n34\\n15\\n12\\n32\\n90\\n186\\n\", \"16\\n16\\n20\\n30\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n18\\n21\\n35\\n12\\n14\\n32\\n106\\n207\\n\", \"18\\n20\\n21\\n34\\n15\\n12\\n32\\n90\\n186\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n32\\n106\\n207\\n\", \"18\\n20\\n21\\n34\\n15\\n12\\n32\\n90\\n191\\n\", \"18\\n18\\n21\\n35\\n12\\n12\\n32\\n106\\n207\\n\", \"18\\n20\\n21\\n34\\n15\\n12\\n32\\n96\\n191\\n\", \"18\\n18\\n21\\n35\\n12\\n12\\n32\\n109\\n207\\n\", \"18\\n18\\n18\\n35\\n12\\n12\\n32\\n109\\n207\\n\", \"18\\n18\\n18\\n35\\n12\\n12\\n32\\n117\\n207\\n\", \"15\\n15\\n21\\n21\\n15\\n13\\n39\\n90\\n186\\n\", \"16\\n15\\n21\\n21\\n15\\n13\\n32\\n97\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n90\\n189\\n\", \"16\\n15\\n21\\n21\\n15\\n13\\n32\\n105\\n190\\n\", \"16\\n23\\n21\\n21\\n15\\n13\\n40\\n90\\n186\\n\", \"16\\n15\\n21\\n30\\n15\\n13\\n32\\n90\\n190\\n\", \"22\\n16\\n21\\n21\\n15\\n13\\n40\\n90\\n202\\n\", \"15\\n15\\n21\\n21\\n15\\n14\\n32\\n90\\n207\\n\", \"16\\n15\\n23\\n21\\n15\\n14\\n32\\n106\\n207\\n\", \"18\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n195\\n\", \"16\\n15\\n27\\n21\\n15\\n13\\n32\\n90\\n203\\n\", \"16\\n18\\n21\\n21\\n15\\n14\\n32\\n110\\n207\\n\", \"16\\n16\\n19\\n21\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n34\\n90\\n203\\n\", \"18\\n15\\n25\\n34\\n15\\n12\\n32\\n90\\n186\\n\", \"16\\n18\\n21\\n46\\n12\\n14\\n32\\n106\\n207\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n32\\n108\\n207\\n\", \"18\\n20\\n21\\n34\\n15\\n12\\n32\\n98\\n191\\n\", \"18\\n18\\n18\\n35\\n12\\n12\\n32\\n106\\n207\\n\", \"18\\n18\\n18\\n35\\n13\\n12\\n32\\n117\\n207\\n\", \"16\\n18\\n18\\n35\\n12\\n12\\n32\\n117\\n207\\n\", \"15\\n15\\n21\\n21\\n15\\n13\\n42\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n97\\n189\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n31\\n90\\n190\\n\", \"16\\n15\\n28\\n21\\n15\\n14\\n32\\n106\\n207\\n\", \"16\\n18\\n21\\n21\\n15\\n14\\n32\\n110\\n206\\n\", \"16\\n15\\n19\\n21\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n34\\n98\\n203\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n32\\n107\\n207\\n\", \"18\\n21\\n18\\n35\\n13\\n12\\n32\\n117\\n207\\n\", \"18\\n18\\n18\\n35\\n9\\n12\\n32\\n117\\n207\\n\", \"15\\n15\\n23\\n21\\n15\\n13\\n42\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n97\\n185\\n\", \"16\\n23\\n21\\n21\\n21\\n13\\n40\\n90\\n186\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n31\\n102\\n190\\n\", \"16\\n15\\n28\\n21\\n15\\n14\\n32\\n106\\n195\\n\", \"16\\n17\\n19\\n21\\n15\\n13\\n32\\n90\\n191\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n32\\n102\\n207\\n\", \"18\\n21\\n18\\n35\\n13\\n12\\n32\\n125\\n207\\n\", \"16\\n16\\n21\\n21\\n15\\n13\\n32\\n114\\n185\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n31\\n118\\n190\\n\", \"16\\n15\\n28\\n27\\n15\\n14\\n32\\n106\\n195\\n\", \"16\\n17\\n19\\n21\\n15\\n13\\n32\\n92\\n191\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n36\\n102\\n207\\n\", \"18\\n18\\n18\\n35\\n9\\n12\\n32\\n126\\n207\\n\", \"16\\n21\\n21\\n21\\n15\\n13\\n32\\n114\\n185\\n\", \"16\\n15\\n21\\n21\\n15\\n14\\n32\\n118\\n190\\n\", \"16\\n15\\n29\\n27\\n15\\n14\\n32\\n106\\n195\\n\", \"16\\n17\\n19\\n21\\n15\\n13\\n32\\n98\\n191\\n\", \"16\\n18\\n21\\n35\\n12\\n12\\n36\\n117\\n207\\n\", \"16\\n21\\n21\\n21\\n15\\n13\\n32\\n130\\n185\\n\", \"16\\n15\\n29\\n27\\n15\\n14\\n32\\n99\\n195\\n\", \"16\\n19\\n19\\n21\\n15\\n13\\n32\\n98\\n191\\n\", \"16\\n21\\n21\\n21\\n15\\n14\\n32\\n130\\n185\\n\", \"16\\n19\\n19\\n21\\n12\\n13\\n32\\n98\\n191\\n\", \"19\\n21\\n21\\n21\\n15\\n14\\n32\\n130\\n185\\n\", \"16\\n19\\n19\\n21\\n12\\n13\\n26\\n98\\n191\\n\", \"19\\n21\\n21\\n21\\n15\\n14\\n32\\n130\\n198\\n\", \"16\\n19\\n22\\n21\\n12\\n13\\n26\\n98\\n191\\n\", \"16\\n19\\n23\\n21\\n12\\n13\\n26\\n98\\n191\\n\", \"16\\n17\\n23\\n21\\n12\\n13\\n26\\n98\\n191\\n\", \"16\\n17\\n20\\n21\\n12\\n13\\n26\\n98\\n191\\n\", \"16\\n17\\n20\\n21\\n12\\n13\\n26\\n98\\n210\\n\", \"16\\n18\\n20\\n21\\n12\\n13\\n26\\n98\\n210\\n\", \"16\\n18\\n20\\n21\\n12\\n13\\n26\\n109\\n210\\n\", \"15\\n15\\n21\\n21\\n15\\n13\\n32\\n92\\n186\\n\", \"16\\n16\\n21\\n21\\n23\\n13\\n32\\n90\\n186\\n\", \"16\\n16\\n21\\n21\\n12\\n13\\n40\\n90\\n186\\n\", \"16\\n15\\n21\\n21\\n19\\n13\\n32\\n90\\n190\\n\", \"16\\n17\\n21\\n21\\n15\\n13\\n40\\n90\\n202\\n\", \"15\\n15\\n21\\n21\\n15\\n13\\n32\\n90\\n186\"]}", "source": "taco"} | International Center for Picassonian Cubism is a Spanish national museum of cubist artworks, dedicated to Pablo Picasso. The center held a competition for an artwork that will be displayed in front of the facade of the museum building. The artwork is a collection of cubes that are piled up on the ground and is intended to amuse visitors, who will be curious how the shape of the collection of cubes changes when it is seen from the front and the sides.
The artwork is a collection of cubes with edges of one foot long and is built on a flat ground that is divided into a grid of one foot by one foot squares. Due to some technical reasons, cubes of the artwork must be either put on the ground, fitting into a unit square in the grid, or put on another cube in the way that the bottom face of the upper cube exactly meets the top face of the lower cube. No other way of putting cubes is possible.
You are a member of the judging committee responsible for selecting one out of a plenty of artwork proposals submitted to the competition. The decision is made primarily based on artistic quality but the cost for installing the artwork is another important factor. Your task is to investigate the installation cost for each proposal. The cost is proportional to the number of cubes, so you have to figure out the minimum number of cubes needed for installation.
Each design proposal of an artwork consists of the front view and the side view (the view seen from the right-hand side), as shown in Figure 1.
<image>
Figure 1: An example of an artwork proposal
The front view (resp., the side view) indicates the maximum heights of piles of cubes for each column line (resp., row line) of the grid.
There are several ways to install this proposal of artwork, such as the following figures.
<image>
In these figures, the dotted lines on the ground indicate the grid lines. The left figure makes use of 16 cubes, which is not optimal. That is, the artwork can be installed with a fewer number of cubes. Actually, the right one is optimal and only uses 13 cubes. Note that, a single pile of height three in the right figure plays the roles of two such piles in the left one.
Notice that swapping columns of cubes does not change the side view. Similarly, swapping rows does not change the front view. Thus, such swaps do not change the costs of building the artworks.
For example, consider the artwork proposal given in Figure 2.
<image>
Figure 2: Another example of artwork proposal
An optimal installation of this proposal of artwork can be achieved with 13 cubes, as shown in the following figure, which can be obtained by exchanging the rightmost two columns of the optimal installation of the artwork of Figure 1.
<image>
Input
The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. Each dataset is formatted as follows.
w d
h1 h2 ... hw
h'1 h'2 ... h'd
The integers w and d separated by a space are the numbers of columns and rows of the grid, respectively. You may assume 1 ≤ w ≤ 10 and 1 ≤ d ≤ 10. The integers separated by a space in the second and third lines specify the shape of the artwork. The integers hi (1 ≤ hi ≤ 20, 1 ≤ i ≤ w) in the second line give the front view, i.e., the maximum heights of cubes per each column line, ordered from left to right (seen from the front). The integers hi (1 ≤ hi ≤ 20, 1 ≤ i ≤ d) in the third line give the side view, i.e., the maximum heights of cubes per each row line, ordered from left to right (seen from the right-hand side).
Output
For each dataset, output a line containing the minimum number of cubes. The output should not contain any other extra characters.
You can assume that, for each dataset, there is at least one way to install the artwork.
Example
Input
5 5
1 2 3 4 5
1 2 3 4 5
5 5
2 5 4 1 3
4 1 5 3 2
5 5
1 2 3 4 5
3 3 3 4 5
3 3
7 7 7
7 7 7
3 3
4 4 4
4 3 4
4 3
4 2 2 4
4 2 1
4 4
2 8 8 8
2 3 8 3
10 10
9 9 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 9 9 9
10 9
20 1 20 20 20 20 20 18 20 20
20 20 20 20 7 20 20 20 20
0 0
Output
15
15
21
21
15
13
32
90
186
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2\", \"3 7 3\\n0 1 1 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 2\\n4 2 1 2\", \"5 10 5\\n0 1 1 4\\n0 2 1 2\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2\", \"3 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 0\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"3 7 3\\n0 1 2 1\\n1 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 2\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n0 1 1 1\\n2 2 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 0\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 1\\n0 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n4 2 1 2\", \"5 10 0\\n0 1 1 1\\n0 2 1 2\\n0 1 3 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 4\\n4 1 1 2\\n4 2 0 2\", \"5 10 7\\n0 1 1 4\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 2\", \"5 10 7\\n0 1 1 4\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 1\\n3 3 2 2\\n4 1 1 2\\n2 2 1 1\", \"5 10 7\\n1 1 1 4\\n1 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 2 1 1\\n4 1 1 1\\n3 3 2 3\\n4 1 1 2\\n0 2 1 1\", \"3 7 3\\n0 1 2 1\\n1 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n1 1 1 2\\n1 2 2 1\", \"4 7 1\\n0 1 1 1\\n0 1 1 2\\n2 1 1 4\\n1 1 1 1\\n1 3 0 2\\n3 1 1 3\\n2 2 1 1\", \"3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2\", \"3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 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1 3 4\\n1 1 1 1\\n1 2 2 2\\n2 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 1 1 2\\n0 2 1 2\", \"5 10 5\\n0 1 1 2\\n0 3 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 0\\n4 2 0 2\", \"5 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n1 1 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 2\\n4 2 1 0\\n4 2 1 2\", \"5 10 5\\n0 1 2 2\\n1 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 4\\n2 1 1 1\\n2 1 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\", \"3 7 3\\n0 1 0 1\\n1 1 1 0\\n1 1 3 4\\n1 1 2 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 0 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 1\\n4 2 1 0\\n3 2 1 2\", \"3 7 3\\n0 1 1 1\\n0 2 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 2 3\\n2 2 2 1\", \"3 7 3\\n0 1 2 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n3 1 1 3\\n4 2 2 1\", \"3 7 3\\n0 1 1 1\\n0 1 1 0\\n1 1 1 4\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n2 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 0\", \"3 7 3\\n0 1 0 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 3 2 2\\n3 1 2 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n0 1 1 2\\n3 3 2 1\\n4 1 1 2\\n2 2 1 2\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 2 1\\n2 0 0 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\", \"5 10 5\\n0 1 1 4\\n0 2 1 0\\n0 2 2 3\\n1 2 0 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 0 2\", \"3 7 3\\n0 1 0 1\\n0 1 1 1\\n1 1 3 1\\n1 1 1 1\\n1 3 1 2\\n3 1 1 3\\n2 2 2 1\", \"3 7 3\\n0 1 1 1\\n0 1 1 2\\n1 1 3 4\\n1 1 1 1\\n1 2 1 2\\n2 1 1 3\\n2 2 2 1\", \"5 10 5\\n0 1 1 2\\n0 2 1 2\\n0 1 2 3\\n1 2 1 2\\n1 4 2 3\\n2 1 1 1\\n2 1 1 2\\n3 3 2 3\\n4 1 1 2\\n4 2 1 2\"], \"outputs\": [\"9\\n\", \"13\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"15\\n\", \"6\\n\", \"7\\n\", \"11\\n\", \"10\\n\", \"0\\n\", \"17\\n\", \"16\\n\", \"18\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"13\\n\", \"9\\n\", \"13\\n\", \"13\\n\", \"8\\n\", \"8\\n\", \"12\\n\", \"13\\n\", \"8\\n\", \"12\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"13\\n\", \"9\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"13\\n\", \"13\\n\", \"9\\n\", \"12\\n\", \"14\\n\", \"8\\n\", \"8\\n\", \"9\\n\", \"9\\n\", \"14\\n\", \"12\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"9\\n\", \"12\\n\", \"14\\n\", \"9\\n\", \"9\\n\", \"14\\n\", \"12\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"14\\n\", \"7\\n\", \"9\\n\", \"9\\n\", \"14\\n\", \"15\\n\", \"6\\n\", \"6\\n\", \"12\\n\", \"14\\n\", \"7\\n\", \"14\\n\", \"14\\n\", \"14\\n\", \"9\\n\", \"13\\n\", \"7\\n\", \"9\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"13\\n\", \"13\\n\", \"8\\n\", \"13\\n\", \"12\\n\", \"14\\n\", \"8\\n\", \"12\\n\", \"9\\n\", \"9\\n\", \"9\\n\", \"13\\n\", \"9\\n\", \"12\\n\", \"13\\n\", \"15\\n\", \"6\\n\", \"9\", \"13\"]}", "source": "taco"} | Problem
Yamano Mifune Gakuen's 1st grade G group is a class where female students carrying misfortune gather. They face various challenges every day with the goal of being happy.
In their class, they can take practical happiness courses as part of the test of happiness.
From Monday to Friday, there are classes from 1st to Nth, and there are M courses that can be taken.
Subject i starts from the ai period of the day of the week di (di = 0, 1, 2, 3, 4 corresponds to Monday, Tuesday, Wednesday, Thursday, and Friday, respectively), and is performed in consecutive ki frames. The degree of happiness obtained when taking the course is ti.
Each student is free to choose up to L subjects so that they do not overlap each other. How do you choose the subject to get the highest level of happiness? Please find the maximum value of happiness that can be obtained from the information of the given subject.
Constraints
* 2 ≤ N ≤ 8
* 0 ≤ M ≤ 300
* 0 ≤ L ≤ min (N × 5, M)
* 0 ≤ di ≤ 4
* 1 ≤ ai ≤ N
* 1 ≤ ki
* ai + ki --1 ≤ N
* 1 ≤ ti ≤ 100
Input
The input is given in the following format.
N M L
d1 a1 k1 t1
d2 a2 k2 t2
...
dM aM kM tM
The first line is given three integers N, M, L separated by blanks.
The four integers di, ai, ki, and ti are given on the 2nd to M + 1th lines, separated by blanks.
Output
Output the maximum value of the sum of happiness on one line.
Examples
Input
3 7 3
0 1 1 1
0 1 1 2
1 1 3 4
1 1 1 1
1 2 1 2
2 1 1 3
2 2 2 1
Output
9
Input
5 10 5
0 1 1 2
0 2 1 2
0 1 2 3
1 2 1 2
1 4 2 3
2 1 1 1
2 1 1 2
3 3 2 3
4 1 1 2
4 2 1 2
Output
13
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.625 |
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\"1\\n2\\n0\\n0\\n1\\n0\\n0\\n0\\n1\\n0\\n0\\n1\\n2\\n\", \"1\\n2\\n1\\n0\\n1\\n2\\n\", \"2\\n2\\n2\\n1\\n1\\n2\\n1\\n2\\n2\\n2\\n1\\n1\\n2\\n1\\n\", \"2\\n0\\n0\\n1\\n1\\n2\\n1\\n0\\n1\\n1\\n1\\n1\\n\", \"1\\n2\\n2\\n0\\n1\\n2\\n1\\n\", \"1\\n2\\n1\\n1\\n2\\n2\\n1\\n0\\n1\\n0\\n1\\n1\\n2\\n2\\n\", \"2\\n2\\n1\\n2\\n2\\n\", \"1\\n1\\n2\\n0\\n2\\n2\\n1\\n1\\n2\\n\", \"1\\n2\\n1\\n0\\n1\\n1\\n1\\n0\\n\", \"1\\n1\\n1\\n0\\n1\\n\", \"1\\n2\\n1\\n2\\n\", \"1\\n2\\n0\\n1\\n1\\n1\\n\", \"1\\n1\\n2\\n1\\n1\\n1\\n1\\n2\\n\", \"2\\n1\\n2\\n0\\n1\\n1\\n2\\n\", \"2\\n2\\n2\\n0\\n1\\n2\\n2\\n\", \"1\\n2\\n1\\n1\\n1\\n2\\n\", \"1\\n1\\n0\\n1\\n1\\n2\\n\", \"2\\n1\\n2\\n0\\n1\\n2\\n1\\n\", \"2\\n2\\n0\\n0\\n1\\n2\\n1\\n2\\n1\\n2\\n1\\n1\\n2\\n1\\n\", \"2\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"1\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"2\\n2\\n0\\n1\\n1\\n2\\n1\\n2\\n1\\n2\\n1\\n2\\n2\\n1\\n\", \"2\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"1\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"2\\n1\\n0\\n0\\n1\\n1\\n1\\n2\\n1\\n2\\n1\\n1\\n2\\n2\\n\", \"1\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"1\\n2\\n2\\n0\\n1\\n2\\n1\\n2\\n\", \"2\\n2\\n1\\n0\\n1\\n2\\n1\\n2\\n1\\n2\\n1\\n1\\n2\\n1\\n\"]}", "source": "taco"} | This is the easy version of the problem. The difference between the versions is that the easy version does not require you to output the numbers of the rods to be removed. You can make hacks only if all versions of the problem are solved.
Stitch likes experimenting with different machines with his friend Sparky. Today they built another machine.
The main element of this machine are $n$ rods arranged along one straight line and numbered from $1$ to $n$ inclusive. Each of these rods must carry an electric charge quantitatively equal to either $1$ or $-1$ (otherwise the machine will not work). Another condition for this machine to work is that the sign-variable sum of the charge on all rods must be zero.
More formally, the rods can be represented as an array of $n$ numbers characterizing the charge: either $1$ or $-1$. Then the condition must hold: $a_1 - a_2 + a_3 - a_4 + \ldots = 0$, or $\sum\limits_{i=1}^n (-1)^{i-1} \cdot a_i = 0$.
Sparky charged all $n$ rods with an electric current, but unfortunately it happened that the rods were not charged correctly (the sign-variable sum of the charge is not zero). The friends decided to leave only some of the rods in the machine. Sparky has $q$ questions. In the $i$th question Sparky asks: if the machine consisted only of rods with numbers $l_i$ to $r_i$ inclusive, what minimal number of rods could be removed from the machine so that the sign-variable sum of charges on the remaining ones would be zero? Perhaps the friends got something wrong, and the sign-variable sum is already zero. In that case, you don't have to remove the rods at all.
If the number of rods is zero, we will assume that the sign-variable sum of charges is zero, that is, we can always remove all rods.
Help your friends and answer all of Sparky's questions!
-----Input-----
Each test contains multiple test cases.
The first line contains one positive integer $t$ ($1 \le t \le 10^3$), denoting the number of test cases. Description of the test cases follows.
The first line of each test case contains two positive integers $n$ and $q$ ($1 \le n, q \le 3 \cdot 10^5$) — the number of rods and the number of questions.
The second line of each test case contains a non-empty string $s$ of length $n$, where the charge of the $i$-th rod is $1$ if $s_i$ is the "+" symbol, or $-1$ if $s_i$ is the "-" symbol.
Each next line from the next $q$ lines contains two positive integers $l_i$ ans $r_i$ ($1 \le l_i \le r_i \le n$) — numbers, describing Sparky's questions.
It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$, and the sum of $q$ over all test cases does not exceed $3 \cdot 10^5$.
-----Output-----
For each test case, print a single integer — the minimal number of rods that can be removed.
-----Examples-----
Input
3
14 1
+--++---++-++-
1 14
14 3
+--++---+++---
1 14
6 12
3 10
4 10
+-+-
1 1
1 2
1 3
1 4
2 2
2 3
2 4
3 3
3 4
4 4
Output
2
2
1
0
1
2
1
2
1
2
1
1
2
1
-----Note-----
In the first test case for the first query you can remove the rods numbered $5$ and $8$, then the following set of rods will remain: +--+--++-++-. It is easy to see that here the sign-variable sum is zero.
In the second test case:
For the first query, we can remove the rods numbered $1$ and $11$, then the following set of rods will remain: --++---++---. It is easy to see that here the sign-variable sum is zero.
For the second query we can remove the rod numbered $9$, then the following set of rods will remain: ---++-. It is easy to see that here the variable sum is zero.
For the third query we can not remove the rods at all.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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13\\n8 9\\n2 9\\n22 9\\n29 5\\n47 18\\n9 15\\n26 9\\n27 9\\n28 9\\n35 8\\n35 9\\n23 9\\n32 2\\n1011010000 999999999\\n232709804 999999999\\n1011611339 999999999\\n1000010100 5\\n1000000000 3\\n1000010010 9\\n1737891047 6\\n1058606099 5\\n999999992 12\\n974657870 9\\n\", \"4\\n0 3\\n3 3\\n3 4\\n4 4\\n\"], \"outputs\": [\"Bob\\nAlice\\nBob\\nAlice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\n\", \"Bob\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\n\", \"Alice\\n\", \"Bob\\n\", 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\"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nBob\\nAlice\\nBob\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\n\", \"Alice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\n\", \"Bob\\n\", \"Alice\\n\", \"Bob\\n\", \"Alice\\n\", \"Alice\\nAlice\\nBob\\nAlice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\n\", \"Bob\\n\", \"Bob\\n\", \"Alice\\nBob\\nBob\\nBob\\n\", \"Alice\\n\", \"Bob\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nBob\\nBob\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\n\", \"Alice\\n\", \"Alice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nAlice\\nBob\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\nAlice\\nBob\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\nBob\\nAlice\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Bob\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Bob\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Alice\\n\", \"Bob\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Alice\\n\", \"Bob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\n\", \"Bob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nAlice\\nBob\\nAlice\\nBob\\nAlice\\nAlice\\nBob\\nBob\\nBob\\nAlice\\nAlice\\nAlice\\nBob\\n\", \"Bob\\nAlice\\nBob\\nAlice\\n\"]}", "source": "taco"} | Alice and Bob play a game. There is a paper strip which is divided into n + 1 cells numbered from left to right starting from 0. There is a chip placed in the n-th cell (the last one).
Players take turns, Alice is first. Each player during his or her turn has to move the chip 1, 2 or k cells to the left (so, if the chip is currently in the cell i, the player can move it into cell i - 1, i - 2 or i - k). The chip should not leave the borders of the paper strip: it is impossible, for example, to move it k cells to the left if the current cell has number i < k. The player who can't make a move loses the game.
Who wins if both participants play optimally?
Alice and Bob would like to play several games, so you should determine the winner in each game.
-----Input-----
The first line contains the single integer T (1 ≤ T ≤ 100) — the number of games. Next T lines contain one game per line. All games are independent.
Each of the next T lines contains two integers n and k (0 ≤ n ≤ 10^9, 3 ≤ k ≤ 10^9) — the length of the strip and the constant denoting the third move, respectively.
-----Output-----
For each game, print Alice if Alice wins this game and Bob otherwise.
-----Example-----
Input
4
0 3
3 3
3 4
4 4
Output
Bob
Alice
Bob
Alice
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5\\n1 2 1 3 6\\n\", \"5\\n3 2 5 4 10\\n\", \"4\\n1 1 1 1\\n\", \"1\\n1000000000\\n\", \"2\\n921 921\\n\", \"2\\n1000000000 1\\n\", \"11\\n3 10 20 13 18 12 6 5 19 10 8\\n\", \"19\\n3 1 16 11 12 10 3 13 12 9 1 9 8 4 19 16 19 3 3\\n\", \"4\\n11 6 1 16\\n\", \"19\\n10 10 8 11 6 1 6 13 8 20 8 14 9 18 18 7 5 20 6\\n\", \"12\\n6 20 12 12 1 8 15 19 5 19 5 16\\n\", \"2\\n6 16\\n\", \"8\\n10 4 7 6 14 4 2 2\\n\", \"8\\n10 4 7 6 14 4 2 2\\n\", \"2\\n1000000000 1\\n\", \"2\\n6 16\\n\", \"19\\n3 1 16 11 12 10 3 13 12 9 1 9 8 4 19 16 19 3 3\\n\", \"19\\n10 10 8 11 6 1 6 13 8 20 8 14 9 18 18 7 5 20 6\\n\", \"2\\n921 921\\n\", \"11\\n3 10 20 13 18 12 6 5 19 10 8\\n\", \"12\\n6 20 12 12 1 8 15 19 5 19 5 16\\n\", \"4\\n11 6 1 16\\n\", \"1\\n1000000000\\n\", \"8\\n10 4 7 6 14 2 2 2\\n\", \"2\\n1001000000 1\\n\", \"2\\n5 16\\n\", \"19\\n3 1 16 11 12 10 3 13 12 9 1 9 8 4 19 16 24 3 3\\n\", \"2\\n696 921\\n\", \"11\\n3 10 20 13 18 12 8 5 19 10 8\\n\", \"12\\n6 20 12 12 1 8 15 19 9 19 5 16\\n\", \"4\\n11 3 1 16\\n\", \"5\\n1 2 1 3 11\\n\", \"2\\n696 1350\\n\", \"2\\n1 12\\n\", \"2\\n696 965\\n\", \"2\\n1 7\\n\", \"2\\n1316 965\\n\", \"2\\n1 10\\n\", \"2\\n1316 730\\n\", \"2\\n0 10\\n\", \"19\\n11 10 6 11 1 1 6 13 8 20 8 27 9 18 18 7 7 20 12\\n\", \"2\\n0 12\\n\", \"2\\n300 730\\n\", \"2\\n300 890\\n\", \"2\\n84 890\\n\", \"19\\n11 10 6 11 2 1 6 13 8 38 8 27 9 22 18 7 14 20 12\\n\", \"2\\n84 1417\\n\", \"2\\n38 1417\\n\", \"19\\n11 10 6 12 2 1 6 13 8 38 8 27 9 22 18 1 14 20 12\\n\", \"2\\n27 1417\\n\", \"2\\n3 17\\n\", \"2\\n10 1417\\n\", \"2\\n1 17\\n\", \"2\\n5 1417\\n\", \"2\\n3 1417\\n\", \"2\\n0 24\\n\", \"2\\n1 1417\\n\", \"2\\n0 28\\n\", \"2\\n2 1417\\n\", \"2\\n2 326\\n\", \"2\\n2 263\\n\", \"2\\n1 263\\n\", \"2\\n0 263\\n\", \"2\\n0 465\\n\", \"2\\n1 465\\n\", \"2\\n2 465\\n\", \"2\\n3 465\\n\", \"2\\n5 465\\n\", \"2\\n5 22\\n\", \"2\\n6 10\\n\", \"19\\n10 10 8 11 6 1 6 13 8 20 8 14 9 18 18 7 5 20 12\\n\", \"2\\n921 354\\n\", \"19\\n10 10 8 11 6 1 6 13 8 20 8 27 9 18 18 7 5 20 6\\n\", \"8\\n10 4 7 6 14 2 2 3\\n\", \"2\\n1001001000 1\\n\", \"2\\n5 12\\n\", \"19\\n3 1 16 11 12 10 3 13 12 9 1 4 8 4 19 16 24 3 3\\n\", \"19\\n18 10 8 11 6 1 6 13 8 20 8 27 9 18 18 7 5 20 6\\n\", \"12\\n6 20 12 24 1 8 15 19 9 19 5 16\\n\", \"4\\n11 2 1 16\\n\", \"5\\n1 2 2 3 11\\n\", \"19\\n3 1 7 11 12 10 3 13 12 9 1 4 8 4 19 16 24 3 3\\n\", \"19\\n11 10 8 11 6 1 6 13 8 20 8 27 9 18 18 7 5 20 6\\n\", \"12\\n6 20 12 24 1 8 15 19 9 35 5 16\\n\", \"5\\n0 2 2 3 11\\n\", \"19\\n3 1 7 11 12 10 3 13 12 9 1 4 8 4 19 16 3 3 3\\n\", \"19\\n11 10 8 11 1 1 6 13 8 20 8 27 9 18 18 7 5 20 6\\n\", \"12\\n6 13 12 24 1 8 15 19 9 35 5 16\\n\", \"19\\n3 1 7 11 12 10 3 13 12 9 1 4 8 4 19 16 4 3 3\\n\", \"19\\n11 10 6 11 1 1 6 13 8 20 8 27 9 18 18 7 5 20 6\\n\", \"12\\n0 13 12 24 1 8 15 19 9 35 5 16\\n\", \"19\\n3 1 7 11 12 10 3 13 12 9 1 4 2 4 19 16 4 3 3\\n\", \"19\\n11 10 6 11 1 1 6 13 8 20 8 27 9 18 18 7 7 20 6\\n\", \"2\\n1212 730\\n\", \"2\\n0 6\\n\", \"2\\n853 730\\n\", \"19\\n11 10 6 11 1 1 6 13 8 38 8 27 9 18 18 7 7 20 12\\n\", \"2\\n1 11\\n\", \"19\\n11 10 6 11 2 1 6 13 8 38 8 27 9 18 18 7 7 20 12\\n\", \"2\\n2 11\\n\", \"19\\n11 10 6 11 2 1 6 13 8 38 8 27 9 22 18 7 7 20 12\\n\", \"2\\n4 11\\n\", \"2\\n4 9\\n\", \"19\\n11 10 6 12 2 1 6 13 8 38 8 27 9 22 18 7 14 20 12\\n\", \"2\\n4 17\\n\", \"19\\n11 10 6 12 2 1 6 13 8 40 8 27 9 22 18 1 14 20 12\\n\", \"19\\n11 10 6 12 2 1 9 13 8 40 8 27 9 22 18 1 14 20 12\\n\", \"2\\n0 17\\n\", \"19\\n11 10 6 12 2 1 9 13 8 40 8 27 9 22 18 1 14 32 12\\n\", \"19\\n11 10 4 12 2 1 9 13 8 40 8 27 9 22 18 1 14 32 12\\n\", \"19\\n11 10 4 12 1 1 9 13 8 40 8 27 9 22 18 1 14 32 12\\n\", \"19\\n11 10 4 12 1 1 9 13 8 40 8 27 9 22 33 1 14 32 12\\n\", \"19\\n11 10 2 12 1 1 9 13 8 40 8 27 9 22 33 1 14 32 12\\n\", \"19\\n11 10 2 12 1 1 9 13 8 40 8 27 18 22 33 1 14 32 12\\n\", \"19\\n11 10 2 12 1 1 9 13 8 40 16 27 18 22 33 1 14 32 12\\n\", \"2\\n5 2\\n\", \"8\\n10 4 7 6 26 4 2 2\\n\", \"19\\n3 1 16 11 12 10 3 13 12 9 1 9 8 4 19 15 19 3 3\\n\", \"11\\n3 10 20 13 18 12 6 2 19 10 8\\n\", \"12\\n6 20 12 12 1 8 5 19 5 19 5 16\\n\", \"4\\n11 7 1 16\\n\", \"4\\n1 1 1 2\\n\", \"5\\n3 2 9 4 10\\n\", \"4\\n1 1 1 1\\n\", \"5\\n3 2 5 4 10\\n\", \"5\\n1 2 1 3 6\\n\"], \"outputs\": [\"10\", \"20\", \"1\", \"1000000000\", \"1841\", \"1\", \"36\", \"6\", \"17\", \"21\", \"31\", \"22\", \"3\", \"3\", \"1\", \"22\", \"6\", \"21\", \"1841\", \"36\", \"31\", \"17\", \"1000000000\", \"3\\n\", \"1\\n\", \"21\\n\", \"6\\n\", \"1617\\n\", \"36\\n\", \"31\\n\", \"17\\n\", \"15\\n\", \"2046\\n\", \"13\\n\", \"1661\\n\", \"8\\n\", \"1929\\n\", \"11\\n\", \"1459\\n\", \"10\\n\", \"51\\n\", \"12\\n\", \"1030\\n\", \"1190\\n\", \"974\\n\", \"61\\n\", \"1501\\n\", \"1455\\n\", \"34\\n\", \"1444\\n\", \"20\\n\", \"1427\\n\", \"18\\n\", \"1422\\n\", \"1420\\n\", \"24\\n\", \"1418\\n\", \"28\\n\", \"1419\\n\", \"328\\n\", \"265\\n\", \"264\\n\", \"263\\n\", \"465\\n\", \"466\\n\", \"467\\n\", \"468\\n\", \"470\\n\", \"27\\n\", \"16\\n\", \"38\\n\", \"707\\n\", \"21\\n\", \"6\\n\", \"1\\n\", \"17\\n\", \"6\\n\", \"21\\n\", \"31\\n\", \"17\\n\", \"17\\n\", \"6\\n\", \"21\\n\", \"31\\n\", \"17\\n\", \"6\\n\", \"21\\n\", \"31\\n\", \"6\\n\", \"21\\n\", \"31\\n\", \"6\\n\", \"21\\n\", \"1459\\n\", \"6\\n\", \"1459\\n\", \"51\\n\", \"12\\n\", \"51\\n\", \"13\\n\", \"51\\n\", \"15\\n\", \"13\\n\", \"61\\n\", \"21\\n\", \"34\\n\", \"34\\n\", \"17\\n\", \"34\\n\", \"34\\n\", \"34\\n\", \"34\\n\", \"34\\n\", \"34\\n\", \"34\\n\", \"3\\n\", \"3\\n\", \"6\\n\", \"24\\n\", \"31\\n\", \"17\\n\", \"3\\n\", \"20\\n\", \"1\", \"20\", \"10\"]}", "source": "taco"} | You went to the store, selling $n$ types of chocolates. There are $a_i$ chocolates of type $i$ in stock.
You have unlimited amount of cash (so you are not restricted by any prices) and want to buy as many chocolates as possible. However if you buy $x_i$ chocolates of type $i$ (clearly, $0 \le x_i \le a_i$), then for all $1 \le j < i$ at least one of the following must hold: $x_j = 0$ (you bought zero chocolates of type $j$) $x_j < x_i$ (you bought less chocolates of type $j$ than of type $i$)
For example, the array $x = [0, 0, 1, 2, 10]$ satisfies the requirement above (assuming that all $a_i \ge x_i$), while arrays $x = [0, 1, 0]$, $x = [5, 5]$ and $x = [3, 2]$ don't.
Calculate the maximum number of chocolates you can buy.
-----Input-----
The first line contains an integer $n$ ($1 \le n \le 2 \cdot 10^5$), denoting the number of types of chocolate.
The next line contains $n$ integers $a_i$ ($1 \le a_i \le 10^9$), denoting the number of chocolates of each type.
-----Output-----
Print the maximum number of chocolates you can buy.
-----Examples-----
Input
5
1 2 1 3 6
Output
10
Input
5
3 2 5 4 10
Output
20
Input
4
1 1 1 1
Output
1
-----Note-----
In the first example, it is optimal to buy: $0 + 0 + 1 + 3 + 6$ chocolates.
In the second example, it is optimal to buy: $1 + 2 + 3 + 4 + 10$ chocolates.
In the third example, it is optimal to buy: $0 + 0 + 0 + 1$ chocolates.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5\\n1 2 2 1 3\\n\", \"5\\n1 2 2 1 1\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"5\\n1 2 4 1 3\\n\", \"5\\n1 2 1 1 1\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 63 9 82 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 66 41 21 77 63 17 62 91\\n\", \"5\\n2 2 2 1 3\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 17 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 10 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 12 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 2 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 10 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 10 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 12 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 11 8 2 6 3 3 10 7 10 11 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 7 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 8 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 11 2 6\\n\", \"100\\n1 4 5 5 10 10 5 8 5 7 4 5 4 6 11 8 2 6 3 3 10 7 10 11 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 7 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 8 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 3 4 4 1 5 1 6 6 6 8 8 11 2 6\\n\", \"100\\n1 4 5 5 10 10 5 8 5 7 4 5 4 6 11 8 2 6 3 3 10 7 10 11 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 7 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 8 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 3 4 4 1 5 1 6 6 6 8 8 11 2 11\\n\", \"100\\n1 4 5 5 10 10 5 8 5 7 4 5 4 6 11 8 2 6 3 3 10 7 10 11 3 1 8 3 10 7 7 2 9 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 8 9 7 6 2 1 6 1 8 10 4 10 3 1 10 5 5 4 8 3 5 3 7 10 2 7 4 6 3 10 1 6 5 5 4 6 3 4 4 1 5 1 6 6 6 8 3 11 2 11\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 45 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n82 60 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 52 21 78 20 63 8 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 66 41 21 77 63 17 62 91\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 5 76 80 60 100 86 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 66 29 92 3 49 17 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 16 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 45 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 5 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 8 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n1 2 1 2 1\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 12 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n1 2 1 1 2\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n2 1 2 1 3\\n\", \"5\\n1 2 1 4 1\\n\", \"5\\n1 3 1 1 2\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 10 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 4 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 10 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 4 4 10 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 6 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n1 2 2 1 2\\n\", \"5\\n1 3 2 1 1\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 42 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 8 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 7 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 52 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 66 41 21 77 63 17 62 91\\n\", \"5\\n2 2 2 1 4\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 7 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 12 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n1 2 1 4 2\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 15 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 8 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 10 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 10 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 4 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 4 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 1 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 8 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 5 4 10 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 11 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 3 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 10 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 1 10 5 4 4 10 3 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 3 3 3 10 7 10 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 6 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 66 29 92 3 49 17 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"5\\n1 4 2 1 2\\n\", \"5\\n1 3 2 1 2\\n\", \"100\\n82 51 81 22 37 17 78 92 64 15 8 42 89 8 87 77 66 10 15 12 100 25 92 47 21 78 20 63 13 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 58 12 9 3 55 37 85 46 22 84 52 98 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 5 8 6 2 8 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 7 1 6 6 6 8 8 6 2 6\\n\", \"100\\n82 51 81 14 37 17 78 92 64 15 8 86 89 8 87 77 66 10 15 12 100 25 92 52 21 78 20 63 8 49 41 36 41 79 16 87 87 69 3 76 80 60 100 49 70 59 72 8 38 71 45 97 71 14 76 54 81 4 59 46 39 29 92 3 49 22 53 99 59 52 74 31 92 43 42 23 44 9 82 47 7 40 12 9 3 55 37 85 46 22 84 52 66 41 21 77 63 17 62 91\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 17 7 3 8 6 2 7 3 9 7 7 2 4 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 7 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 2 8 3 9 7 7 2 6 5 2 4 9 5 10 2 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 12 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"5\\n1 2 2 4 2\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 1 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 15 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 11 7 7 2 6 5 2 8 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 1 4 5 4 6 8 11 2 6 3 3 10 7 3 8 6 2 7 3 9 10 7 2 4 5 2 4 9 5 10 1 10 9 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 10 10 4 10 3 4 10 5 5 4 10 4 5 3 5 10 2 7 3 6 9 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 5 9 7 7 4 6 5 2 4 9 5 10 1 10 5 10 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 10 4 5 3 7 10 2 7 3 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 7 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 2 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 2 6 9 9 9 10 6 2 5 6 1 8 10 4 10 3 4 10 5 5 4 2 4 5 3 7 10 2 7 4 6 3 6 1 6 5 5 4 6 6 4 4 1 5 1 6 6 6 8 8 6 2 6\\n\", \"100\\n7 4 5 5 10 10 5 8 5 7 4 5 4 6 8 8 2 6 3 3 10 7 10 8 6 1 8 3 9 7 7 4 6 5 2 4 9 5 10 1 10 5 3 4 1 3 4 1 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\"81\\n\", \"80\\n\", \"79\\n\", \"80\\n\", \"82\\n\", \"78\\n\", \"81\\n\", \"79\\n\", \"79\\n\", \"81\\n\", \"82\\n\", \"79\\n\", \"81\\n\", \"79\\n\", \"81\\n\", \"82\\n\", \"79\\n\", \"80\\n\", \"82\\n\", \"81\\n\", \"82\\n\", \"81\\n\", \"76\\n\", \"59\\n\", \"1\\n\", \"77\\n\", \"1\\n\", \"0\\n\", \"78\\n\", \"76\\n\", \"60\\n\", \"1\\n\", \"1\\n\", \"77\\n\", \"1\\n\", \"79\\n\", \"1\\n\", \"2\\n\", \"78\\n\", \"77\\n\", \"78\\n\", \"77\\n\", \"77\\n\", \"78\\n\", \"78\\n\", \"79\\n\", \"77\\n\", \"77\\n\", \"77\\n\", \"77\\n\", \"59\\n\", \"1\\n\", \"61\\n\", \"77\\n\", \"59\\n\", \"1\\n\", \"79\\n\", \"79\\n\", \"75\\n\", \"0\\n\", \"78\\n\", \"76\\n\", \"77\\n\", \"78\\n\", \"79\\n\", \"77\\n\", \"77\\n\", \"78\\n\", \"\\n2\\n\", \"\\n1\\n\"]}", "source": "taco"} | One day you wanted to read something, so you went to your bookshelf to grab some book. But when you saw how messy the bookshelf was you decided to clean it up first.
There are $n$ books standing in a row on the shelf, the $i$-th book has color $a_i$.
You'd like to rearrange the books to make the shelf look beautiful. The shelf is considered beautiful if all books of the same color are next to each other.
In one operation you can take one book from any position on the shelf and move it to the right end of the shelf.
What is the minimum number of operations you need to make the shelf beautiful?
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 5 \cdot 10^5$) — the number of books.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$) — the book colors.
-----Output-----
Output the minimum number of operations to make the shelf beautiful.
-----Examples-----
Input
5
1 2 2 1 3
Output
2
Input
5
1 2 2 1 1
Output
1
-----Note-----
In the first example, we have the bookshelf $[1, 2, 2, 1, 3]$ and can, for example:
take a book on position $4$ and move to the right end: we'll get $[1, 2, 2, 3, 1]$;
take a book on position $1$ and move to the right end: we'll get $[2, 2, 3, 1, 1]$.
In the second example, we can move the first book to the end of the bookshelf and get $[2,2,1,1,1]$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"6 1\\n10.245\\n\", \"6 2\\n10.245\\n\", \"3 100\\n9.2\\n\", \"12 5\\n872.04488525\\n\", \"35 8\\n984227318.2031144444444444494637612\\n\", \"320 142\\n2704701300865535.432223312233434114130011113220102420131323010344144201124303144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447444444444444444444444444444444615444444482101673308979557675074444444444444446867245414595534444693160202254444449544495367\\n\", \"5 10\\n1.555\\n\", \"6 1\\n0.9454\\n\", \"7 1000000000\\n239.923\\n\", \"7 235562\\n999.999\\n\", \"9 2\\n23999.448\\n\", \"9 3\\n23999.448\\n\", \"13 1\\n761.044449428\\n\", \"3 1\\n0.1\\n\", \"3 1\\n9.9\\n\", \"3 1\\n0.9\\n\", \"31 15\\n2707786.24030444444444444724166\\n\", \"4 100\\n99.9\\n\", \"3 10\\n9.9\\n\", \"22 100\\n11111111111111111111.5\\n\", \"3 1\\n9.5\\n\", \"8 100\\n9.444445\\n\", \"6 2\\n999.45\\n\", \"3 100\\n9.9\\n\", \"18 100\\n9.4444444444454444\\n\", \"16 999\\n9595959.95959595\\n\", \"4 100\\n99.5\\n\", \"5 1\\n999.9\\n\", \"4 1\\n5.59\\n\", \"4 1\\n99.5\\n\", \"4 1\\n99.9\\n\", \"18 6\\n102345678999.44449\\n\", \"3 3\\n9.9\\n\", \"5 1\\n99.99\\n\", \"7 1\\n99999.9\\n\", \"3 121\\n9.9\\n\", \"8 6\\n9.444445\\n\", \"3 100\\n8.9\\n\", \"10 1\\n999.999999\\n\", \"5 100\\n6.666\\n\", \"4 100\\n9.99\\n\", \"6 1\\n9.9999\\n\", \"4 10\\n99.9\\n\", \"5 1\\n9.999\\n\", \"3 1231\\n9.9\\n\", \"5 2\\n999.9\\n\", \"5 100\\n144.5\\n\", \"5 100\\n99.45\\n\", \"10 1\\n0.50444445\\n\", \"7 1\\n1.51111\\n\", \"5 1\\n199.9\\n\", \"3 100\\n9.5\\n\", \"7 1000\\n409.659\\n\", \"4 10\\n99.5\\n\", \"4 10\\n10.9\\n\", \"4 1\\n19.5\\n\", \"7 1000\\n409.659\\n\", \"4 10\\n99.9\\n\", \"5 100\\n6.666\\n\", \"4 1\\n5.59\\n\", \"8 6\\n9.444445\\n\", \"9 2\\n23999.448\\n\", \"6 1\\n0.9454\\n\", \"31 15\\n2707786.24030444444444444724166\\n\", \"16 999\\n9595959.95959595\\n\", \"7 235562\\n999.999\\n\", \"13 1\\n761.044449428\\n\", \"5 1\\n99.99\\n\", \"3 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409535\\n999.999\\n\", \"3 101\\n9.9\\n\", \"320 130\\n2704701300865535.432223312233434114130011113220102420131323010344144201124303144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447444444444444444444444444444444615444444482101673308979557675074444444444444446867245414595534444693160202254444449544495367\\n\", \"9 10\\n23999.448\\n\", \"3 2\\n0.9\\n\", \"4 110\\n9.99\\n\", \"18 110\\n9.4444444444454444\\n\", \"7 1101\\n409.659\\n\", \"4 3\\n99.9\\n\", \"7 230581\\n999.999\\n\", \"18 1\\n102345678999.54283\\n\", \"6 2\\n10.245\\n\", \"3 100\\n9.2\\n\", \"6 1\\n10.245\\n\"], \"outputs\": [\"10.25\\n\", \"10.3\\n\", \"9.2\\n\", \"872.1\\n\", \"984227318.2031144445\\n\", \"2704701300865535.4322233122334341141300111132201024201313230103441442011243032\\n\", \"2\\n\", \"1\\n\", \"240\\n\", \"1000\\n\", \"23999.5\\n\", \"24000\\n\", \"761.04445\\n\", \"0.1\\n\", \"10\\n\", \"1\\n\", \"2707786.24031\\n\", \"100\\n\", 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\"10\\n\", \"6\\n\", \"20\\n\", \"102345679000\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"20\\n\", \"10\\n\", \"1000\\n\", \"10\\n\", \"2704701300865535.4322233122334341141300111132201024201313230103441442011243032\\n\", \"24000\\n\", \"1\\n\", \"10\\n\", \"10\\n\", \"410\\n\", \"100\\n\", \"1000\\n\", \"102345679000\\n\", \"10.3\\n\", \"9.2\\n\", \"10.25\\n\"]}", "source": "taco"} | Efim just received his grade for the last test. He studies in a special school and his grade can be equal to any positive decimal fraction. First he got disappointed, as he expected a way more pleasant result. Then, he developed a tricky plan. Each second, he can ask his teacher to round the grade at any place after the decimal point (also, he can ask to round to the nearest integer).
There are t seconds left till the end of the break, so Efim has to act fast. Help him find what is the maximum grade he can get in no more than t seconds. Note, that he can choose to not use all t seconds. Moreover, he can even choose to not round the grade at all.
In this problem, classic rounding rules are used: while rounding number to the n-th digit one has to take a look at the digit n + 1. If it is less than 5 than the n-th digit remain unchanged while all subsequent digits are replaced with 0. Otherwise, if the n + 1 digit is greater or equal to 5, the digit at the position n is increased by 1 (this might also change some other digits, if this one was equal to 9) and all subsequent digits are replaced with 0. At the end, all trailing zeroes are thrown away.
For example, if the number 1.14 is rounded to the first decimal place, the result is 1.1, while if we round 1.5 to the nearest integer, the result is 2. Rounding number 1.299996121 in the fifth decimal place will result in number 1.3.
-----Input-----
The first line of the input contains two integers n and t (1 ≤ n ≤ 200 000, 1 ≤ t ≤ 10^9) — the length of Efim's grade and the number of seconds till the end of the break respectively.
The second line contains the grade itself. It's guaranteed that the grade is a positive number, containing at least one digit after the decimal points, and it's representation doesn't finish with 0.
-----Output-----
Print the maximum grade that Efim can get in t seconds. Do not print trailing zeroes.
-----Examples-----
Input
6 1
10.245
Output
10.25
Input
6 2
10.245
Output
10.3
Input
3 100
9.2
Output
9.2
-----Note-----
In the first two samples Efim initially has grade 10.245.
During the first second Efim can obtain grade 10.25, and then 10.3 during the next second. Note, that the answer 10.30 will be considered incorrect.
In the third sample the optimal strategy is to not perform any rounding at all.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[\"Joe had a bad day\"], [\"Joe had some bad days\"], [\"Joe is having no fun\"], [\"Sometimes joe cries for hours\"], [\"Joe is having lots of fun\"], [\"Joe is working hard a lot\"], [\"Joe listened to the noise and it was an onamonapia\"], [\"Joe listened to the noises and there were some onamonapias\"]], \"outputs\": [[\"Good work Joe!\"], [\"Good work Joe!\"], [\"Keep It Simple Stupid\"], [\"Keep It Simple Stupid\"], [\"Good work Joe!\"], [\"Keep It Simple Stupid\"], [\"Good work Joe!\"], [\"Keep It Simple Stupid\"]]}", "source": "taco"} | KISS stands for Keep It Simple Stupid.
It is a design principle for keeping things simple rather than complex.
You are the boss of Joe.
Joe is submitting words to you to publish to a blog. He likes to complicate things.
Define a function that determines if Joe's work is simple or complex.
Input will be non emtpy strings with no punctuation.
It is simple if:
``` the length of each word does not exceed the amount of words in the string ```
(See example test cases)
Otherwise it is complex.
If complex:
```python
return "Keep It Simple Stupid"
```
or if it was kept simple:
```python
return "Good work Joe!"
```
Note: Random test are random and nonsensical. Here is a silly example of a random test:
```python
"jump always mostly is touchy dancing choice is pineapples mostly"
```
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.875 |
{"tests": "{\"inputs\": [[[1, 1, 1, 2, 1, 1]], [[0, 0, 0.55, 0, 0]], [[4, 4, 4, 3, 4, 4, 4, 4]], [[5, 5, 5, 5, 4, 5, 5, 5]], [[6, 6, 6, 6, 6, 5, 6, 6]], [[7, 7, 7, 7, 7, 7, 6, 7]], [[8, 8, 8, 8, 8, 8, 8, 7]], [[3, 3, 3, 3, 3, 3, 3, 2]], [[2, 2, 2, 2, 2, 2, 2, 1]], [[0, 1, 1, 1, 1, 1, 1, 1]]], \"outputs\": [[2], [0.55], [3], [4], [5], [6], [7], [2], [1], [0]]}", "source": "taco"} | There is an array with some numbers. All numbers are equal except for one. Try to find it!
```python
find_uniq([ 1, 1, 1, 2, 1, 1 ]) == 2
find_uniq([ 0, 0, 0.55, 0, 0 ]) == 0.55
```
It’s guaranteed that array contains at least 3 numbers.
The tests contain some very huge arrays, so think about performance.
This is the first kata in series:
1. Find the unique number (this kata)
2. [Find the unique string](https://www.codewars.com/kata/585d8c8a28bc7403ea0000c3)
3. [Find The Unique](https://www.codewars.com/kata/5862e0db4f7ab47bed0000e5)
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.125 |
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\"2 4\\n\"], \"outputs\": [\"4\\n\", \"5\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"500000001\\n\", \"500000001\\n\", \"1999936805\\n\", \"1006177186\\n\", \"1757835091\\n\", \"509460797\\n\", \"261146454\\n\", \"1307707417\\n\", \"1956733985\\n\", \"1839852485\\n\", \"1017851489\\n\", \"61439312\\n\", \"150481024\\n\", \"239522736\\n\", \"1956733985\\n\", \"1839852485\\n\", \"1017851489\\n\", \"402231543\\n\", \"491273255\\n\", \"432831319\\n\", \"1015808858\\n\", \"1193887001\\n\", \"1077006614\\n\", \"597537504\\n\", \"775621118\\n\", \"953699599\\n\", \"621912604\\n\", \"388152264\\n\", \"1456626719\\n\", \"1222892906\\n\", \"1887160182\\n\", \"973204768\\n\", \"710242885\\n\", \"741469514\\n\", \"621912604\\n\", \"388152264\\n\", \"1456626719\\n\", \"1222892906\\n\", \"1887160182\\n\", \"973204768\\n\", \"710242885\\n\", \"741469514\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"1\\n\", \"1887160182\\n\", \"1006177186\\n\", \"491273255\\n\", \"2\\n\", \"500000001\\n\", \"1015808858\\n\", \"621912604\\n\", \"239522736\\n\", \"3\\n\", \"1456626719\\n\", \"710242885\\n\", \"402231543\\n\", \"1193887001\\n\", \"973204768\\n\", \"3\\n\", \"1017851489\\n\", \"741469514\\n\", \"1222892906\\n\", \"388152264\\n\", \"1222892906\\n\", \"509460797\\n\", \"2\\n\", \"973204768\\n\", \"621912604\\n\", \"1077006614\\n\", \"1956733985\\n\", \"597537504\\n\", \"2\\n\", \"1017851489\\n\", \"1307707417\\n\", \"1757835091\\n\", \"3\\n\", \"432831319\\n\", \"710242885\\n\", \"1839852485\\n\", \"2\\n\", \"1999936805\\n\", \"61439312\\n\", \"388152264\\n\", \"1887160182\\n\", \"150481024\\n\", \"1956733985\\n\", \"741469514\\n\", \"1839852485\\n\", \"4\\n\", \"4\\n\", \"500000001\\n\", \"1456626719\\n\", \"953699599\\n\", \"775621118\\n\", \"261146454\\n\", \"1036254437\\n\", \"655031008\\n\", \"666666668\\n\", \"1097265179\\n\", \"362236222\\n\", \"378410239\\n\", \"4\\n\", \"845939019\\n\", \"829755682\\n\", \"127540154\\n\", \"1820852473\\n\", \"967328934\\n\", \"1027849844\\n\", \"922313912\\n\", \"1333516768\\n\", \"534391104\\n\", \"1782763358\\n\", \"976886358\\n\", \"1363474179\\n\", \"762653393\\n\", \"1488672678\\n\", \"1957734185\\n\", \"1038190007\\n\", \"3\\n\", \"1017851561\\n\", \"915991358\\n\", \"1473642514\\n\", \"577108426\\n\", \"431646413\\n\", \"1839952685\\n\", \"102238471\\n\", \"507818995\\n\", \"107578030\\n\", \"701564970\\n\", \"6\\n\", \"500000051\\n\", \"1945735626\\n\", \"876630065\\n\", \"1022167581\\n\", \"166688446\\n\", \"8\\n\", \"820638586\\n\", \"611428348\\n\", \"666667335\\n\", \"1429863721\\n\", \"353648371\\n\", \"561379745\\n\", \"5\\n\", \"883569966\\n\", \"1020169357\\n\", \"51010925\\n\", \"942225457\\n\", \"1027849799\\n\", \"864539176\\n\", \"941092797\\n\", \"635557622\\n\", \"971848269\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"4\\n\"]}", "source": "taco"} | You are given $a$ uppercase Latin letters 'A' and $b$ letters 'B'.
The period of the string is the smallest such positive integer $k$ that $s_i = s_{i~mod~k}$ ($0$-indexed) for each $i$. Note that this implies that $k$ won't always divide $a+b = |s|$.
For example, the period of string "ABAABAA" is $3$, the period of "AAAA" is $1$, and the period of "AABBB" is $5$.
Find the number of different periods over all possible strings with $a$ letters 'A' and $b$ letters 'B'.
-----Input-----
The first line contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$) — the number of letters 'A' and 'B', respectively.
-----Output-----
Print the number of different periods over all possible strings with $a$ letters 'A' and $b$ letters 'B'.
-----Examples-----
Input
2 4
Output
4
Input
5 3
Output
5
-----Note-----
All the possible periods for the first example: $3$ "BBABBA" $4$ "BBAABB" $5$ "BBBAAB" $6$ "AABBBB"
All the possible periods for the second example: $3$ "BAABAABA" $5$ "BAABABAA" $6$ "BABAAABA" $7$ "BAABAAAB" $8$ "AAAAABBB"
Note that these are not the only possible strings for the given periods.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"5 1 2 0 1 2\\n\", \"1 1 1 -1 -1 2\\n\", \"1 1 1 1 1 0\\n\", \"2 2 1 -2 -2 5\\n\", \"1000000000 1 1 1 1 1000000000000000000\\n\", \"1000000000 1 2 -100 -100 1\\n\", \"3 2 2 -100 -100 2\\n\", \"1000000000 1000000000 1000000000 100 -100 1000000000000000000\\n\", \"907122235 107269653 309181328 26 -64 242045007473044676\\n\", \"804 658 177 -95 37 9\\n\", \"2 1 1 31 -74 2712360435504330\\n\", \"230182675 73108597 42152975 -72 -8 93667970058209518\\n\", \"487599125 469431740 316230350 -77 57 18\\n\", \"1710 654 941 -81 -37 1281183940\\n\", \"568980902 147246752 87068387 -17 58 677739653\\n\", \"38 10 36 19 30 4054886\\n\", \"546978166 115293871 313560296 -33 54 215761558342792301\\n\", \"323544442 39059198 2970015 92 17 98\\n\", \"321575625 2929581 31407414 -40 -44 920902537044\\n\", \"5928 1508 4358 75 -4 794927060433551549\\n\", \"7310962 7564 6333485 -45 41 81980903005818\\n\", \"224 81 30 57 -13 8363\\n\", \"75081054 91 47131957 -94 -54 5588994022550344\\n\", \"185144 100489 52 32 -21 5752324832726786\\n\", \"61728 24280 17963 -19 81 652432745607745078\\n\", \"25699863 23288611 24796719 -45 46 437606836\\n\", \"475875319 333393831 284835031 22 7 90332975949346\\n\", \"372903 106681 40781 54 -40 6188704\\n\", \"923 452 871 -95 -55 273135237285890\\n\", \"672939 589365 391409 -54 -70 205083640\\n\", \"560010572 4172512 514044248 -78 13 97386\\n\", \"717485513 5935 3 -5 -67 28\\n\", \"138971202 137695723 48931985 -28 -3 68901440898766\\n\", \"910958510 60 98575 38 -99 97880\\n\", \"67163467 36963416 50381 -49 -12 76558237\\n\", \"557911547 9 460221236 -58 -96 74518856\\n\", \"85 37 69 30 47 131\\n\", \"852525230 538352221 97088953 -12 98 9197937568\\n\", \"885849694 703278210 46391 33 23 965949118732\\n\", \"976890548 675855343 988 -11 46 796041265897304\\n\", \"108774060 15274597 430014 -85 -94 6\\n\", \"2 2 2 -36 94 9429569334\\n\", \"713835677 404390162 67429 -91 10 178697004637242062\\n\", \"620330674 603592488 3 38 94 34309127789188\\n\", \"95 70 7 -36 -100 5\\n\", \"900854530 82 7 30 -88 6797628981503799\\n\", \"147834 6 2565 15 -35 166779\\n\", \"642762664 588605882 1 -47 82 8\\n\", \"122740849 8646067 70003215 -100 -80 70\\n\", \"73221379 4311914 992324 65 -40 705623357422685593\\n\", \"487599125 469431740 316230350 -77 57 18\\n\", \"321575625 2929581 31407414 -40 -44 920902537044\\n\", \"5928 1508 4358 75 -4 794927060433551549\\n\", \"642762664 588605882 1 -47 82 8\\n\", \"1 1 1 1 1 0\\n\", \"147834 6 2565 15 -35 166779\\n\", \"910958510 60 98575 38 -99 97880\\n\", \"95 70 7 -36 -100 5\\n\", \"923 452 871 -95 -55 273135237285890\\n\", \"75081054 91 47131957 -94 -54 5588994022550344\\n\", \"568980902 147246752 87068387 -17 58 677739653\\n\", \"230182675 73108597 42152975 -72 -8 93667970058209518\\n\", \"976890548 675855343 988 -11 46 796041265897304\\n\", \"38 10 36 19 30 4054886\\n\", \"546978166 115293871 313560296 -33 54 215761558342792301\\n\", \"560010572 4172512 514044248 -78 13 97386\\n\", \"85 37 69 30 47 131\\n\", \"1000000000 1 2 -100 -100 1\\n\", \"67163467 36963416 50381 -49 -12 76558237\\n\", \"138971202 137695723 48931985 -28 -3 68901440898766\\n\", \"372903 106681 40781 54 -40 6188704\\n\", \"25699863 23288611 24796719 -45 46 437606836\\n\", \"61728 24280 17963 -19 81 652432745607745078\\n\", \"907122235 107269653 309181328 26 -64 242045007473044676\\n\", \"2 2 1 -2 -2 5\\n\", \"224 81 30 57 -13 8363\\n\", \"852525230 538352221 97088953 -12 98 9197937568\\n\", \"2 1 1 31 -74 2712360435504330\\n\", \"557911547 9 460221236 -58 -96 74518856\\n\", \"1000000000 1000000000 1000000000 100 -100 1000000000000000000\\n\", \"108774060 15274597 430014 -85 -94 6\\n\", \"900854530 82 7 30 -88 6797628981503799\\n\", \"713835677 404390162 67429 -91 10 178697004637242062\\n\", \"122740849 8646067 70003215 -100 -80 70\\n\", \"475875319 333393831 284835031 22 7 90332975949346\\n\", \"323544442 39059198 2970015 92 17 98\\n\", \"73221379 4311914 992324 65 -40 705623357422685593\\n\", \"7310962 7564 6333485 -45 41 81980903005818\\n\", \"804 658 177 -95 37 9\\n\", \"885849694 703278210 46391 33 23 965949118732\\n\", \"1710 654 941 -81 -37 1281183940\\n\", \"3 2 2 -100 -100 2\\n\", \"2 2 2 -36 94 9429569334\\n\", \"717485513 5935 3 -5 -67 28\\n\", \"672939 589365 391409 -54 -70 205083640\\n\", \"620330674 603592488 3 38 94 34309127789188\\n\", \"1000000000 1 1 1 1 1000000000000000000\\n\", \"185144 100489 52 32 -21 5752324832726786\\n\", \"487599125 469431740 316230350 -77 57 1\\n\", \"321575625 2929581 31407414 -40 -44 1519191219474\\n\", \"2663 1508 4358 75 -4 794927060433551549\\n\", \"642762664 1095286391 1 -47 82 8\\n\", \"147834 6 2565 2 -35 166779\\n\", \"95 58 7 -36 -100 5\\n\", \"923 452 145 -95 -55 273135237285890\\n\", \"225361 91 47131957 -94 -54 5588994022550344\\n\", \"568980902 147246752 87068387 -17 106 677739653\\n\", \"230182675 73108597 42152975 -60 -8 93667970058209518\\n\", \"976890548 675855343 716 -11 46 796041265897304\\n\", \"38 10 36 19 30 5836208\\n\", \"546978166 115293871 313560296 -33 54 335478541730507422\\n\", \"560010572 4172512 514044248 -78 13 393\\n\", \"85 37 69 47 47 131\\n\", \"1000000000 1 2 -100 -100 2\\n\", \"53287047 36963416 50381 -49 -12 76558237\\n\", \"138971202 137695723 48931985 -28 -3 104208678900501\\n\", \"372903 106681 60090 54 -40 6188704\\n\", \"25699863 23288611 24796719 -45 31 437606836\\n\", \"61728 24280 17963 -19 85 652432745607745078\\n\", \"907122235 107269653 309181328 26 -99 242045007473044676\\n\", \"224 81 30 84 -13 8363\\n\", \"852525230 183629206 97088953 -12 98 9197937568\\n\", \"2 1 1 31 -2 2712360435504330\\n\", \"557911547 18 460221236 -58 -96 74518856\\n\", \"1000000000 1000000000 1000000001 100 -100 1000000000000000000\\n\", \"108774060 15274597 705602 -85 -94 6\\n\", \"878821580 82 7 30 -88 6797628981503799\\n\", \"155385515 404390162 67429 -91 10 178697004637242062\\n\", \"122740849 8646067 37990796 -100 -80 70\\n\", \"927291879 333393831 284835031 22 7 90332975949346\\n\", \"323544442 22921761 2970015 92 17 98\\n\", \"121427897 4311914 992324 65 -40 705623357422685593\\n\", \"3969458 7564 6333485 -45 41 81980903005818\\n\", \"804 658 177 -95 49 9\\n\", \"885849694 703278210 46391 59 23 965949118732\\n\", \"1710 851 941 -81 -37 1281183940\\n\", \"856171624 5935 3 -5 -67 28\\n\", \"672939 589365 391409 -54 -70 335066546\\n\", \"620330674 603592488 3 38 94 28927873097115\\n\", \"1000000000 1 1 1 2 1000000000000000000\\n\", \"185144 100489 52 32 -5 5752324832726786\\n\", \"5 1 1 0 1 2\\n\", \"487599125 469431740 316230350 -77 18 1\\n\", \"321575625 2929581 31407414 -40 -44 1229786479249\\n\", \"2663 751 4358 75 -4 794927060433551549\\n\", \"642762664 1095286391 1 -47 82 2\\n\", \"147834 6 2565 2 -35 70061\\n\", \"95 58 7 -36 -198 5\\n\", \"923 702 145 -95 -55 273135237285890\\n\", \"225361 91 47131957 -94 -54 4244131932700081\\n\", \"568980902 147246752 87068387 -17 106 162650338\\n\", \"230182675 73108597 42152975 -60 -8 17474146509129810\\n\", \"525118217 675855343 716 -11 46 796041265897304\\n\", \"546978166 115293871 313560296 -17 54 335478541730507422\\n\", \"1 0 1 -1 -1 2\\n\", \"38 10 36 38 30 5836208\\n\", \"1 1 1 -1 -1 2\\n\", \"5 1 2 0 1 2\\n\"], \"outputs\": [\"3 1\", \"1 1\", \"1 1\", \"1 2\", \"168318977 168318977\", \"999999904 999999905\", \"1 1\", \"969796608 969796608\", \"23731316 525833901\", \"270 173\", \"1 1\", \"34918692 197804272\", \"320939970 167740992\", \"1568 945\", \"150920864 281916196\", \"18 36\", \"353006839 497349709\", \"105890973 69794440\", \"320222592 65760999\", \"4973 5148\", \"5246110 6302893\", \"130 205\", \"6742019 52104963\", \"56326 173503\", \"3174 1169\", \"24072870 13015404\", \"441571464 288459461\", \"161485 86089\", \"563 142\", \"503747 218115\", \"11882888 530616750\", \"71683921 71676253\", \"110585553 85995539\", \"304849180 291538135\", \"23368224 65407811\", \"246089810 106240697\", \"74 38\", \"84737577 321684009\", \"16593182 13087113\", \"652954007 789518296\", \"98184736 83340099\", \"1 1\", \"244834060 560206120\", \"200990066 258175045\", \"85 82\", \"66039616 641057009\", \"54423 144570\", \"355500874 409658689\", \"80795619 19413318\", \"62692638 21726334\", \"320939970 167740992\\n\", \"320222592 65760999\\n\", \"4973 5148\\n\", \"355500874 409658689\\n\", \"1 1\\n\", \"54423 144570\\n\", \"304849180 291538135\\n\", \"85 82\\n\", \"563 142\\n\", \"6742019 52104963\\n\", \"150920864 281916196\\n\", \"34918692 197804272\\n\", \"652954007 789518296\\n\", \"18 36\\n\", \"353006839 497349709\\n\", \"11882888 530616750\\n\", \"74 38\\n\", \"999999904 999999905\\n\", \"23368224 65407811\\n\", \"110585553 85995539\\n\", \"161485 86089\\n\", \"24072870 13015404\\n\", \"3174 1169\\n\", \"23731316 525833901\\n\", \"1 2\\n\", \"130 205\\n\", \"84737577 321684009\\n\", \"1 1\\n\", \"246089810 106240697\\n\", \"969796608 969796608\\n\", \"98184736 83340099\\n\", \"66039616 641057009\\n\", \"244834060 560206120\\n\", \"80795619 19413318\\n\", \"441571464 288459461\\n\", \"105890973 69794440\\n\", \"62692638 21726334\\n\", \"5246110 6302893\\n\", \"270 173\\n\", \"16593182 13087113\\n\", \"1568 945\\n\", \"1 1\\n\", \"1 1\\n\", \"71683921 71676253\\n\", \"503747 218115\\n\", \"200990066 258175045\\n\", \"168318977 168318977\\n\", \"56326 173503\\n\", \"279895503 126694247\\n\", \"120223512 198409074\\n\", \"389 1509\\n\", \"320528807 510768777\\n\", \"16002 56766\\n\", \"73 82\\n\", \"66 765\\n\", \"27230 88653\\n\", \"143912592 374499854\\n\", \"16750976 172064165\\n\", \"2626187 139190204\\n\", \"12 24\\n\", \"418606322 525783167\\n\", \"380399702 330296629\\n\", \"74 21\\n\", \"999999617 999999618\\n\", \"19953107 44768397\\n\", \"3332809 58377494\\n\", \"283847 227760\\n\", \"10347180 14352102\\n\", \"22898 11189\\n\", \"633770521 244700421\\n\", \"1 67\\n\", \"417513812 156658029\\n\", \"1 1\\n\", \"93759711 511822136\\n\", \"599261184 599261185\\n\", \"65363776 50794727\\n\", \"435298056 502362319\\n\", \"85912110 136087114\\n\", \"49959627 79305756\\n\", \"795972506 238859718\\n\", \"57661599 37702503\\n\", \"22445520 47409295\\n\", \"2625572 1982539\\n\", \"678 689\\n\", \"469992994 514074487\\n\", \"777 1667\\n\", \"219535425 219527757\\n\", \"262555 304876\\n\", \"438322854 50543531\\n\", \"138115585 138115585\\n\", \"133366 83543\\n\", \"3 5\\n\", \"279895503 126694208\\n\", \"119400263 144296725\\n\", \"56 1933\\n\", \"144091653 334330849\\n\", \"127171 50651\\n\", \"52 46\\n\", \"32 481\\n\", \"120860 200838\\n\", \"46382203 77863842\\n\", \"131451882 166442130\\n\", \"82039669 207099627\\n\", \"545631344 304908185\\n\", \"1 1\\n\", \"12 24\\n\", \"1 1\\n\", \"3 1\\n\"]}", "source": "taco"} | Our bear's forest has a checkered field. The checkered field is an n × n table, the rows are numbered from 1 to n from top to bottom, the columns are numbered from 1 to n from left to right. Let's denote a cell of the field on the intersection of row x and column y by record (x, y). Each cell of the field contains growing raspberry, at that, the cell (x, y) of the field contains x + y raspberry bushes.
The bear came out to walk across the field. At the beginning of the walk his speed is (dx, dy). Then the bear spends exactly t seconds on the field. Each second the following takes place: Let's suppose that at the current moment the bear is in cell (x, y). First the bear eats the raspberry from all the bushes he has in the current cell. After the bear eats the raspberry from k bushes, he increases each component of his speed by k. In other words, if before eating the k bushes of raspberry his speed was (dx, dy), then after eating the berry his speed equals (dx + k, dy + k). Let's denote the current speed of the bear (dx, dy) (it was increased after the previous step). Then the bear moves from cell (x, y) to cell (((x + dx - 1) mod n) + 1, ((y + dy - 1) mod n) + 1). Then one additional raspberry bush grows in each cell of the field.
You task is to predict the bear's actions. Find the cell he ends up in if he starts from cell (sx, sy). Assume that each bush has infinitely much raspberry and the bear will never eat all of it.
-----Input-----
The first line of the input contains six space-separated integers: n, sx, sy, dx, dy, t (1 ≤ n ≤ 10^9; 1 ≤ sx, sy ≤ n; - 100 ≤ dx, dy ≤ 100; 0 ≤ t ≤ 10^18).
-----Output-----
Print two integers — the coordinates of the cell the bear will end up in after t seconds.
-----Examples-----
Input
5 1 2 0 1 2
Output
3 1
Input
1 1 1 -1 -1 2
Output
1 1
-----Note-----
Operation a mod b means taking the remainder after dividing a by b. Note that the result of the operation is always non-negative. For example, ( - 1) mod 3 = 2.
In the first sample before the first move the speed vector will equal (3,4) and the bear will get to cell (4,1). Before the second move the speed vector will equal (9,10) and he bear will get to cell (3,1). Don't forget that at the second move, the number of berry bushes increased by 1.
In the second sample before the first move the speed vector will equal (1,1) and the bear will get to cell (1,1). Before the second move, the speed vector will equal (4,4) and the bear will get to cell (1,1). Don't forget that at the second move, the number of berry bushes increased by 1.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"25\\n5\\n\", \"19\\n14\\n\", \"25\\n8\\n\", \"55\\n15\\n\", \"24\\n11\\n\", \"26\\n7\\n\", \"48\\n13\\n\", \"16\\n17\\n\", \"36\\n9\\n\", \"33\\n16\\n\", \"18\\n13\\n\", \"27\\n16\\n\", \"42\\n6\\n\", \"34\\n8\\n\", \"16\\n7\\n\", \"26\\n10\\n\", \"13\\n11\\n\", \"46\\n7\\n\", \"15\\n17\\n\", \"15\\n5\\n\", \"55\\n16\\n\", \"10\\n11\\n\", \"48\\n15\\n\", \"39\\n13\\n\", \"15\\n12\\n\", \"11\\n21\\n\", \"33\\n11\\n\", \"29\\n7\\n\", \"16\\n4\\n\", \"13\\n12\\n\", \"15\\n6\\n\", \"19\\n9\\n\", \"55\\n22\\n\", \"15\\n13\\n\", \"36\\n10\\n\", \"18\\n12\\n\", \"29\\n9\\n\", \"22\\n14\\n\", \"14\\n6\\n\", \"55\\n25\\n\", \"10\\n12\\n\", \"13\\n18\\n\", \"33\\n15\\n\", \"18\\n5\\n\", \"19\\n7\\n\", \"55\\n26\\n\", \"18\\n7\\n\", \"28\\n17\\n\", \"33\\n17\\n\", \"33\\n18\\n\", \"34\\n19\\n\", \"24\\n16\\n\", \"29\\n8\\n\", \"17\\n12\\n\", \"17\\n12\\n\", \"17\\n12\\n\", \"17\\n12\\n\", \"22\\n12\\n\", \"35\\n8\\n\", \"17\\n12\\n\", \"\\n17\\n12\\n\"]}", "source": "taco"} | Little Dormi received a histogram with $n$ bars of height $a_1, a_2, \ldots, a_n$ for Christmas. However, the more he played with his new histogram, the more he realized its imperfections, so today he wanted to modify it to his liking.
To modify the histogram, Little Dormi is able to perform the following operation an arbitrary number of times:
Select an index $i$ ($1 \le i \le n$) where $a_i>0$, and assign $a_i := a_i-1$.
Little Dormi defines the ugliness score of his histogram (after performing some number of operations) as the sum of the vertical length of its outline and the number of operations he performed on it. And to make the histogram as perfect as possible, he would like to minimize the ugliness score after modifying it with some number of operations.
However, as his histogram is very large, Little Dormi is having trouble minimizing the ugliness score, so as Little Dormi's older brother, help him find the minimal ugliness.
Consider the following example where the histogram has $4$ columns of heights $4,8,9,6$:
The blue region represents the histogram, and the red lines represent the vertical portion of the outline. Currently, the vertical length of the outline is $4+4+1+3+6 = 18$, so if Little Dormi does not modify the histogram at all, the ugliness would be $18$.
However, Little Dormi can apply the operation once on column $2$ and twice on column $3$, resulting in a histogram with heights $4,7,7,6$:
Now, as the total vertical length of the outline (red lines) is $4+3+1+6=14$, the ugliness is $14+3=17$ dollars. It can be proven that this is optimal.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). Description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1 \le n \le 4 \cdot 10^5$).
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $4 \cdot 10^5$.
-----Output-----
For each test case output one integer, the minimal ugliness Little Dormi can achieve with the histogram in that test case.
-----Examples-----
Input
2
4
4 8 9 6
6
2 1 7 4 0 0
Output
17
12
-----Note-----
Example $1$ is the example described in the statement.
The initial histogram for example $2$ is given below:
The ugliness is currently $2+1+6+3+4=16$.
By applying the operation once on column $1$, six times on column $3$, and three times on column $4$, we can end up with a histogram with heights $1,1,1,1,0,0$:
The vertical length of the outline is now $1+1=2$ and Little Dormi made $1+6+3=10$ operations, so the final ugliness is $2+10=12$, which can be proven to be optimal.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"50 4 12\\nto tail\\n00000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000001000100000000000000000000000000000000000000010000000010000000000000000000000000000000000000000001\\n\", \"3 1 3\\nto head\\n10111111111111111011110110111111110111011111111111111111110101111111111111101111111111011110111110111111111111111111111111111110111111111111111110001011101111101110111111111111111111110101111111110011\\n\", \"2 2 1\\nto tail\\n01\\n\", \"5 1 4\\nto head\\n1000000000001\\n\", \"10 2 1\\nto tail\\n000000001\\n\", \"9 7 2\\nto head\\n1000100010110000101010010000000000010010000010100000001001000000001000000101100000000001\\n\", \"3 2 3\\nto head\\n0000000000000000001\\n\", \"13 9 8\\nto tail\\n000000000000000000000000000010011100000000000100100000000010000100000000000000000000000000000000000000010000011\\n\", \"2 1 2\\nto head\\n1101\\n\", \"2 2 1\\nto tail\\n10111111111111111110111011111111111111111111111111111110111111111110111111101111111111111111111111011111111111111011111111110111111101111111111101111111111111111101111111111111111111111111111001111111\\n\", \"5 4 2\\nto tail\\n1\\n\", \"4 3 1\\nto tail\\n1000001001101\\n\", \"4 1 3\\nto head\\n011000011000001\\n\", \"10 3 6\\nto head\\n0000001001010100000001010001000110001100011100000100100001100000001100000000000010000001000100100011\\n\", \"50 42 13\\nto head\\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\\n\", \"8 8 7\\nto head\\n0000000000001\\n\", \"42 24 17\\nto head\\n00000000000000000000100010000000000000000000001000100000000000000000001000000000000010000100100000100000001000000010010000000000101000000000000000010000000000000000000000000011001\\n\", \"10 8 2\\nto tail\\n0000000000000001000000000000000000000000001000000000010000000000001000000000000000100000000000000001\\n\", \"10 1 8\\nto tail\\n0000000000000000001000010000000001000001000000010000000000000000010010001000001000110010000001010011\\n\", \"7 1 7\\nto head\\n011001001000100000000000000100001100000001100000000010000010011\\n\", \"17 14 17\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"2 1 2\\nto head\\n01\\n\", \"49 44 14\\nto head\\n0000000000000000000000000000000000100000100000000000000000000000010000000000001000000000000000100000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000111001\\n\", \"4 2 1\\nto tail\\n1000001\\n\", \"2 1 2\\nto head\\n111111\\n\", \"3 3 2\\nto tail\\n0001\\n\", \"2 2 1\\nto tail\\n1101\\n\", \"4 2 4\\nto head\\n01101111110010111111111111011110111101000011111110111100111010111110111011010111010110011101101010111100000011001011011101101111010111101001001011101111111111100011110110011010111010111011001011111001\\n\", \"8 8 7\\nto head\\n0000000000000100101000110101011\\n\", \"5 3 4\\nto tail\\n0001000000101000010010010000100110011\\n\", \"50 50 14\\nto head\\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\\n\", \"38 7 18\\nto tail\\n00000000000000000000000000000000000000000000000000000000000000000000000000000001001000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\\n\", \"50 43 39\\nto head\\n01100111001110101111000001011111111100101101011010010001000001110001010011001010010100101100110011010011110110011111011101001111110001111001001100011110000111100100010001000011001001100000000010001111\\n\", \"4 1 4\\nto head\\n010001\\n\", \"50 9 39\\nto tail\\n00000000000000001000000000000000000000000000000000000000000010000000100000000000000001000100000000000000010000000001000000000000000000000000010000000000000000000000000000000000001000000000000000000101\\n\", \"2 2 1\\nto tail\\n11111101111111011111111111111111111111111111110111111110111111111101111111111001111110111111101011101110110011111011111011101011111111101111111110111111011111111111111111110111111111111111101111101111\\n\", \"5 5 3\\nto tail\\n01010000000001\\n\", \"6 4 5\\nto tail\\n0010000101101011001000000100111101101001010011001\\n\", \"10 3 8\\nto head\\n01\\n\", \"4 3 1\\nto tail\\n00011110000000010001\\n\", \"3 1 3\\nto head\\n11111111101111101111011011001011101100101101111111111011011111110011110101010111111101101010010111110110111111011111111111111111111110011111011011101110111111111111100111001110111110111011100111111111\\n\", \"20 15 7\\nto head\\n10011111001101010111101110101101101111011110111101001000101111011111011001110010001111111111111101111101011011111010011111111101111011111111\\n\", \"20 13 9\\nto head\\n1111111111111111111111111111111111111111\\n\", \"5 1 3\\nto head\\n1000000000001\\n\", \"3 3 1\\nto tail\\n1001000001\\n\", \"31 7 15\\nto tail\\n0010000000000000100000010000010000100000000000000000000001000001100100000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000100001\\n\", \"50 43 15\\nto tail\\n00000000000001000000000000000000000000001000000000000000000000001010000000000000000000000010000001000000000000100000000000000000000000000000100000000100000000000001000000000011000000101000010000000001\\n\", \"26 10 11\\nto head\\n0000000001001000100000010000110000000011100001000010000000000010000000000000110100000001000000010000110011000000100000000010001100010000000100001110001\\n\", \"8 5 6\\nto tail\\n01110101111111111111111111001111111011011111111111101111111111011111101\\n\", \"45 21 37\\nto tail\\n00000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\\n\", \"50 4 9\\nto tail\\n00000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000001000100000000000000000000000000000000000000010000000010000000000000000000000000000000000000000001\\n\", \"2 1 2\\nto head\\n1001\\n\", \"7 1 6\\nto head\\n011001001000100000000000000100001100000001100000000010000010011\\n\", \"4 3 1\\nto tail\\n1000001\\n\", \"4 3 1\\nto tail\\n00111110000000010001\\n\", \"3 1 3\\nto head\\n11111111101111101111011011001011101100101101111111111011011111110111110101010111111101101010010111110110111111011111111111111111111110011111011011101110111111111111100111001110111110111011100111111111\\n\", \"3 3 2\\nto tail\\n1001000001\\n\", \"31 7 15\\nto tail\\n0010000000000000100000010000010000100000000000000100000001000001100100000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000100001\\n\", \"45 21 15\\nto tail\\n00000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\\n\", \"15 9 8\\nto tail\\n000000000000000000000000000010011100000000000100100000000010000100000000000000000000000000000000000000010000011\\n\", \"16 3 6\\nto head\\n0000001001010100000001010001000110001100011100000100100001100000001100000000000010000001000100100011\\n\", \"10 8 2\\nto tail\\n0000000000000001000000000000000001000000001000000000010000000000001000000000000000100000000000000001\\n\", \"7 2 7\\nto head\\n011001001000100000000000000100001100000001100000000010000010011\\n\", \"4 3 4\\nto head\\n01101111110010111111111111011110111101000011111110111100111010111110111011010111010110011101101010111100000011001011011101101111010111101001001011101111111111100011110110011010111010111011001011111001\\n\", \"8 8 7\\nto head\\n0001000000001\\n\", \"42 24 21\\nto head\\n00000000000000000000100010000000000000000000001000100000000000000000001000000000000010000100100000100000001000000010010000000000101000000000000000010000000000000000000000000011001\\n\", \"32 14 17\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"49 44 17\\nto head\\n0000000000000000000000000000000000100000100000000000000000000000010000000000001000000000000000100000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000111001\\n\", \"50 50 14\\nto head\\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111\\n\", \"50 43 39\\nto head\\n01100111001110101111000101011111111100101101011010010001000001110001010011001010010100101100110011010011110110011111011101001111110001111001001100011110000111100100010001000011001001100000000010001111\\n\", \"40 15 7\\nto head\\n10011111001101010111101110101101101111011110111101001000101111011111011001110010001111111111111101111101011011111010011111111101111011111111\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000000001000000000000000000000001010000000000000000000000010000001000000000000100000000000000000000000000000100000000100000000000001000000000011000000101000010000000001\\n\", \"8 5 2\\nto tail\\n01110101111111111111111111001111111011011111111111101111111111011111101\\n\", \"32 22 17\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"50 50 14\\nto head\\n11111111111111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111111111111111\\n\", \"50 43 21\\nto head\\n01100111001110101111000101011111111100101101011010010001000001110001010011001010010100101100110011010011110110011111011101001111110001111001001100011110000111100100010001000011001001100000000010001111\\n\", \"4 3 2\\nto tail\\n00111110000000010001\\n\", \"40 15 7\\nto head\\n10011111001101010111101110101101101111011110111101001000111111011111011001110010001111111111111101111101011011111010011111111101111011111111\\n\", \"31 13 15\\nto tail\\n0010000000000000100000010000010000100000000000000100000001000001100100000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000100001\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000000001000000000000000000000001010000000000000000000000010000001000000000000100000000000000000000000000000100000000100000000000001000000100011000000101000010000000001\\n\", \"7 5 2\\nto tail\\n01110101111111111111111111001111111011011111111111101111111111011111101\\n\", \"32 22 18\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"50 43 21\\nto head\\n01100111001110100111000101011111111100101101011010010001000001110001010011001010010100101100110011010011110110011111011101001111110001111001001100011110000111100100010001000011001001100000000010001111\\n\", \"40 15 6\\nto head\\n10011111001101010111101110101101101111011110111101001000111111011111011001110010001111111111111101111101011011111010011111111101111011111111\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000000001000000000000000000000001010000000000000000000000010000001000000010000100000000000000000000000000000100000000100000000000001000000100011000000101000010000000001\\n\", \"32 22 11\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"50 43 21\\nto head\\n01100111001110100111000101011111111110101101011010010001000001110001010011001010010100101100110011010011110110011111011101001111110001111001001100011110000111100100010001000011001001100000000010001111\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000000001000000000000000000000001010000000000010000000000010000001000000010000100000000000000000000000000000100000000100000000000001000000100011000000101000010000000001\\n\", \"32 22 11\\nto head\\n0000001010000000000000100011000000100000001010000001011000000001001000100000000010100000010001000000000000000100000000000001\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000010001000000000000000000000001010000000000010000000000010000001000000010000100000000000000000000000000000100000000100000000000001000000100011000000101000010000000001\\n\", \"32 22 6\\nto head\\n0000001010000000000000100011000000100000001010000001011000000001001000100000000010100000010001000000000000000100000000000001\\n\", \"50 43 12\\nto tail\\n00000000000001000000000000000000000010001000000000000000000000001010000000000010000000000010000001000000010000100000000000000000000000001000100000000100000000000001000000100011000000101000010000000001\\n\", \"50 14 12\\nto tail\\n00000000000001000000000000000000000010001000000000000000000000001010000000000010000000000010000001000000010000100000000000000000000000001000100000000100000000000001000000100011000000101000010000000001\\n\", \"50 14 24\\nto tail\\n00000000000001000000000000000000000010001000000000000000000000001010000000000010000000000010000001000000010000100000000000000000000000001000100000000100000000000001000000100011000000101000010000000001\\n\", \"50 4 21\\nto tail\\n00000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000001000100000000000000000000000000000000000000010000000010000000000000000000000000000000000000000001\\n\", \"2 2 1\\nto tail\\n1\\n\", \"10 2 1\\nto tail\\n000000011\\n\", \"42 24 17\\nto head\\n00000000000000000000000010000000000000000000001000100000000000000000001000000000000010000100100000100000001000000010010000000000101000000000000000010000000000000000000000000011001\\n\", \"17 14 13\\nto head\\n0000001010000000000000100011000000100000001010000001011000000000001000100000000010100000010001000000000000000100000000000001\\n\", \"2 1 2\\nto head\\n1\\n\", \"49 44 14\\nto head\\n0000000000000000000000000000000000100000100000000000000000000000010000000000001000000000000000100000000000000000000000000000000001000000000000000000000000000001000000000000000000000000000000000111001\\n\", \"50 26 14\\nto head\\n11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\\n\", \"4 2 4\\nto head\\n010001\\n\", \"50 18 39\\nto tail\\n00000000000000001000000000000000000000000000000000000000000010000000100000000000000001000100000000000000010000000001000000000000000000000000010000000000000000000000000000000000001000000000000000000101\\n\", \"11 3 8\\nto head\\n01\\n\", \"5 3 1\\nto tail\\n00011110000000010001\\n\", \"20 15 5\\nto head\\n10011111001101010111101110101101101111011110111101001000101111011111011001110010001111111111111101111101011011111010011111111101111011111111\\n\", \"20 13 17\\nto head\\n1111111111111111111111111111111111111111\\n\", \"31 7 15\\nto tail\\n0010000000000000100000010000010000100000000000000000000001000001100100000000000000000000000000000000000000100000000000000000000000000000000000000000100000000000100001\\n\", \"5 3 2\\nto head\\n0001001\\n\", \"3 2 1\\nto tail\\n0001\\n\"], \"outputs\": [\"Stowaway\\n\", \"Controller 148\\n\", \"Controller 1\\n\", \"Controller 7\\n\", \"Stowaway\\n\", \"Controller 33\\n\", \"Controller 2\\n\", \"Controller 5\\n\", \"Controller 3\\n\", \"Controller 2\\n\", \"Stowaway\\n\", \"Controller 6\\n\", \"Controller 14\\n\", \"Controller 5\\n\", \"Controller 61\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 8\\n\", \"Controller 11\\n\", \"Controller 24\\n\", \"Stowaway\\n\", \"Controller 1\\n\", \"Controller 157\\n\", \"Controller 6\\n\", \"Stowaway\\n\", \"Controller 1\\n\", \"Controller 3\\n\", \"Controller 42\\n\", \"Controller 13\\n\", \"Controller 9\\n\", \"Stowaway\\n\", \"Controller 57\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 7\\n\", \"Controller 10\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 3\\n\", \"Controller 28\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 6\\n\", \"Controller 6\\n\", \"Controller 106\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 96\\n\", \"Stowaway\\n\", \"Controller 2\\n\", \"Controller 23\\n\", \"Controller 6\\n\", \"Controller 12\\n\", \"Controller 28\\n\", \"Controller 3\\n\", \"Controller 106\\n\", \"Controller 30\\n\", \"Controller 7\\n\", \"Controller 5\\n\", \"Controller 8\\n\", \"Controller 24\\n\", \"Controller 42\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 2\\n\", \"Stowaway\\n\", \"Controller 106\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 12\\n\", \"Stowaway\\n\", \"Stowaway\\n\", \"Controller 106\\n\", \"Stowaway\\n\", \"Controller 2\\n\"]}", "source": "taco"} | A stowaway and a controller play the following game.
The train is represented by n wagons which are numbered with positive integers from 1 to n from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions — moving or idle. Every minute the players move.
The controller's move is as follows. The controller has the movement direction — to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the 1-st or the n-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.
The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of n wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.
Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.
If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.
At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner.
Input
The first line contains three integers n, m and k. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (2 ≤ n ≤ 50, 1 ≤ m, k ≤ n, m ≠ k).
The second line contains the direction in which a controller moves. "to head" means that the controller moves to the train's head and "to tail" means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon 1 is the head, and wagon n is the tail.
The third line has the length from 1 to 200 and consists of symbols "0" and "1". The i-th symbol contains information about the train's state at the i-th minute of time. "0" means that in this very minute the train moves and "1" means that the train in this very minute stands idle. The last symbol of the third line is always "1" — that's the terminal train station.
Output
If the stowaway wins, print "Stowaway" without quotes. Otherwise, print "Controller" again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught.
Examples
Input
5 3 2
to head
0001001
Output
Stowaway
Input
3 2 1
to tail
0001
Output
Controller 2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"\\nNo\\n\", \"\\nYes\\n\", \"\\nNo\\n\", \"\\nYes\\n\"]}", "source": "taco"} | In recent years John has very successfully settled at his new job at the office. But John doesn't like to idly sit around while his code is compiling, so he immediately found himself an interesting distraction. The point of his distraction was to maintain a water level in the water cooler used by other zebras.
Originally the cooler contained exactly $k$ liters of water. John decided that the amount of water must always be at least $l$ liters of water but no more than $r$ liters. John will stay at the office for exactly $t$ days. He knows that each day exactly $x$ liters of water will be used by his colleagues. At the beginning of each day he can add exactly $y$ liters of water to the cooler, but at any point in time the amount of water in the cooler must be in the range $[l, r]$.
Now John wants to find out whether he will be able to maintain the water level at the necessary level for $t$ days. Help him answer this question!
-----Input-----
The first line of the input contains six integers $k$, $l$, $r$, $t$, $x$ and $y$ ($1 \le l \le k \le r \le 10^{18}; 1 \le t \le 10^{18}; 1 \le x \le 10^6; 1 \le y \le 10^{18}$) — initial water level, the required range, the number of days, daily water usage and the exact amount of water that can be added, respectively.
-----Output-----
Print "Yes" if John can maintain the water level for $t$ days and "No" otherwise.
-----Examples-----
Input
8 1 10 2 6 4
Output
No
Input
8 1 10 2 6 5
Output
Yes
Input
9 1 10 9 2 9
Output
No
Input
20 15 25 3 5 7
Output
Yes
-----Note-----
In the first example, John can't increase the amount of water at the beginning of the first day, since it would exceed the limit $r$. That is why after the first day the cooler will contain $2$ liters of water. The next day John adds $4$ liters to the cooler but loses $6$ liters, leaving John with $0$ liters, which is outside the range $[1, 10]$.
In the second example, after the first day John is left with $2$ liters of water. At the beginning of the next day he adds $5$ liters, then $6$ liters get used, leaving John with $1$ liter of water which is in range $[1, 10]$.
In the third example, after the first day John is left with $7$ liters, after the second day — $5$ liters, after the fourth — $1$ liter. At the beginning of the fifth day John will add $9$ liters and lose $2$ liters. Meaning, after the fifth day he will have $8$ liters left. Then each day the water level will decrease by $2$ liters and after the eighth day John will have $2$ liters and after the ninth day — $0$ liters. $0$ is outside range $[1, 10]$, so the answer is "No".
In the fourth example, after the first day John is left with $15$ liters of water. At the beginning of the second day he adds $7$ liters and loses $5$, so after the second day he is left with $17$ liters. At the beginning of the third day he adds $7$ more liters of water and loses $5$, so after the third day he is left with $19$ liters. $19$ is in range $[15, 25]$ so the answer is "Yes".
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"8\\n1 0 1 1 0 1 1 0\\n1 1 2 2 3 3 5\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"8\\n1 0 1 1 0 1 1 0\\n1 1 2 2 5 2 4\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 12 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 22 43 17 26 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 83 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"9\\n1 1 0 1 0 0 1 0 1\\n1 1 2 2 3 3 4 4\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 22 43 17 17 16 43 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 83 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"8\\n1 0 1 1 1 1 1 0\\n1 1 2 2 3 5 3\\n\", \"6\\n0 0 1 0 0 1\\n1 2 1 2 1\\n\", \"6\\n0 0 1 0 1 1\\n1 2 2 2 3\\n\", \"8\\n0 0 0 1 0 0 1 0\\n1 1 2 2 3 3 4\\n\", \"6\\n1 0 1 1 1 1\\n1 2 1 1 5\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 57 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 16 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 12 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 22 43 17 26 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 83 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"6\\n1 0 1 0 0 1\\n1 2 1 2 1\\n\", \"6\\n1 1 1 1 1 1\\n1 2 1 1 5\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 22 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 3 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 57 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 16 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 22 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 36 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 3 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 57 5 61 72 10 5 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 1 12 8 11 22 8 17 19 5 15 27 14 22 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 10 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 5 5 28 77 61 40 18 36 21 43 3 9 15 81 70 56 65\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 23 1 14 39 26 22 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 36 34 5 61 72 10 83 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"5\\n1 0 1 0 0\\n1 1 1 1\\n\", \"8\\n1 0 0 1 0 1 1 0\\n1 1 2 2 3 1 3\\n\", \"100\\n0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1\\n1 2 3 4 2 6 5 5 4 8 10 8 1 14 5 16 3 11 13 11 12 8 11 22 8 17 19 5 15 27 14 13 12 4 6 2 10 25 36 14 16 14 19 15 37 12 45 39 34 48 18 3 4 29 1 14 39 26 22 43 17 17 16 27 24 53 57 25 21 55 12 63 12 34 4 2 54 34 5 61 72 10 83 5 28 77 61 40 18 87 21 43 3 9 15 81 70 56 65\\n\", \"6\\n1 0 1 1 0 1\\n1 2 1 2 1\\n\", \"9\\n1 1 0 1 1 0 1 0 1\\n1 1 2 4 3 3 3 4\\n\", \"6\\n1 0 1 1 0 1\\n1 2 2 2 2\\n\", \"9\\n1 1 0 0 1 0 1 0 1\\n1 1 2 2 3 3 4 4\\n\", \"5\\n1 0 1 0 1\\n1 1 1 1\\n\", \"8\\n1 0 0 1 0 1 1 0\\n1 1 2 2 3 3 3\\n\"], \"outputs\": [\"1\\n\", \"4\\n\", \"4\\n\", \"5\\n\", \"42\\n\", \"1\\n\", \"1\", \"42\", \"42\\n\", \"1\\n\", \"4\\n\", \"5\\n\", \"41\\n\", \"3\\n\", \"43\\n\", \"44\\n\", \"5\\n\", \"41\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"42\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"5\\n\", \"5\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"43\\n\", \"4\\n\", \"5\\n\", \"43\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"1\\n\", \"42\\n\", \"5\\n\", \"4\\n\", \"41\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"42\\n\", \"3\\n\", \"5\\n\", \"3\\n\", \"43\\n\", \"4\\n\", \"43\\n\", \"4\\n\", \"42\\n\", \"5\\n\", \"41\\n\", \"4\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"43\\n\", \"42\\n\", \"44\\n\", \"42\\n\", \"4\\n\", \"3\\n\", \"43\\n\", \"43\\n\", \"44\\n\", \"44\\n\", \"43\\n\", \"42\\n\", \"43\\n\", \"4\\n\", \"5\\n\", \"42\\n\", \"4\\n\", \"5\\n\", \"1\", \"5\", \"4\", \"4\"]}", "source": "taco"} | Now Serval is a junior high school student in Japari Middle School, and he is still thrilled on math as before.
As a talented boy in mathematics, he likes to play with numbers. This time, he wants to play with numbers on a rooted tree.
A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. A parent of a node $v$ is the last different from $v$ vertex on the path from the root to the vertex $v$. Children of vertex $v$ are all nodes for which $v$ is the parent. A vertex is a leaf if it has no children.
The rooted tree Serval owns has $n$ nodes, node $1$ is the root. Serval will write some numbers into all nodes of the tree. However, there are some restrictions. Each of the nodes except leaves has an operation $\max$ or $\min$ written in it, indicating that the number in this node should be equal to the maximum or minimum of all the numbers in its sons, respectively.
Assume that there are $k$ leaves in the tree. Serval wants to put integers $1, 2, \ldots, k$ to the $k$ leaves (each number should be used exactly once). He loves large numbers, so he wants to maximize the number in the root. As his best friend, can you help him?
-----Input-----
The first line contains an integer $n$ ($2 \leq n \leq 3\cdot 10^5$), the size of the tree.
The second line contains $n$ integers, the $i$-th of them represents the operation in the node $i$. $0$ represents $\min$ and $1$ represents $\max$. If the node is a leaf, there is still a number of $0$ or $1$, but you can ignore it.
The third line contains $n-1$ integers $f_2, f_3, \ldots, f_n$ ($1 \leq f_i \leq i-1$), where $f_i$ represents the parent of the node $i$.
-----Output-----
Output one integer — the maximum possible number in the root of the tree.
-----Examples-----
Input
6
1 0 1 1 0 1
1 2 2 2 2
Output
1
Input
5
1 0 1 0 1
1 1 1 1
Output
4
Input
8
1 0 0 1 0 1 1 0
1 1 2 2 3 3 3
Output
4
Input
9
1 1 0 0 1 0 1 0 1
1 1 2 2 3 3 4 4
Output
5
-----Note-----
Pictures below explain the examples. The numbers written in the middle of the nodes are their indices, and the numbers written on the top are the numbers written in the nodes.
In the first example, no matter how you arrange the numbers, the answer is $1$. [Image]
In the second example, no matter how you arrange the numbers, the answer is $4$. [Image]
In the third example, one of the best solution to achieve $4$ is to arrange $4$ and $5$ to nodes $4$ and $5$. [Image]
In the fourth example, the best solution is to arrange $5$ to node $5$. [Image]
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"syvncqmfhautvxudqdhggz\\nhrpxzeghsocjpicuixskfuzupytsgjsdiyb\\nybcmnmnbpndbxlxbzhbfnqvwcffvrdhtickyqhupmcehls\\n\", \"iefouqzxoyuieqdzalfktehtvdbvjmeubju\\nocotspetkkhvwfgaqynhovjwjhciefouqzxoyuieqdzalfktehtvdbvjmeubjubcmnvpwgdpnchqhzjrchyrfpvigubp\\nycnhjwgbocotspetkkhvwfgaqynhovjwjhcief\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgsujgqu\\njlxqvcuivagmw\\n\", \"jwdezvgfm\\nmdoqvylpuvyk\\nqylldbziva\\n\", \"rdtevvmiqmfgvafkdypxjthzhfsbavmhgkavkfonscaokdxoscenpxrc\\nijbvueenzsmgkmkrskjspvfchwkqdglkxnrdtevvmiqmfgvafkdypxjthz\\nkqdglkxnrdtevvmiqmfgvafkdypxjthzhfsbavmhgkavkfonscaokdxoscenpxrcivydtkrxjy\\n\", \"xufuzdlsjxmevrtessfbwlnzzclcqwevnnucxyvhngnxhcbdfwq\\nwlwobhnmmgtfolfaeckbrnnglylydxtgtvrlmeeszoiuatzzzxufuzdlsjxmevrt\\nbrnnglylydxtgtvrlmeeszoiuatzzzx\\n\", \"syvncqmfhautvxudqdhggz\\nhrpxzeghsocjpicuixskfuzupytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgsujgqu\\njlxqvcmivaguw\\n\", \"jxdezvgfm\\nmdoqvylpuvyk\\nqylldbziva\\n\", \"ab\\ncc\\ncd\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgsujgqu\\nwugavimcvqlxj\\n\", \"ab\\ncc\\ndd\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgusjgqu\\nwugavimcvqlxj\\n\", \"fmdejvgzx\\nmdoqvylpuvyk\\nqylldbziva\\n\", \"syvncqmfhausvxueqdhggz\\nbyidsjgstyouzufksxiucpijcoshgezxprh\\nslhecmpuhqykcitqdrvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"ujgruqxclovuwnqkmbd\\nwdwkhkdgusjgqu\\njxlqvcnivafuw\\n\", \"syvncqmfhautvxueqdhggz\\nhrpxzeghsocjpicuixskfuzupytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgsujgqu\\njxlqvcmivaguw\\n\", \"zxdejvgfm\\nmdoqvylpuvyk\\nqylldbziva\\n\", \"ab\\ncc\\ndc\\n\", \"syvncqmfhautvxueqdhggz\\nhrpxzeghsocjipcuixskfuzupytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"fxdejvgzm\\nmdoqvylpuvyk\\nqylldbziva\\n\", \"syvncrmfhautvxueqdhggz\\nhrpxzeghsocjipcuixskfuzupytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"ba\\ncc\\ndd\\n\", \"syvncrmfhausvxueqdhggz\\nhrpxzeghsocjipcuixskfuzupytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"ujgquqxdlowuwnqkmbd\\nwdwkhkdgusjgqu\\nwufavimcvqlxj\\n\", \"fmdejvgzx\\nkyvuplyvqodm\\nqylldbziva\\n\", \"aa\\ncc\\ndd\\n\", \"syvncrmfhausvxueqdhggz\\nhrpxzeghsocjipcuixskfuzuoytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnpbnmnmcby\\n\", \"ujgruqxdlowuwnqkmbd\\nwdwkhkdgusjgqu\\nwufavimcvqlxj\\n\", \"fmdejvgzx\\nlyvuplyvqodm\\nqylldbziva\\n\", \"aa\\ndc\\ndd\\n\", \"syvncrmfhausvxueqdhggz\\nhrpxzeghsocjipcuixskfuzuoytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnobnmnmcby\\n\", \"ujgruqxdlowuwnqkmbd\\nwdwkhkdgusjgqu\\nwufavincvqlxj\\n\", \"fmdejvgzx\\nlyvuplyvqodm\\nqylmdbziva\\n\", \"aa\\ndc\\ncd\\n\", \"syvncqmfhausvxueqdhggz\\nhrpxzeghsocjipcuixskfuzuoytsgjsdiyb\\nslhecmpuhqykcithdrvffcwvqnfbhzbxlxbdnobnmnmcby\\n\", \"ujgruqxdlovuwnqkmbd\\nwdwkhkdgusjgqu\\nwufavincvqlxj\\n\", \"fmdejvgzx\\nlyvuplyvqodm\\navizbdmlyq\\n\", \"aa\\ndc\\nbd\\n\", \"syvncqmfhausvxueqdhggz\\nhrpxzeghsocjipcuixskfuzuoytsgjsdiyb\\nslhecmpuhqykcitqdrvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"ujgruqxclovuwnqkmbd\\nwdwkhkdgusjgqu\\nwufavincvqlxj\\n\", \"fmdejwgzx\\nlyvuplyvqodm\\nqylmdbziva\\n\", \"fmdejwgzx\\nkyvuplyvqodm\\nqylmdbziva\\n\", \"syvncqmfhausvxueqdhggz\\nboidsjgstyyuzufksxiucpijcoshgezxprh\\nslhecmpuhqykcitqdrvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"ujgruqxclovuwnqkmbd\\nwdgkhkdwusjgqu\\njxlqvcnivafuw\\n\", \"fmdejwgzx\\nmdoqvylpuvyk\\nqylmdbziva\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxprh\\nslhecmpuhqykcitqdrvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxprh\\nslhecmpuhqykcitqdqvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxpqh\\nslhecmpuhqykcitqdqvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxpqh\\nslhecmpuhqykbitqdqvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxqqh\\nslhecmpuhqykbitqdqvffcwvhnfbhzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxqqh\\nslhecmpuhqykbitqdqvffcwvhnfchzbxlxbdnobnmnmcby\\n\", \"syvncqmfhausvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxqqh\\nslhecmpvhqykbitqdqvffcwvhnfchzbxlxbdnobnmnmcby\\n\", \"syvncqmfhbusvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxqqh\\nslhecmpvhqykbitqdqvffcwvhnfchzbxlxbdnobnmnmcby\\n\", \"syvncqmfhbusvxueqdgggz\\nboidsjgstyyuzufksxiucpijcoshgezxqqh\\nslhecnpvhqykbitqdqvffcwvhnfchzbxlxbdnobnmnmcby\\n\", \"abacaba\\nabaaba\\nx\\n\", \"ab\\nbc\\ncd\\n\"], \"outputs\": [\"100\\n\", \"100\\n\", \"40\\n\", \"30\\n\", \"100\\n\", \"100\\n\", \"103\\n\", \"40\\n\", \"30\\n\", \"5\\n\", \"41\\n\", \"6\\n\", \"45\\n\", \"31\\n\", \"101\\n\", \"44\\n\", \"103\\n\", \"40\\n\", \"30\\n\", \"5\\n\", \"103\\n\", \"30\\n\", \"103\\n\", \"6\\n\", \"103\\n\", \"45\\n\", \"31\\n\", \"6\\n\", \"103\\n\", \"45\\n\", \"31\\n\", \"5\\n\", \"103\\n\", \"45\\n\", \"31\\n\", \"5\\n\", \"103\\n\", \"45\\n\", \"31\\n\", \"5\\n\", \"103\\n\", \"45\\n\", \"31\\n\", \"31\\n\", \"103\\n\", \"44\\n\", \"31\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"103\\n\", \"11\\n\", \"4\\n\"]}", "source": "taco"} | Sometimes it is hard to prepare tests for programming problems. Now Bob is preparing tests to new problem about strings — input data to his problem is one string. Bob has 3 wrong solutions to this problem. The first gives the wrong answer if the input data contains the substring s1, the second enters an infinite loop if the input data contains the substring s2, and the third requires too much memory if the input data contains the substring s3. Bob wants these solutions to fail single test. What is the minimal length of test, which couldn't be passed by all three Bob's solutions?
Input
There are exactly 3 lines in the input data. The i-th line contains string si. All the strings are non-empty, consists of lowercase Latin letters, the length of each string doesn't exceed 105.
Output
Output one number — what is minimal length of the string, containing s1, s2 and s3 as substrings.
Examples
Input
ab
bc
cd
Output
4
Input
abacaba
abaaba
x
Output
11
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"20 17\\n407 2799 2032 2154 8119 9404 6718 7914 916 4720 1267 9403 5497 4518 9072 7828 8364 8230 3057 7770\\n\", \"2 1\\n1 2\\n\", \"1 2\\n10\\n\", \"2 1\\n8 20\\n\", \"5 1\\n1 2 3 4 5\\n\", \"50 25\\n1498786 501094 6396443 1167317 719496 636212 1912961 3111395 9572144 6277130 9288513 7311574 4038261 7897312 6769622 3412399 9996933 4060756 9948079 1769012 7600286 9897826 2087275 5962282 4953810 9654443 5333662 433180 3588803 4130095 9598090 5151122 9842663 2514194 1676006 1626458 6001092 8600794 1723930 8161219 1356724 4329774 8289408 3197404 7978402 1561752 3254820 3668793 6778571 7700292\\n\", \"3 2\\n1 2 3\\n\", \"2 2\\n10000000 1000000\\n\", \"5 2\\n10 9 19 12 14\\n\", \"50 50\\n873312389 604039796 470980211 604092901 317645830 865841782 30190128 90700018 361113641 948274316 775347907 312933768 745800411 976357881 652424427 420068005 77994941 746874884 912886330 875358567 675008609 780785718 874337107 541592914 532566154 316033689 257781802 361740423 72046192 816493561 290190407 245507086 581576441 739752998 801377026 469634060 850496001 558296112 702877640 836956173 304850066 276508329 703262292 394254651 789172012 655966182 103434486 635267748 872287742 750895678\\n\", \"2 1\\n2 1\\n\", \"20 50\\n366890701 326770801 264406917 201841167 245146846 423010984 902787383 250242526 915591714 753137694 212804025 728751237 707187607 713393006 915812218 208754076 88791411 661347329 647317959 484135977\\n\", \"40 11\\n60208 236973 84548 315924 250944 161962 297861 210884 314453 279066 6713 301121 238667 162406 271727 215696 44559 217356 265375 162107 289254 27492 179940 37333 304851 292475 216268 324087 57771 193073 309245 77531 58743 46448 125774 80238 70527 80833 24488 206156\\n\", \"4 3\\n1 1000000000 100000000 10000000\\n\", \"5 4\\n1 2 3 4 5\\n\", \"4 4\\n1 2 3 4\\n\", \"1 1\\n1\\n\", \"44 38\\n1462767 3166364 2098867 3314373 272988 1780023 2892344 3453931 131181 2304994 1855709 770970 3125250 2260136 1472897 2688663 2516513 1842215 187194 725629 1982324 3030991 3106666 2504895 211807 3306495 3315809 2391117 1748124 110461 1156562 1210236 190189 504062 371439 3202405 503823 2844645 568415 3139160 1616378 3185067 3099571 2832834\\n\", \"37 15\\n438778 549860 49173 79840 234277 898394 923784 647192 886153 382676 312989 525192 837433 210204 822734 218858 732642 336426 241548 478143 133580 508509 279685 393941 361559 59454 924509 236866 531648 567554 476854 399527 678235 527942 854506 697967 609944\\n\", \"48 42\\n140920201 439599146 631470789 326348765 777305542 246501797 98842561 66698125 328893187 320920834 442056583 300823217 102856871 894833295 183971312 540000242 77621006 301282781 633518310 368397657 266701251 254744062 276445863 624102545 317896643 457301959 840650755 37020968 787211200 835830799 696187545 77377229 666128476 254311406 706645277 592561555 487913577 799871742 248143253 499058221 533238063 603652509 401508758 545626159 728850086 173008168 373273227 772142675\\n\", \"2 2\\n100000000 1000000000\\n\", \"17 27\\n22 8 17 12 24 28 25 20 7 9 4 15 6 33 19 5 10\\n\", \"3 4\\n5 1 4\\n\", \"50 2\\n611819205 916034844 226292837 817298502 176794540 727900268 460009451 154197232 671291076 641633528 316549457 84943963 581078373 360295861 299532522 279193498 61088105 776327911 952977833 796036148 193827182 248414821 822409059 451009120 316494610 702170585 194014479 567762248 201775925 186588924 630333192 849644874 978885690 826471389 136002889 659371057 392112709 74463003 491124655 336372608 480423293 428908070 423023163 749932199 880227915 227662209 304705869 82537803 424363417 744202499\\n\", \"10 5\\n68 78 70 3 77 2 24 17 96 63\\n\", \"5 2\\n1 2 5 4 3\\n\", \"30 7\\n483242884 141465390 673274235 374698924 293895324 745776711 38293296 624522417 759055572 343124219 260836408 738391263 503711346 394651562 297415680 772345540 864523609 288584413 650320686 449000886 409412162 15908489 635266274 210759446 839533571 807852364 888754168 98417552 843606733 776397228\\n\", \"3 1\\n1 2 3\\n\", \"40 30\\n115644639 84968781 502201719 185562964 985439338 904909761 987469310 392279024 34042735 634622221 839483595 370724480 578485357 293110515 426715668 623544321 361578399 344575100 906293095 989519195 455225 952837951 263384814 771897504 859893161 171980440 959878829 233550924 365529816 203041523 562264000 739766404 289946473 250809088 370936224 210349657 657189623 5710590 638043996 944609028\\n\", \"50 1\\n282174632 865088564 656352811 984648256 521352785 57911680 996749451 85805091 790762915 281422127 195283931 253923622 554865826 31466324 214732274 790749112 441328969 537583501 612245057 877161587 763349710 784532543 192804116 844363612 235045603 185195996 13097680 541100831 561866993 317797406 403001652 484887637 16410460 587211083 582483610 461878975 571808452 827167600 562613044 787964041 370263360 15717800 907380817 301112202 488431522 827024725 622035351 983160960 309839543 725826915\\n\", \"2 1\\n2 3\\n\", \"2 2\\n7 2\\n\", \"2 40\\n33 29\\n\", \"5 10\\n7 5 9 10 8\\n\", \"9 8\\n83 6 90 96 42 71 11 82 51\\n\", \"32 50\\n7 5 50 2 42 36 28 8 44 3 40 15 33 18 1 6 25 20 39 24 45 35 14 27 17 47 19 49 13 34 22 26\\n\", \"1 1\\n1000000000\\n\", \"50 49\\n88725980 83881995 59295833 19992230 98694184 93275377 61249454 52781239 92644863 72826940 50546968 49705218 12163764 2370616 74789070 66649536 44427957 38263003 29482181 32784244 68697287 58653702 72057831 71170858 7965262 28000704 62154588 20020410 74475651 17112704 51168707 67055363 94596285 74161506 20821879 13196082 72415147 47307630 29342412 42369019 97867158 37513173 21502544 32181980 10790305 28119093 11323148 54617694 24131594 56797138\\n\", \"50 40\\n96796700 70298164 77962801 85411997 38782814 34003824 38719796 99639116 67985686 99451905 61978628 21844407 12207253 79918 49399043 20719647 39110240 7094466 69163751 33236841 22249070 77179977 59576055 65178969 85705829 95074132 34273099 39626456 4907488 86213552 61097999 82889263 50311083 51771059 1255360 54093385 26718724 93604207 70082669 67044340 47726300 29504508 9910007 22933280 6155028 44655282 92452176 72975646 64485568 28849515\\n\", \"4 1\\n1 2 999999991 999999999\\n\", \"1 1\\n2\\n\", \"49 50\\n237449581 667894738 947395330 631153874 73096515 526873659 442758248 458113553 593707922 871777170 341397492 276382904 953470766 481575900 456794298 949850484 901479039 641744893 906465923 889863668 865607102 676085245 15087113 733126439 805674805 419604807 578669881 662288768 867202435 312642277 690318191 928184117 255005653 221548485 89241021 776806523 716418093 628174070 549089059 180504011 699093407 914610155 999333080 522769440 884252814 601964726 433999999 961290550 79463155\\n\", \"20 22\\n407 2799 2032 2154 8119 9404 6718 7914 916 4720 1267 9403 5497 4518 9072 7828 8364 8230 3057 7770\\n\", \"5 1\\n1 2 3 4 1\\n\", \"50 25\\n1498786 501094 6396443 1167317 719496 636212 1912961 3111395 9572144 6277130 9288513 7311574 4038261 7897312 6769622 3412399 9996933 4060756 9948079 1769012 7600286 9897826 2087275 5962282 4953810 9654443 5333662 433180 3588803 4130095 9598090 5151122 9842663 2514194 1676006 387026 6001092 8600794 1723930 8161219 1356724 4329774 8289408 3197404 7978402 1561752 3254820 3668793 6778571 7700292\\n\", \"2 2\\n10000000 0000000\\n\", \"5 4\\n10 9 19 12 14\\n\", \"50 50\\n873312389 604039796 470980211 604092901 317645830 865841782 59176968 90700018 361113641 948274316 775347907 312933768 745800411 976357881 652424427 420068005 77994941 746874884 912886330 875358567 675008609 780785718 874337107 541592914 532566154 316033689 257781802 361740423 72046192 816493561 290190407 245507086 581576441 739752998 801377026 469634060 850496001 558296112 702877640 836956173 304850066 276508329 703262292 394254651 789172012 655966182 103434486 635267748 872287742 750895678\\n\", \"2 1\\n0 1\\n\", \"40 11\\n60208 236973 84548 315924 250944 161962 52984 210884 314453 279066 6713 301121 238667 162406 271727 215696 44559 217356 265375 162107 289254 27492 179940 37333 304851 292475 216268 324087 57771 193073 309245 77531 58743 46448 125774 80238 70527 80833 24488 206156\\n\", \"4 3\\n1 1000000000 100000010 10000000\\n\", \"44 38\\n1462767 3166364 555494 3314373 272988 1780023 2892344 3453931 131181 2304994 1855709 770970 3125250 2260136 1472897 2688663 2516513 1842215 187194 725629 1982324 3030991 3106666 2504895 211807 3306495 3315809 2391117 1748124 110461 1156562 1210236 190189 504062 371439 3202405 503823 2844645 568415 3139160 1616378 3185067 3099571 2832834\\n\", \"37 15\\n438778 549860 49173 79840 234277 898394 923784 647192 886153 382676 312989 525192 837433 210204 822734 218858 732642 336426 241548 478143 133580 682923 279685 393941 361559 59454 924509 236866 531648 567554 476854 399527 678235 527942 854506 697967 609944\\n\", \"48 42\\n140920201 439599146 177691067 326348765 777305542 246501797 98842561 66698125 328893187 320920834 442056583 300823217 102856871 894833295 183971312 540000242 77621006 301282781 633518310 368397657 266701251 254744062 276445863 624102545 317896643 457301959 840650755 37020968 787211200 835830799 696187545 77377229 666128476 254311406 706645277 592561555 487913577 799871742 248143253 499058221 533238063 603652509 401508758 545626159 728850086 173008168 373273227 772142675\\n\", \"2 2\\n100000000 1000001000\\n\", \"50 2\\n611819205 916034844 226292837 817298502 176794540 727900268 460009451 154197232 671291076 641633528 316549457 84943963 320598147 360295861 299532522 279193498 61088105 776327911 952977833 796036148 193827182 248414821 822409059 451009120 316494610 702170585 194014479 567762248 201775925 186588924 630333192 849644874 978885690 826471389 136002889 659371057 392112709 74463003 491124655 336372608 480423293 428908070 423023163 749932199 880227915 227662209 304705869 82537803 424363417 744202499\\n\", \"10 5\\n68 78 97 3 77 2 24 17 96 63\\n\", \"30 7\\n483242884 141465390 673274235 494375538 293895324 745776711 38293296 624522417 759055572 343124219 260836408 738391263 503711346 394651562 297415680 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130884928\\n\", \"233550924 233550924\\n\", \"4329774 4329774\\n\", \"10010010 10010010\\n\", \"609944 609944\\n\", \"-1\\n\", \"1 1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"4953810 4953810\\n\", \"10 10\\n\", \"59176968 59176968\\n\", \"-1\\n\", \"1 1\\n\", \"371439 371439\\n\", \"549860 549860\\n\", \"140920201 140920201\\n\", \"-1\\n\", \"-1\\n\", \"772345540 772345540\\n\", \"250809088 250809088\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"7965262 7965262\\n\", \"22933280 22933280\\n\", \"-1\\n\", \"2 2\\n\", \"2 2\\n\", \"-1\\n\", \"-1\\n\", \"4953810 4953810\\n\", \"10 10\\n\", \"59176968 59176968\\n\", \"-1\\n\", \"269197 269197\\n\", \"10000010 10000010\\n\", \"1 1\\n\", \"371439 371439\\n\", \"-1\\n\", \"-1\\n\", \"978885690 978885690\\n\", \"-1\\n\", \"-1\\n\", \"7965262 7965262\\n\", \"22933280 22933280\\n\", \"-1\\n\", \"2 2\\n\", \"3 3\\n\", \"-1\\n\", \"-1\\n\", \"10 10\\n\", \"59176968 59176968\\n\", \"-1\\n\", \"265375 265375\\n\", \"371439 371439\\n\", \"130884928 130884928\\n\", \"-1\\n\", \"978885690 978885690\\n\", \"233550924 233550924\\n\", \"4 4\\n\", \"3 3\\n\", \"-1\\n\"]}", "source": "taco"} | Vasya has found a piece of paper with a coordinate system written on it. There are n distinct squares drawn in this coordinate system. Let's number the squares with integers from 1 to n. It turned out that points with coordinates (0, 0) and (ai, ai) are the opposite corners of the i-th square.
Vasya wants to find such integer point (with integer coordinates) of the plane, that belongs to exactly k drawn squares. We'll say that a point belongs to a square, if the point is located either inside the square, or on its boundary.
Help Vasya find a point that would meet the described limits.
Input
The first line contains two space-separated integers n, k (1 ≤ n, k ≤ 50). The second line contains space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).
It is guaranteed that all given squares are distinct.
Output
In a single line print two space-separated integers x and y (0 ≤ x, y ≤ 109) — the coordinates of the point that belongs to exactly k squares. If there are multiple answers, you are allowed to print any of them.
If there is no answer, print "-1" (without the quotes).
Examples
Input
4 3
5 1 3 4
Output
2 1
Input
3 1
2 4 1
Output
4 0
Input
4 50
5 1 10 2
Output
-1
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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3 0 19 0\\n0 14 17 16 0 6 9 15 0 10 8 11 4 0 0 0 0 0 12\\n\", \"18\\n0 0 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16\\n\", \"3\\n0 0 0\\n3 1 2\\n\", \"2\\n0 2\\n0 1\\n\", \"19\\n0 0 0 0 0 0 0 0 0 18 17 16 15 14 13 12 11 10 9\\n0 0 0 0 0 0 0 19 0 0 0 1 2 3 4 5 6 7 8\\n\", \"3\\n0 0 1\\n2 0 3\\n\", \"5\\n0 0 0 0 0\\n1 2 3 5 4\\n\", \"2\\n0 0\\n1 2\\n\", \"14\\n9 0 14 8 0 6 0 0 0 0 0 0 2 0\\n3 12 0 10 1 0 0 13 11 4 7 0 0 5\\n\", \"17\\n0 0 0 0 0 0 0 8 9 10 11 0 13 14 15 16 0\\n12 0 0 0 0 17 0 0 0 0 1 2 3 4 5 6 7\\n\", \"7\\n0 0 1 2 3 4 6\\n0 5 0 0 7 0 0\\n\", \"3\\n0 3 0\\n0 1 2\\n\", \"2\\n0 1\\n0 2\\n\", \"15\\n0 11 0 14 0 0 15 6 13 0 5 0 0 0 10\\n12 3 0 9 2 0 8 0 7 1 0 4 0 0 0\\n\", \"20\\n15 10 6 0 0 11 19 17 0 0 0 0 0 1 14 0 3 4 0 12\\n20 7 0 0 0 0 0 0 5 8 2 16 18 0 0 13 9 0 0 0\\n\", \"9\\n0 0 0 0 0 0 5 4 3\\n0 0 6 7 8 9 0 1 2\\n\", \"18\\n0 0 10 0 0 0 0 9 3 0 8 0 7 0 2 18 0 0\\n11 15 12 16 0 1 6 17 5 14 0 0 0 0 4 0 0 13\\n\", \"1\\n1\\n0\\n\", \"13\\n0 7 1 0 0 5 6 12 4 8 0 9 0\\n0 0 11 0 0 3 13 0 0 2 0 10 0\\n\", \"11\\n0 0 0 0 0 0 0 1 0 0 0\\n0 3 2 4 6 5 9 8 7 11 10\\n\", \"16\\n0 0 0 0 0 0 0 0 0 0 0 0 14 13 12 10\\n15 16 11 0 0 0 0 1 2 3 4 5 6 7 8 9\\n\", \"5\\n0 0 0 4 0\\n0 1 2 3 5\\n\", \"5\\n0 0 3 0 0\\n1 2 0 4 5\\n\", \"16\\n0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0\\n2 3 4 0 5 7 8 6 11 12 13 9 10 14 15 16\\n\", \"5\\n0 0 3 0 0\\n0 1 2 4 5\\n\", \"2\\n1 2\\n0 0\\n\", \"2\\n1 0\\n0 2\\n\", \"3\\n0 0 0\\n2 1 3\\n\", \"9\\n1 0 0 0 0 0 5 4 3\\n0 0 6 8 7 9 0 0 2\\n\", \"3\\n0 1 0\\n2 3 0\\n\", \"3\\n0 2 0\\n3 0 1\\n\", \"3\\n0 2 0\\n1 0 3\\n\", \"11\\n0 0 0 5 0 0 0 4 0 0 11\\n9 2 6 0 8 1 7 0 3 0 10\\n\"], \"outputs\": [\"2\", \"4\", \"18\", \"11\", \"5\", \"11\", \"1\", \"0\", \"1\", \"3\", \"4\", \"0\", \"6\", \"5\", \"1\", \"1\", \"4\", \"7\", \"7\", \"7\", \"7\", \"6\", \"10\", \"7\", \"17\", \"14\", \"16\", \"22\", \"24\", \"25\", \"20\", \"28\", \"30\", \"29\", \"30\", \"7\", \"24\", \"10\", \"2\", \"11\", \"37\", \"7\", \"4\\n\", \"7\\n\", \"37\\n\", \"11\\n\", \"28\\n\", \"5\\n\", \"7\\n\", \"16\\n\", \"6\\n\", \"10\\n\", \"1\\n\", \"0\\n\", \"11\\n\", \"17\\n\", \"29\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"11\\n\", \"4\\n\", \"7\\n\", \"0\\n\", \"24\\n\", \"10\\n\", \"7\\n\", \"1\\n\", \"3\\n\", \"25\\n\", \"30\\n\", \"7\\n\", \"30\\n\", \"1\\n\", \"22\\n\", \"14\\n\", \"24\\n\", \"7\\n\", \"6\\n\", \"20\\n\", \"7\\n\", \"2\\n\", \"3\\n\", \"5\\n\", \"17\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"18\\n\"]}", "source": "taco"} | Nauuo is a girl who loves playing cards.
One day she was playing cards but found that the cards were mixed with some empty ones.
There are $n$ cards numbered from $1$ to $n$, and they were mixed with another $n$ empty cards. She piled up the $2n$ cards and drew $n$ of them. The $n$ cards in Nauuo's hands are given. The remaining $n$ cards in the pile are also given in the order from top to bottom.
In one operation she can choose a card in her hands and play it — put it at the bottom of the pile, then draw the top card from the pile.
Nauuo wants to make the $n$ numbered cards piled up in increasing order (the $i$-th card in the pile from top to bottom is the card $i$) as quickly as possible. Can you tell her the minimum number of operations?
-----Input-----
The first line contains a single integer $n$ ($1\le n\le 2\cdot 10^5$) — the number of numbered cards.
The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0\le a_i\le n$) — the initial cards in Nauuo's hands. $0$ represents an empty card.
The third line contains $n$ integers $b_1,b_2,\ldots,b_n$ ($0\le b_i\le n$) — the initial cards in the pile, given in order from top to bottom. $0$ represents an empty card.
It is guaranteed that each number from $1$ to $n$ appears exactly once, either in $a_{1..n}$ or $b_{1..n}$.
-----Output-----
The output contains a single integer — the minimum number of operations to make the $n$ numbered cards piled up in increasing order.
-----Examples-----
Input
3
0 2 0
3 0 1
Output
2
Input
3
0 2 0
1 0 3
Output
4
Input
11
0 0 0 5 0 0 0 4 0 0 11
9 2 6 0 8 1 7 0 3 0 10
Output
18
-----Note-----
Example 1
We can play the card $2$ and draw the card $3$ in the first operation. After that, we have $[0,3,0]$ in hands and the cards in the pile are $[0,1,2]$ from top to bottom.
Then, we play the card $3$ in the second operation. The cards in the pile are $[1,2,3]$, in which the cards are piled up in increasing order.
Example 2
Play an empty card and draw the card $1$, then play $1$, $2$, $3$ in order.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[[1, 1, 5, 6, 9, 16, 27], 4], [[1, 1, 3, 3], 2], [[4, 8, 12, 12, 3, 6, 2], 6], [[1, 2, 3, 4, 5, 6, 7], 7], [[1, 6, 2, 3, 7, 8, 7], 0], [[1, 2, 3, 4], 0], [[1, 1, 1, 1], 0], [[], 3]], \"outputs\": [[3], [4], [3], [0], [1], [0], [6], [0]]}", "source": "taco"} | Write a function that accepts two arguments: an array/list of integers and another integer (`n`).
Determine the number of times where two integers in the array have a difference of `n`.
For example:
```
[1, 1, 5, 6, 9, 16, 27], n=4 --> 3 # (1,5), (1,5), (5,9)
[1, 1, 3, 3], n=2 --> 4 # (1,3), (1,3), (1,3), (1,3)
```
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[[1, 2, 3, 4, 6, 9, 10, 15, 69], 11], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 69], 11], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 29, 69], 11], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 29, 38, 47, 56, 65, 69, 74, 83, 92], 11], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 18, 23, 69], 18], [[1, 2, 3, 4, 6, 9, 10, 15, 69], 34], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 29, 34, 38, 47, 56, 65, 69, 74, 83, 92], 34], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 18, 27, 29, 34, 36, 38, 45, 47, 54, 56, 63, 65, 69, 72, 74, 81, 83, 92], 9], [[1, 2, 3, 4, 6, 9, 10, 11, 15, 18, 27, 29, 34, 36, 38, 45, 47, 54, 56, 63, 65, 69, 72, 74, 81, 83, 90, 92], 9]], \"outputs\": [[11], [29], [38], [null], [99], [34], [null], [null], [null]]}", "source": "taco"} | At the start of each season, every player in a football team is assigned their own unique squad number. Due to superstition or their history certain numbers are more desirable than others.
Write a function generateNumber() that takes two arguments, an array of the current squad numbers (squad) and the new player's desired number (n). If the new player's desired number is not already taken, return n, else if the desired number can be formed by adding two digits between 1 and 9, return the number formed by joining these two digits together. E.g. If 2 is taken, return 11 because 1 + 1 = 2. Otherwise return null.
Note: Often there will be several different ways to form a replacement number. In these cases the number with lowest first digit should be given priority. E.g. If n = 15, but squad already contains 15, return 69, not 78.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"(1?1)\\n1 0\\n\", \"(2?(1?2))\\n1 1\\n\", \"((1?(5?7))?((6?2)?7))\\n3 2\\n\", \"((1?(5?7))?((6?2)?7))\\n2 3\\n\", \"((4?3)?(((2?(4?((4?((2?(3?(7?3)))?(((((3?(6?2))?3)?(((((6?6)?(1?5))?((8?8)?1))?(5?((7?((6?((((3?8)?8)?(8?5))?7))?8))?((8?(2?8))?3))))?6))?(8?(7?5)))?8)))?((((7?(4?3))?4)?5)?((1?(((2?2)?((((4?((7?6)?(1?4)))?(8?(1?(((1?3)?(((2?2)?(3?(8?(9?((2?(4?6))?(7?8))))))?(9?(7?9))))?(7?3)))))?((2?((2?((8?6)?1))?(3?1)))?(7?1)))?5))?((((6?(9?(((5?4)?7)?((5?8)?8))))?5)?7)?(2?2))))?4)))))?2)?(7?(4?((6?6)?6)))))\\n50 49\\n\", \"(((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((4?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)\\n50 49\\n\", \"(4?(((3?2)?((((((4?(4?((2?3)?((7?((3?3)?(6?(((2?(3?6))?6)?(((1?5)?8)?(((8?1)?(5?7))?6))))))?(3?8)))))?((8?8)?5))?(7?(8?((((8?((((2?(8?(((3?6)?8)?7)))?5)?(8?(7?((4?(3?4))?(5?((1?(2?((2?(4?7))?(((6?1)?(4?(8?1)))?(1?(3?(((2?(2?(3?(8?9))))?(((((2?4)?6)?7)?(8?9))?7))?(((9?(7?3))?2)?((((((2?8)?6)?(1?3))?1)?7)?1)))))))))?(5?(6?(9?(5?4))))))))))?7))?5)?(8?(8?((5?7)?2))))?2))))?4)?(2?((7?4)?6)))?6))?6))\\n50 49\\n\", \"8\\n0 0\\n\", \"(9?((1?(3?(5?((9?7)?(((((4?5)?2)?1)?(7?6))?(3?(9?7)))))))?(1?4)))\\n0 16\\n\", \"(((4?7)?(9?((6?(3?2))?((6?3)?7))))?((5?((7?(7?(8?3)))?(4?2)))?2))\\n16 0\\n\", 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\"(2?(3?2))\\n0 2\\n\", \"(2?3)\\n1 0\\n\", \"(2?(1?3))\\n0 2\\n\", \"(3?2)\\n1 0\\n\", \"((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((6?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?5)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))\\n100 12\\n\", \"((1?(5?7))?((6?2)?7))\\n3 2\\n\", \"(1?1)\\n1 0\\n\", \"((1?(5?7))?((6?2)?7))\\n2 3\\n\", \"(2?(1?2))\\n1 1\\n\"], \"outputs\": [\"2\\n\", \"1\\n\", \"18\\n\", \"16\\n\", \"423\\n\", \"422\\n\", \"439\\n\", \"8\\n\", \"11\\n\", \"85\\n\", \"550\\n\", \"86\\n\", \"422\", \"8\", \"85\", \"423\", \"86\", \"550\", \"11\", \"439\", \"549\\n\", \"16\\n\", \"438\\n\", \"3\\n\", \"2\\n\", \"4\\n\", \"423\\n\", \"17\\n\", \"5\\n\", \"14\\n\", \"19\\n\", \"439\\n\", \"1\\n\", \"421\\n\", \"548\\n\", \"420\\n\", \"15\\n\", \"22\\n\", \"6\\n\", \"85\\n\", \"0\\n\", \"86\\n\", \"549\\n\", \"3\\n\", \"549\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"4\\n\", \"5\\n\", \"549\\n\", \"18\", \"2\", \"16\", \"1\"]}", "source": "taco"} | Ancient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression.
An Ahmes arithmetic expression can be defined as: "d" is an Ahmes arithmetic expression, where d is a one-digit positive integer; "(E_1 op E_2)" is an Ahmes arithmetic expression, where E_1 and E_2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). For example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions.
On his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task:
Given the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators.
-----Input-----
The first line contains a string E (1 ≤ |E| ≤ 10^4) — a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'.
The second line contains two space-separated integers P and M (0 ≤ min(P, M) ≤ 100) — the number of plus and minus operators, respectively.
It is guaranteed that P + M = the number of erased operators.
-----Output-----
Print one line containing the answer to the problem.
-----Examples-----
Input
(1?1)
1 0
Output
2
Input
(2?(1?2))
1 1
Output
1
Input
((1?(5?7))?((6?2)?7))
3 2
Output
18
Input
((1?(5?7))?((6?2)?7))
2 3
Output
16
-----Note----- The first sample will be (1 + 1) = 2. The second sample will be (2 + (1 - 2)) = 1. The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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The arc is made of a semicircle with radius r (the cupboard's top) and two walls of height h (the cupboard's sides). The cupboard's depth is r, that is, it looks like a rectangle with base r and height h + r from the sides. The figure below shows what the cupboard looks like (the front view is on the left, the side view is on the right). [Image]
Xenia got lots of balloons for her birthday. The girl hates the mess, so she wants to store the balloons in the cupboard. Luckily, each balloon is a sphere with radius $\frac{r}{2}$. Help Xenia calculate the maximum number of balloons she can put in her cupboard.
You can say that a balloon is in the cupboard if you can't see any part of the balloon on the left or right view. The balloons in the cupboard can touch each other. It is not allowed to squeeze the balloons or deform them in any way. You can assume that the cupboard's walls are negligibly thin.
-----Input-----
The single line contains two integers r, h (1 ≤ r, h ≤ 10^7).
-----Output-----
Print a single integer — the maximum number of balloons Xenia can put in the cupboard.
-----Examples-----
Input
1 1
Output
3
Input
1 2
Output
5
Input
2 1
Output
2
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"No\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"Yes\\nYes\\n\", \"No\\nYes\"]}", "source": "taco"} | Nathan O. Davis is challenging a kind of shooter game. In this game, enemies emit laser beams from outside of the screen. A laser beam is a straight line with a certain thickness. Nathan moves a circular-shaped machine within the screen, in such a way it does not overlap a laser beam. As in many shooters, the machine is destroyed when the overlap happens.
Nathan is facing an uphill stage. Many enemies attack simultaneously in this stage, so eventually laser beams fill out almost all of the screen. Surprisingly, it is even possible he has no "safe area" on the screen. In other words, the machine cannot survive wherever it is located in some cases.
The world is as kind as it is cruel! There is a special item that helps the machine to survive any dangerous situation, even if it is exposed in a shower of laser beams, for some seconds. In addition, another straight line (called "a warning line") is drawn on the screen for a few seconds before a laser beam is emit along that line.
The only problem is that Nathan has a little slow reflexes. He often messes up the timing to use the special item. But he knows a good person who can write a program to make up his slow reflexes - it's you! So he asked you for help.
Your task is to write a program to make judgement whether he should use the item or not, for given warning lines and the radius of the machine.
Input
The input is a sequence of datasets. Each dataset corresponds to one situation with warning lines in the following format:
W H N R
x1,1 y1,1 x1,2 y1,2 t1
x2,1 y2,1 x2,2 y2,2 t2
...
xN,1 yN,1 xN,2 yN,2 tN
The first line of a dataset contains four integers W, H, N and R (2 < W ≤ 640, 2 < H ≤ 480, 0 ≤ N ≤ 100 and 0 < R < min{W, H}/2). The first two integers W and H indicate the width and height of the screen, respectively. The next integer N represents the number of laser beams.
The last integer R indicates the radius of the machine. It is guaranteed that the output would remain unchanged if the radius of the machine would become larger by 10-5 than R.
The following N lines describe the N warning lines. The (i+1)-th line of the dataset corresponds to the i-th warning line, which is represented as a straight line which passes through two given different coordinates (xi,1, yi,1 ) and (xi,2 , yi,2 ). The last integer ti indicates the thickness of the laser beam corresponding to the i-th warning line.
All given coordinates (x, y) on the screen are a pair of integers (0 ≤ x ≤ W, 0 ≤ y ≤ H). Note that, however, the machine is allowed to be located at non-integer coordinates during the play.
The input is terminated by a line with four zeros. This line should not be processed.
Output
For each case, print "Yes" in a line if there is a safe area, or print "No" otherwise.
Example
Input
100 100 1 1
50 0 50 100 50
640 480 1 1
0 0 640 480 100
0 0 0 0
Output
No
Yes
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"1\\n1\\n1\\n\", \"1\\n1\\n1000000000\\n\", \"5\\n16 2 8 19 4\\n10 9 10 10 10\\n\", \"5\\n12 19 11 13 16\\n14 14 14 14 15\\n\", \"2\\n1 5\\n3 4\\n\", \"5\\n19 9 3 20 2\\n11 11 10 11 10\\n\", \"20\\n53 86 76 100 16 12 13 97 79 23 28 64 42 10 23 56 59 76 48 12\\n48 49 49 49 48 49 48 49 49 49 48 48 48 49 49 49 49 49 49 48\\n\", \"10\\n17 3 7 14 7 10 4 15 20 10\\n11 11 11 11 11 10 10 11 10 11\\n\", \"4\\n1 3 5 7\\n2 2 6 6\\n\", \"1\\n0\\n1\\n\", \"1\\n1\\n1000000001\\n\", \"5\\n16 2 2 19 4\\n10 9 10 10 10\\n\", \"5\\n12 19 11 13 16\\n13 14 14 14 15\\n\", \"2\\n1 9\\n3 4\\n\", \"5\\n19 9 3 20 2\\n11 11 10 13 10\\n\", \"20\\n53 86 76 100 16 12 13 97 79 23 28 64 42 10 23 56 59 76 48 12\\n48 49 49 49 48 49 48 49 49 49 89 48 48 49 49 49 49 49 49 48\\n\", \"10\\n17 3 7 3 7 10 4 15 20 10\\n11 11 11 11 11 10 10 11 10 11\\n\", \"4\\n1 3 5 7\\n3 2 6 6\\n\", \"3\\n1 8 10\\n3 5 7\\n\", \"5\\n0 2 7 4 9\\n5 4 5 5 5\\n\", \"1\\n1\\n2\\n\", \"1\\n1\\n1001000001\\n\", \"5\\n16 2 2 19 4\\n6 9 10 10 10\\n\", \"5\\n15 19 11 13 16\\n13 14 14 14 15\\n\", \"2\\n2 9\\n3 4\\n\", \"5\\n19 9 3 14 2\\n11 11 10 13 10\\n\", \"20\\n53 86 76 100 16 12 13 97 79 23 28 64 42 10 23 56 59 76 48 12\\n48 49 49 49 48 49 48 49 49 49 89 24 48 49 49 49 49 49 49 48\\n\", \"10\\n17 3 7 3 7 10 4 15 20 10\\n11 11 11 11 11 10 10 22 10 11\\n\", \"4\\n1 2 5 7\\n3 2 6 6\\n\", \"3\\n1 8 10\\n3 5 4\\n\", \"5\\n0 2 7 4 9\\n5 4 8 5 5\\n\", \"1\\n1\\n3\\n\", \"1\\n2\\n1001000001\\n\", \"5\\n16 2 2 19 4\\n6 9 14 10 10\\n\", \"5\\n15 19 11 13 16\\n5 14 14 14 15\\n\", \"2\\n2 9\\n3 1\\n\", \"5\\n19 9 3 14 2\\n11 11 6 13 10\\n\", \"20\\n53 86 76 100 16 12 13 97 79 23 28 64 42 10 23 56 59 76 20 12\\n48 49 49 49 48 49 48 49 49 49 89 24 48 49 49 49 49 49 49 48\\n\", \"10\\n17 3 7 3 7 10 4 26 20 10\\n11 11 11 11 11 10 10 22 10 11\\n\", \"4\\n1 2 5 7\\n3 0 6 6\\n\", \"3\\n1 8 10\\n5 5 4\\n\", \"5\\n0 2 7 8 9\\n5 4 8 5 5\\n\", \"1\\n1\\n5\\n\", \"1\\n0\\n1001000001\\n\", \"5\\n16 2 2 19 4\\n6 0 14 10 10\\n\", \"5\\n15 2 11 13 16\\n5 14 14 14 15\\n\", \"2\\n2 9\\n3 0\\n\", \"5\\n19 9 3 14 2\\n11 11 4 13 10\\n\", \"20\\n53 86 76 110 16 12 13 97 79 23 28 64 42 10 23 56 59 76 20 12\\n48 49 49 49 48 49 48 49 49 49 89 24 48 49 49 49 49 49 49 48\\n\", \"10\\n17 3 7 3 7 10 4 26 20 10\\n11 11 11 12 11 10 10 22 10 11\\n\", \"3\\n1 5 10\\n3 5 7\\n\", \"5\\n2 2 7 4 9\\n5 4 5 5 5\\n\"], \"outputs\": [\"YES\\n0\\n\", \"NO\\n\", \"YES\\n4\\n2 1 6\\n2 4 1\\n5 4 6\\n3 4 2\\n\", \"YES\\n4\\n3 5 2\\n3 2 1\\n1 2 2\\n4 2 1\\n\", \"NO\\n\", \"YES\\n3\\n5 1 8\\n3 4 7\\n2 4 2\\n\", \"YES\\n19\\n14 1 4\\n14 16 7\\n14 17 10\\n14 12 15\\n14 3 2\\n6 3 25\\n6 18 11\\n20 18 16\\n20 9 20\\n7 9 10\\n7 2 25\\n5 2 12\\n5 8 20\\n10 8 25\\n15 8 3\\n15 4 22\\n11 4 21\\n13 4 7\\n19 4 1\\n\", \"YES\\n7\\n2 4 3\\n2 8 4\\n7 1 6\\n3 9 3\\n5 9 4\\n6 9 1\\n10 9 1\\n\", \"YES\\n2\\n1 2 1\\n3 4 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n3\\n1 3 2\\n2 5 3\\n4 5 1\\n\"]}", "source": "taco"} | There are n stones arranged on an axis. Initially the i-th stone is located at the coordinate s_i. There may be more than one stone in a single place.
You can perform zero or more operations of the following type:
* take two stones with indices i and j so that s_i ≤ s_j, choose an integer d (0 ≤ 2 ⋅ d ≤ s_j - s_i), and replace the coordinate s_i with (s_i + d) and replace coordinate s_j with (s_j - d). In other words, draw stones closer to each other.
You want to move the stones so that they are located at positions t_1, t_2, …, t_n. The order of the stones is not important — you just want for the multiset of the stones resulting positions to be the same as the multiset of t_1, t_2, …, t_n.
Detect whether it is possible to move the stones this way, and if yes, construct a way to do so. You don't need to minimize the number of moves.
Input
The first line contains a single integer n (1 ≤ n ≤ 3 ⋅ 10^5) – the number of stones.
The second line contains integers s_1, s_2, …, s_n (1 ≤ s_i ≤ 10^9) — the initial positions of the stones.
The second line contains integers t_1, t_2, …, t_n (1 ≤ t_i ≤ 10^9) — the target positions of the stones.
Output
If it is impossible to move the stones this way, print "NO".
Otherwise, on the first line print "YES", on the second line print the number of operations m (0 ≤ m ≤ 5 ⋅ n) required. You don't have to minimize the number of operations.
Then print m lines, each containing integers i, j, d (1 ≤ i, j ≤ n, s_i ≤ s_j, 0 ≤ 2 ⋅ d ≤ s_j - s_i), defining the operations.
One can show that if an answer exists, there is an answer requiring no more than 5 ⋅ n operations.
Examples
Input
5
2 2 7 4 9
5 4 5 5 5
Output
YES
4
4 3 1
2 3 1
2 5 2
1 5 2
Input
3
1 5 10
3 5 7
Output
NO
Note
Consider the first example.
* After the first move the locations of stones is [2, 2, 6, 5, 9].
* After the second move the locations of stones is [2, 3, 5, 5, 9].
* After the third move the locations of stones is [2, 5, 5, 5, 7].
* After the last move the locations of stones is [4, 5, 5, 5, 5].
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[1], [5], [10], [20], [40], [41], [80], [26], [0], [499]], \"outputs\": [[0.1], [0.49], [0.97], [1.93], [3.85], [3.95], [7.7], [2.52], [0.0], [48.06]]}", "source": "taco"} | You and your best friend Stripes have just landed your first high school jobs! You'll be delivering newspapers to your neighbourhood on weekends. For your services you'll be charging a set price depending on the quantity of the newspaper bundles.
The cost of deliveries is:
- $3.85 for 40 newspapers
- $1.93 for 20
- $0.97 for 10
- $0.49 for 5
- $0.10 for 1
Stripes is taking care of the footwork doing door-to-door drops and your job is to take care of the finances. What you'll be doing is providing the cheapest possible quotes for your services.
Write a function that's passed an integer representing the amount of newspapers and returns the cheapest price. The returned number must be rounded to two decimal places.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.875 |
{"tests": "{\"inputs\": [\"10 2 5\\n\", \"21 4 6\\n\", \"1337 7 7\\n\", \"455678451 22 17\\n\", \"21 7 9\\n\", \"51 9 11\\n\", \"302 17 21\\n\", \"3 4 14\\n\", \"2 14 19\\n\", \"58 11 7\\n\", \"65 14 11\\n\", \"31 5 18\\n\", \"59 19 5\\n\", \"98 12 22\\n\", \"181 21 13\\n\", \"18 14 5\\n\", \"25 15 20\\n\", \"97 14 11\\n\", \"3 6 8\\n\", \"22 10 8\\n\", \"103 20 7\\n\", \"44 12 7\\n\", \"23 3 13\\n\", \"37 12 5\\n\", \"19 16 3\\n\", \"3 8 5\\n\", \"22 19 4\\n\", \"24 14 18\\n\", \"28 16 10\\n\", \"93 15 8\\n\", \"21 11 7\\n\", \"267 21 17\\n\", \"127 19 17\\n\", \"9 8 3\\n\", \"5 20 3\\n\", \"57 17 21\\n\", \"53 10 11\\n\", \"7 4 14\\n\", \"33 13 4\\n\", \"57 13 7\\n\", \"61 14 19\\n\", \"96 16 11\\n\", \"9 14 18\\n\", \"20 16 3\\n\", \"7 21 6\\n\", \"99 15 17\\n\", \"222038698 2 3\\n\", \"643939127 13 9\\n\", \"287889285 9 19\\n\", \"870811053 8 10\\n\", \"708087026 21 16\\n\", \"293342304 10 1\\n\", \"764513658 9 22\\n\", \"9712222 2 7\\n\", \"706836718 14 15\\n\", \"904712274 16 18\\n\", \"18252055 22 19\\n\", \"303470827 2 18\\n\", \"241979028 4 3\\n\", \"299650696 12 21\\n\", \"384552874 17 13\\n\", \"107241427 8 13\\n\", \"507522203 20 7\\n\", \"665490250 20 16\\n\", \"846989062 22 3\\n\", \"333287224 2 2\\n\", \"354488216 15 21\\n\", \"688952192 13 13\\n\", \"701398512 19 10\\n\", \"237889301 20 8\\n\", \"298977583 20 21\\n\", \"714004569 8 8\\n\", \"146655741 15 11\\n\", \"787054573 20 10\\n\", \"52903182 3 11\\n\", \"450620306 11 11\\n\", \"593187929 22 11\\n\", \"151354651 11 20\\n\", \"539482526 22 18\\n\", \"42367658 8 3\\n\", \"453127569 8 7\\n\", \"367744690 6 3\\n\", \"821932744 16 13\\n\", \"198712525 7 12\\n\", \"68454295 1 8\\n\", \"696632478 8 5\\n\", \"597444826 19 15\\n\", \"421217944 2 6\\n\", \"938117852 15 5\\n\", \"977227787 16 7\\n\", \"327596433 7 17\\n\", \"282583311 9 1\\n\", \"689400531 17 12\\n\", \"805539125 11 10\\n\", \"891324441 7 7\\n\", \"994788144 4 10\\n\", \"995380030 7 11\\n\", \"565943561 9 16\\n\", \"859484959 11 6\\n\", \"474993107 3 12\\n\", \"945389518 5 10\\n\", \"323203319 22 22\\n\", \"146792562 1 3\\n\", \"466923905 2 9\\n\", \"437390251 16 6\\n\", \"870191169 16 16\\n\", \"393059956 18 21\\n\", \"560325296 2 21\\n\", \"522495698 17 8\\n\", \"404406397 18 10\\n\", \"861745051 18 17\\n\", \"72445200 3 17\\n\", \"420049445 20 1\\n\", \"12979558 5 13\\n\", \"345974867 13 6\\n\", \"696892941 8 18\\n\", \"743307746 14 13\\n\", \"566651837 6 20\\n\", \"645519279 6 8\\n\", \"696671555 14 2\\n\", \"251040992 14 21\\n\", \"979605072 22 12\\n\", \"660821654 2 22\\n\", \"418666063 2 10\\n\", \"345069910 7 4\\n\", \"263663319 1 21\\n\", \"396342009 19 8\\n\", \"323561163 11 1\\n\", \"656649950 10 10\\n\", \"321604711 15 7\\n\", \"763544257 15 2\\n\", \"908703023 6 4\\n\", \"660080836 1 5\\n\", \"716103921 16 3\\n\", \"610793415 2 13\\n\", \"546001302 14 3\\n\", \"694791302 19 21\\n\", \"884272279 5 9\\n\", \"527182238 13 20\\n\", \"756851991 12 13\\n\", \"656773658 18 4\\n\", \"888200558 5 19\\n\", \"137003938 17 4\\n\", \"531116819 9 3\\n\", \"679664033 22 15\\n\", \"86684398 1 1\\n\", \"54878753 21 22\\n\", \"315129628 22 21\\n\", \"139139288 21 22\\n\", \"318472928 21 22\\n\", \"891793544 21 22\\n\", \"380717014 22 21\\n\", \"296464432 21 22\\n\", \"161139481 22 21\\n\", \"218779253 21 22\\n\", \"951886699 22 21\\n\", \"852397133 22 21\\n\", \"957708064 22 21\\n\", \"161433965 22 21\\n\", \"853783856 22 21\\n\", \"598468779 21 22\\n\", \"386492150 21 22\\n\", \"310237265 21 22\\n\", \"793993576 22 21\\n\", \"765105615 21 22\\n\", \"93807937 22 21\\n\", \"871654411 21 22\\n\", \"994793183 22 21\\n\", \"539431459 21 22\\n\", \"592979555 22 21\\n\", \"283891018 21 22\\n\", \"943657415 21 22\\n\", \"736158757 21 22\\n\", \"867033653 22 21\\n\", \"346893127 22 21\\n\", \"88863426 22 21\\n\", \"834589596 21 22\\n\", \"347159827 22 21\\n\", \"635781140 21 22\\n\", \"474892424 22 21\\n\", \"718179792 21 22\\n\", \"455324676 22 21\\n\", \"292577310 22 21\\n\", \"695295648 21 22\\n\", \"17893050 21 22\\n\", \"956437711 21 22\\n\", \"962574497 21 22\\n\", \"226629211 22 21\\n\", \"82448274 21 22\\n\", \"1000000000 1 1\\n\", \"1000000000 2 1\\n\", \"1000000000 22 1\\n\", \"1000000000 2 22\\n\", \"1000000000 22 22\\n\", \"1000000000 21 22\\n\", \"1000000000 20 22\\n\", \"1000000000 5 22\\n\", \"7750099 21 19\\n\", \"883938 19 21\\n\", \"2166699 19 21\\n\", \"15838420 21 19\\n\", \"420 21 19\\n\", \"985629174 22 19\\n\"], \"outputs\": [\"5\\n\", \"9\\n\", \"672\\n\", \"221997195\\n\", \"12\\n\", \"27\\n\", \"151\\n\", \"3\\n\", \"2\\n\", \"29\\n\", \"33\\n\", \"16\\n\", \"30\\n\", \"48\\n\", \"91\\n\", \"9\\n\", \"15\\n\", \"47\\n\", \"3\\n\", \"12\\n\", \"52\\n\", \"22\\n\", \"12\\n\", \"18\\n\", \"9\\n\", \"3\\n\", \"11\\n\", \"14\\n\", \"14\\n\", \"45\\n\", \"11\\n\", \"134\\n\", \"68\\n\", \"5\\n\", \"3\\n\", \"34\\n\", \"30\\n\", \"4\\n\", \"16\\n\", \"29\\n\", \"30\\n\", \"48\\n\", \"9\\n\", \"10\\n\", \"6\\n\", \"50\\n\", \"88815480\\n\", \"321969564\\n\", \"143944643\\n\", \"387027136\\n\", \"344474771\\n\", \"133337411\\n\", \"369925964\\n\", \"4316544\\n\", \"341231520\\n\", \"425746960\\n\", \"8903442\\n\", \"151735414\\n\", \"103705299\\n\", \"136204864\\n\", \"192276437\\n\", \"51067348\\n\", \"244362544\\n\", \"295773450\\n\", \"406554750\\n\", \"166643612\\n\", \"177244109\\n\", \"344476099\\n\", \"338606179\\n\", \"101952560\\n\", \"145842727\\n\", \"357002288\\n\", \"73327871\\n\", \"262351530\\n\", \"26451591\\n\", \"225310155\\n\", \"197729312\\n\", \"73236123\\n\", \"269741264\\n\", \"19258028\\n\", \"211459535\\n\", \"122581564\\n\", \"396795120\\n\", \"94126986\\n\", \"30424132\\n\", \"321522683\\n\", \"298722413\\n\", \"210608972\\n\", \"469058927\\n\", \"467369812\\n\", \"163798217\\n\", \"141291656\\n\", \"332814051\\n\", \"383590060\\n\", \"445662224\\n\", \"426337776\\n\", \"497690015\\n\", \"271652910\\n\", \"404463511\\n\", \"189997244\\n\", \"315129840\\n\", \"161601660\\n\", \"73396281\\n\", \"212238139\\n\", \"198813751\\n\", \"435095585\\n\", \"181412296\\n\", \"267981664\\n\", \"250797936\\n\", \"202203199\\n\", \"418561885\\n\", \"36222600\\n\", \"200023546\\n\", \"6489779\\n\", \"163882833\\n\", \"321642897\\n\", \"357888921\\n\", \"261531618\\n\", \"276651120\\n\", \"348335778\\n\", \"100416400\\n\", \"460990624\\n\", \"330410828\\n\", \"209333032\\n\", \"156849960\\n\", \"131831660\\n\", \"190831339\\n\", \"161780582\\n\", \"328324980\\n\", \"160802356\\n\", \"359314945\\n\", \"363481211\\n\", \"330040418\\n\", \"339207121\\n\", \"285036927\\n\", \"256941790\\n\", \"347395651\\n\", \"442136140\\n\", \"255603511\\n\", \"363288960\\n\", \"298533482\\n\", \"444100279\\n\", \"65239971\\n\", \"265558410\\n\", \"330647368\\n\", \"43342199\\n\", \"26801253\\n\", \"153900516\\n\", \"67951754\\n\", \"155533294\\n\", \"435527085\\n\", \"185931566\\n\", \"144784962\\n\", \"78696030\\n\", \"106845690\\n\", \"464874900\\n\", \"416286975\\n\", \"467717901\\n\", \"78839849\\n\", \"416964219\\n\", \"292275459\\n\", \"188751990\\n\", \"151511225\\n\", \"387764307\\n\", \"373656234\\n\", \"45813180\\n\", \"425691693\\n\", \"485829233\\n\", \"263443278\\n\", \"289594671\\n\", \"138644457\\n\", \"460855953\\n\", \"359519395\\n\", \"423435047\\n\", \"169412923\\n\", \"43398424\\n\", \"407590276\\n\", \"169543179\\n\", \"310497768\\n\", \"231924210\\n\", \"350738976\\n\", \"222367866\\n\", \"142886604\\n\", \"339562996\\n\", \"8738476\\n\", \"467097497\\n\", \"470094531\\n\", \"110679387\\n\", \"40265442\\n\", \"500000000\\n\", \"333333334\\n\", \"478260870\\n\", \"500000000\\n\", \"500000006\\n\", \"488372094\\n\", \"476190480\\n\", \"481481482\\n\", \"3875050\\n\", \"441969\\n\", \"1083350\\n\", \"7919210\\n\", \"210\\n\", \"480794720\\n\"]}", "source": "taco"} | Let's call the set of positive integers $S$ correct if the following two conditions are met:
$S \subseteq \{1, 2, \dots, n\}$;
if $a \in S$ and $b \in S$, then $|a-b| \neq x$ and $|a-b| \neq y$.
For the given values $n$, $x$, and $y$, you have to find the maximum size of the correct set.
-----Input-----
A single line contains three integers $n$, $x$ and $y$ ($1 \le n \le 10^9$; $1 \le x, y \le 22$).
-----Output-----
Print one integer — the maximum size of the correct set.
-----Examples-----
Input
10 2 5
Output
5
Input
21 4 6
Output
9
Input
1337 7 7
Output
672
Input
455678451 22 17
Output
221997195
-----Note-----
None
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n4 1 7\\n\", \"1\\n10\\n\", \"4\\n1 3 5 9\\n\", \"4\\n4 3 4 5\\n\", \"2\\n2 4\\n\", \"4\\n1 3 4 5\\n\", \"2\\n3 3\\n\", \"2\\n13 2\\n\", \"5\\n2 2 2 2 2\\n\", \"6\\n11 1 7 9 5 13\\n\", \"2\\n100000000 1\\n\", \"5\\n2 3 1 4 6\\n\", \"5\\n1 2 2 3 4\\n\", \"3\\n1 4 2\\n\", \"3\\n8 8 8\\n\", \"5\\n2 2 2 2 3\\n\", \"1\\n100000000\\n\", \"20\\n27 6 3 18 54 33 9 15 39 12 57 48 21 51 60 30 24 36 42 45\\n\", \"40\\n100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\\n\", \"49\\n81787 163451 104059 89211 96635 133755 148603 141179 159739 122619 123 144891 70651 11259 63227 3835 44667 37243 100347 26107 137467 18683 156027 59515 22395 40955 111483 52091 7547 85499 107771 178299 115195 152315 74363 126331 33531 130043 14971 48379 167163 182011 170875 78075 174587 55803 66939 29819 118907\\n\", \"9\\n1 2 3 3 4 4 5 5 6\\n\", \"7\\n1 1 2 3 4 5 6\\n\", \"2\\n4 1\\n\", \"2\\n2 100000000\\n\", \"8\\n1 2 3 4 11 12 13 14\\n\", \"7\\n5 40 45 50 55 60 65\\n\", \"1\\n1\\n\", \"2\\n1 1\\n\", \"2\\n100000000 2\\n\", \"3\\n2 2 3\\n\", \"5\\n1 3 5 9 13\\n\", \"5\\n1 2 4 8 16\\n\", \"3\\n2 2 5\\n\", \"5\\n1 2 3 4 8\\n\", \"3\\n1 3 4\\n\", \"5\\n1 2 4 6 7\\n\", \"4\\n1 5 9 11\\n\", \"4\\n3 4 5 9\\n\", \"4\\n1 5 6 8\\n\", \"4\\n2 6 8 12\\n\", \"5\\n1 2 3 5 7\\n\", \"6\\n1 2 3 4 6 8\\n\", \"7\\n5 40 45 50 55 60 65\\n\", \"20\\n27 6 3 18 54 33 9 15 39 12 57 48 21 51 60 30 24 36 42 45\\n\", \"2\\n1 1\\n\", \"1\\n1\\n\", \"40\\n100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000\\n\", \"4\\n1 5 9 11\\n\", \"49\\n81787 163451 104059 89211 96635 133755 148603 141179 159739 122619 123 144891 70651 11259 63227 3835 44667 37243 100347 26107 137467 18683 156027 59515 22395 40955 111483 52091 7547 85499 107771 178299 115195 152315 74363 126331 33531 130043 14971 48379 167163 182011 170875 78075 174587 55803 66939 29819 118907\\n\", \"2\\n100000000 1\\n\", \"3\\n2 2 3\\n\", \"2\\n4 1\\n\", \"5\\n2 3 1 4 6\\n\", \"8\\n1 2 3 4 11 12 13 14\\n\", \"3\\n8 8 8\\n\", \"5\\n1 3 5 9 13\\n\", \"5\\n1 2 3 5 7\\n\", \"5\\n1 2 2 3 4\\n\", \"6\\n11 1 7 9 5 13\\n\", \"5\\n2 2 2 2 3\\n\", \"2\\n3 3\\n\", \"5\\n1 2 3 4 8\\n\", \"3\\n1 4 2\\n\", \"6\\n1 2 3 4 6 8\\n\", \"5\\n1 2 4 6 7\\n\", \"5\\n2 2 2 2 2\\n\", \"4\\n2 6 8 12\\n\", \"4\\n1 5 6 8\\n\", \"5\\n1 2 4 8 16\\n\", \"3\\n1 3 4\\n\", \"9\\n1 2 3 3 4 4 5 5 6\\n\", \"2\\n100000000 2\\n\", \"3\\n2 2 5\\n\", \"2\\n13 2\\n\", \"4\\n1 3 4 5\\n\", \"1\\n100000000\\n\", \"7\\n1 1 2 3 4 5 6\\n\", \"4\\n3 4 5 9\\n\", \"2\\n2 100000000\\n\", \"7\\n5 40 45 48 55 60 65\\n\", \"2\\n1 0\\n\", \"1\\n0\\n\", \"2\\n000000000 2\\n\", \"2\\n4 0\\n\", \"2\\n3 1\\n\", \"3\\n2 3 4\\n\", \"2\\n100000001 2\\n\", \"2\\n13 3\\n\", \"4\\n2 3 4 5\\n\", \"2\\n3 100000000\\n\", \"2\\n2 1\\n\", \"2\\n010000000 2\\n\", \"3\\n2 0 1\\n\", \"2\\n7 0\\n\", \"2\\n0 0\\n\", \"3\\n1 3 0\\n\", \"2\\n100010001 2\\n\", \"2\\n15 3\\n\", \"2\\n5 100000000\\n\", \"20\\n27 6 3 18 54 33 9 15 39 12 57 48 21 51 60 30 28 36 42 45\\n\", \"40\\n100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000000 100000000 100000000 100000000 100000000\\n\", \"4\\n1 5 9 20\\n\", \"49\\n81787 163451 104059 89211 96635 133755 148603 141179 159739 122619 123 144891 70651 11259 63227 3835 44667 37243 100347 26107 137467 18683 156027 59515 22395 40955 111483 52091 7547 85499 107771 178299 115195 152315 74363 126331 33531 130043 20006 48379 167163 182011 170875 78075 174587 55803 66939 29819 118907\\n\", \"3\\n2 2 1\\n\", \"5\\n2 3 1 1 6\\n\", \"8\\n1 2 3 4 11 12 20 14\\n\", \"3\\n13 8 8\\n\", \"5\\n1 3 10 9 13\\n\", \"5\\n1 4 3 5 7\\n\", \"5\\n1 2 2 3 7\\n\", \"6\\n1 1 7 9 5 13\\n\", \"5\\n2 2 2 3 3\\n\", \"5\\n1 2 3 0 8\\n\", \"3\\n1 4 0\\n\", \"6\\n1 2 0 4 6 8\\n\", \"5\\n1 2 4 8 7\\n\", \"4\\n2 6 8 14\\n\", \"4\\n1 2 6 8\\n\", \"5\\n1 2 4 2 16\\n\", \"9\\n0 2 3 3 4 4 5 5 6\\n\", \"3\\n0 2 5\\n\", \"1\\n100010000\\n\", \"7\\n1 1 2 3 7 5 6\\n\", \"4\\n3 3 5 9\\n\", \"4\\n4 1 4 5\\n\", \"4\\n2 3 5 9\\n\", \"3\\n4 2 7\\n\", \"1\\n11\\n\", \"7\\n5 40 45 48 55 67 65\\n\", \"20\\n27 6 3 18 54 33 9 15 39 12 57 48 19 51 60 30 28 36 42 45\\n\", \"2\\n2 0\\n\", \"1\\n-1\\n\", \"40\\n100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000000 100000010 100000000 100000100 100000000 100000000 100000000 100000000\\n\", \"4\\n2 5 9 20\\n\", \"49\\n81787 163451 104059 89211 96635 133755 148603 141179 159739 122619 123 158045 70651 11259 63227 3835 44667 37243 100347 26107 137467 18683 156027 59515 22395 40955 111483 52091 7547 85499 107771 178299 115195 152315 74363 126331 33531 130043 20006 48379 167163 182011 170875 78075 174587 55803 66939 29819 118907\\n\", \"5\\n3 3 1 1 6\\n\", \"8\\n1 2 0 4 11 12 20 14\\n\", \"3\\n13 8 5\\n\", \"5\\n1 3 10 9 17\\n\", \"5\\n1 4 5 5 7\\n\", \"5\\n1 2 2 1 7\\n\", \"6\\n1 1 7 9 5 17\\n\", \"5\\n2 2 2 3 2\\n\", \"5\\n1 2 1 0 8\\n\", \"6\\n1 2 0 4 6 4\\n\", \"5\\n1 3 4 8 7\\n\", \"4\\n4 6 8 14\\n\", \"4\\n1 2 11 8\\n\", \"5\\n1 2 0 2 16\\n\", \"3\\n4 3 4\\n\", \"9\\n0 2 2 3 4 4 5 5 6\\n\", \"3\\n1 2 5\\n\", \"4\\n2 4 4 5\\n\", \"1\\n101010000\\n\", \"7\\n1 1 2 3 7 5 8\\n\", \"4\\n3 4 5 16\\n\", \"4\\n3 1 4 5\\n\", \"4\\n2 3 5 7\\n\", \"3\\n0 1 7\\n\", \"1\\n17\\n\", \"2\\n0 1\\n\", \"7\\n5 40 37 48 55 67 65\\n\", \"20\\n27 6 3 18 108 33 9 15 39 12 57 48 19 51 60 30 28 36 42 45\\n\", \"4\\n4 3 4 5\\n\", \"4\\n1 3 5 9\\n\", \"3\\n4 1 7\\n\", \"1\\n10\\n\", \"2\\n2 4\\n\"], \"outputs\": [\"2\\n-2 10\\n\", \"-1\\n\", \"1\\n7\\n\", \"0\\n\", \"3\\n0 3 6\\n\", \"1\\n2\\n\", \"1\\n3\\n\", \"2\\n-9 24\\n\", \"1\\n2\\n\", \"1\\n3\\n\", \"2\\n-99999998 199999999\\n\", \"1\\n5\\n\", \"0\\n\", \"1\\n3\\n\", \"1\\n8\\n\", \"0\\n\", \"-1\\n\", \"2\\n0 63\\n\", \"1\\n100000000\\n\", \"1\\n92923\\n\", \"0\\n\", \"0\\n\", \"2\\n-2 7\\n\", \"3\\n-99999996 50000001 199999998\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"1\\n1\\n\", \"3\\n-99999996 50000001 199999998\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n0 63\\n\", \"1\\n1\\n\", \"-1\\n\", \"1\\n100000000\\n\", \"0\\n\", \"1\\n92923\\n\", \"2\\n-99999998 199999999\\n\", \"0\\n\", \"2\\n-2 7\\n\", \"1\\n5\\n\", \"0\\n\", \"1\\n8\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n3\\n\", \"0\\n\", \"1\\n3\\n\", \"0\\n\", \"1\\n3\\n\", \"0\\n\", \"0\\n\", \"1\\n2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n2\\n\", \"0\\n\", \"3\\n-99999996 50000001 199999998\\n\", \"0\\n\", \"2\\n-9 24\\n\", \"1\\n2\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"3\\n-99999996 50000001 199999998\\n\", \"0\\n\", \"2\\n-1 2\\n\", \"-1\\n\", \"3\\n-2 1 4\\n\", \"3\\n-4 2 8\\n\", \"3\\n-1 2 5\\n\", \"2\\n1 5\\n\", \"2\\n-99999997 200000000\\n\", \"3\\n-7 8 23\\n\", \"2\\n1 6\\n\", \"2\\n-99999994 199999997\\n\", \"2\\n0 3\\n\", \"3\\n-9999996 5000001 19999998\\n\", \"2\\n-1 3\\n\", \"2\\n-7 14\\n\", \"1\\n0\\n\", \"1\\n2\\n\", \"2\\n-100009997 200020000\\n\", \"3\\n-9 9 27\\n\", \"2\\n-99999990 199999995\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"3\\n-2 1 4\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"1\\n2\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"2\\n-1 2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n7\\n\", \"2\\n-2 10\\n\", \"-1\\n\", \"3\\n0 3 6\\n\"]}", "source": "taco"} | Everybody knows what an arithmetic progression is. Let us remind you just in case that an arithmetic progression is such sequence of numbers a_1, a_2, ..., a_{n} of length n, that the following condition fulfills: a_2 - a_1 = a_3 - a_2 = a_4 - a_3 = ... = a_{i} + 1 - a_{i} = ... = a_{n} - a_{n} - 1.
For example, sequences [1, 5], [10], [5, 4, 3] are arithmetic progressions and sequences [1, 3, 2], [1, 2, 4] are not.
Alexander has n cards containing integers. Arthur wants to give Alexander exactly one more card with a number so that he could use the resulting n + 1 cards to make an arithmetic progression (Alexander has to use all of his cards).
Arthur has already bought a card but he hasn't written a number on it. Help him, print all integers that you can write on a card so that the described condition fulfilled.
-----Input-----
The first line contains integer n (1 ≤ n ≤ 10^5) — the number of cards. The next line contains the sequence of integers — the numbers on Alexander's cards. The numbers are positive integers, each of them doesn't exceed 10^8.
-----Output-----
If Arthur can write infinitely many distinct integers on the card, print on a single line -1.
Otherwise, print on the first line the number of integers that suit you. In the second line, print the numbers in the increasing order. Note that the numbers in the answer can exceed 10^8 or even be negative (see test samples).
-----Examples-----
Input
3
4 1 7
Output
2
-2 10
Input
1
10
Output
-1
Input
4
1 3 5 9
Output
1
7
Input
4
4 3 4 5
Output
0
Input
2
2 4
Output
3
0 3 6
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n0\\n0\\n1000000010\", \"4\\n11\\n5\\n10\\n6\", \"4\\n6\\n5\\n10\\n6\", \"4\\n6\\n5\\n20\\n6\", \"4\\n2\\n5\\n20\\n6\", \"4\\n2\\n5\\n10\\n6\", \"4\\n2\\n5\\n10\\n5\", \"4\\n0\\n5\\n10\\n5\", \"4\\n0\\n7\\n10\\n5\", \"4\\n0\\n7\\n10\\n1\", \"4\\n0\\n7\\n10\\n0\", \"3\\n0\\n0\\n0000000000\", \"4\\n7\\n8\\n10\\n6\", \"4\\n11\\n5\\n10\\n10\", \"4\\n6\\n7\\n10\\n6\", \"4\\n6\\n9\\n20\\n6\", \"4\\n2\\n9\\n20\\n6\", \"4\\n2\\n8\\n10\\n6\", \"4\\n2\\n5\\n0\\n5\", \"4\\n0\\n5\\n4\\n5\", \"4\\n0\\n10\\n10\\n5\", \"4\\n0\\n3\\n10\\n1\", \"4\\n0\\n7\\n19\\n0\", \"3\\n1\\n0\\n0000000000\", \"4\\n7\\n8\\n10\\n0\", \"4\\n11\\n5\\n19\\n10\", \"4\\n6\\n7\\n10\\n2\", \"4\\n6\\n9\\n20\\n3\", \"4\\n4\\n9\\n20\\n6\", \"4\\n0\\n8\\n10\\n6\", \"4\\n2\\n9\\n0\\n5\", \"4\\n0\\n5\\n4\\n4\", \"4\\n0\\n10\\n10\\n3\", \"4\\n0\\n3\\n8\\n1\", \"4\\n0\\n7\\n19\\n1\", \"4\\n7\\n8\\n0\\n0\", \"4\\n18\\n5\\n19\\n10\", \"4\\n0\\n7\\n10\\n2\", \"4\\n6\\n12\\n20\\n3\", \"4\\n4\\n9\\n20\\n4\", \"4\\n0\\n9\\n10\\n6\", \"4\\n0\\n5\\n6\\n4\", \"4\\n0\\n11\\n10\\n3\", \"4\\n1\\n3\\n8\\n1\", \"4\\n1\\n7\\n19\\n1\", \"4\\n7\\n1\\n0\\n0\", \"4\\n18\\n5\\n19\\n16\", \"4\\n6\\n12\\n20\\n6\", \"4\\n4\\n9\\n17\\n4\", \"4\\n0\\n9\\n16\\n6\", \"4\\n0\\n10\\n6\\n4\", \"4\\n0\\n12\\n10\\n3\", \"4\\n1\\n6\\n8\\n1\", \"4\\n1\\n7\\n30\\n1\", \"4\\n7\\n2\\n0\\n0\", \"4\\n7\\n5\\n19\\n16\", \"4\\n5\\n12\\n20\\n6\", \"4\\n1\\n9\\n17\\n4\", \"4\\n1\\n9\\n16\\n6\", \"4\\n0\\n13\\n6\\n4\", \"4\\n1\\n6\\n8\\n2\", \"4\\n0\\n7\\n30\\n1\", \"4\\n7\\n5\\n19\\n27\", \"4\\n5\\n12\\n39\\n6\", \"4\\n2\\n9\\n17\\n4\", \"4\\n0\\n9\\n16\\n4\", \"4\\n1\\n13\\n6\\n4\", \"4\\n1\\n11\\n8\\n2\", \"4\\n7\\n5\\n19\\n50\", \"4\\n5\\n12\\n35\\n6\", \"4\\n2\\n9\\n29\\n4\", \"4\\n0\\n9\\n18\\n6\", \"4\\n1\\n13\\n6\\n1\", \"4\\n1\\n11\\n9\\n2\", \"4\\n7\\n5\\n20\\n50\", \"4\\n5\\n7\\n35\\n6\", \"4\\n2\\n9\\n33\\n4\", \"4\\n0\\n9\\n18\\n4\", \"4\\n1\\n13\\n2\\n1\", \"4\\n1\\n11\\n9\\n1\", \"4\\n0\\n5\\n20\\n50\", \"4\\n5\\n7\\n34\\n6\", \"4\\n2\\n9\\n28\\n4\", \"4\\n0\\n9\\n6\\n4\", \"4\\n1\\n12\\n2\\n1\", \"4\\n1\\n11\\n9\\n3\", \"4\\n5\\n9\\n34\\n6\", \"4\\n2\\n9\\n50\\n4\", \"4\\n0\\n9\\n6\\n0\", \"4\\n1\\n9\\n2\\n1\", \"4\\n1\\n3\\n9\\n3\", \"4\\n10\\n9\\n34\\n6\", \"4\\n2\\n9\\n4\\n4\", \"4\\n0\\n2\\n6\\n0\", \"4\\n1\\n9\\n3\\n1\", \"4\\n1\\n3\\n9\\n2\", \"4\\n10\\n9\\n34\\n9\", \"4\\n3\\n9\\n4\\n4\", \"4\\n0\\n2\\n6\\n1\", \"4\\n1\\n7\\n3\\n1\", \"3\\n0\\n0\\n1000000000\", \"4\\n7\\n5\\n10\\n6\"], \"outputs\": [\"1000000010\\n0\\n0\\n\", \"5\\n6\\n10\\n11\\n\", \"5\\n6\\n6\\n10\\n\", \"5\\n6\\n6\\n20\\n\", \"2\\n5\\n6\\n20\\n\", \"2\\n5\\n6\\n10\\n\", \"2\\n5\\n5\\n10\\n\", \"5\\n10\\n5\\n0\\n\", \"7\\n10\\n5\\n0\\n\", \"7\\n10\\n1\\n0\\n\", \"7\\n10\\n0\\n0\\n\", \"0\\n0\\n0\\n\", \"6\\n7\\n8\\n10\\n\", \"5\\n10\\n10\\n11\\n\", \"6\\n6\\n7\\n10\\n\", \"6\\n6\\n9\\n20\\n\", \"2\\n6\\n9\\n20\\n\", \"2\\n6\\n8\\n10\\n\", \"5\\n5\\n2\\n0\\n\", \"5\\n5\\n4\\n0\\n\", \"10\\n10\\n5\\n0\\n\", \"3\\n10\\n1\\n0\\n\", \"7\\n19\\n0\\n0\\n\", \"0\\n0\\n1\\n\", \"8\\n10\\n7\\n0\\n\", \"5\\n10\\n11\\n19\\n\", \"2\\n6\\n7\\n10\\n\", \"3\\n6\\n9\\n20\\n\", \"4\\n6\\n9\\n20\\n\", \"8\\n10\\n6\\n0\\n\", \"5\\n9\\n2\\n0\\n\", \"4\\n5\\n4\\n0\\n\", \"10\\n10\\n3\\n0\\n\", \"3\\n8\\n1\\n0\\n\", \"7\\n19\\n1\\n0\\n\", \"7\\n8\\n0\\n0\\n\", \"5\\n10\\n18\\n19\\n\", \"7\\n10\\n2\\n0\\n\", \"3\\n6\\n12\\n20\\n\", \"4\\n4\\n9\\n20\\n\", \"9\\n10\\n6\\n0\\n\", \"5\\n6\\n4\\n0\\n\", \"10\\n11\\n3\\n0\\n\", \"3\\n8\\n1\\n1\\n\", \"7\\n19\\n1\\n1\\n\", \"7\\n0\\n0\\n1\\n\", \"5\\n16\\n18\\n19\\n\", \"6\\n6\\n12\\n20\\n\", \"4\\n4\\n9\\n17\\n\", \"9\\n16\\n6\\n0\\n\", \"6\\n10\\n4\\n0\\n\", \"10\\n12\\n3\\n0\\n\", \"6\\n8\\n1\\n1\\n\", \"7\\n30\\n1\\n1\\n\", \"2\\n7\\n0\\n0\\n\", \"5\\n7\\n16\\n19\\n\", \"5\\n6\\n12\\n20\\n\", \"4\\n9\\n17\\n1\\n\", \"6\\n9\\n16\\n1\\n\", \"6\\n13\\n4\\n0\\n\", \"2\\n6\\n8\\n1\\n\", \"7\\n30\\n1\\n0\\n\", \"5\\n7\\n19\\n27\\n\", \"5\\n6\\n12\\n39\\n\", \"2\\n4\\n9\\n17\\n\", \"9\\n16\\n4\\n0\\n\", \"4\\n6\\n13\\n1\\n\", \"2\\n8\\n11\\n1\\n\", \"5\\n7\\n19\\n50\\n\", \"5\\n6\\n12\\n35\\n\", \"2\\n4\\n9\\n29\\n\", \"9\\n18\\n6\\n0\\n\", \"6\\n13\\n1\\n1\\n\", \"2\\n9\\n11\\n1\\n\", \"5\\n7\\n20\\n50\\n\", \"5\\n6\\n7\\n35\\n\", \"2\\n4\\n9\\n33\\n\", \"9\\n18\\n4\\n0\\n\", \"2\\n13\\n1\\n1\\n\", \"9\\n11\\n1\\n1\\n\", \"20\\n50\\n5\\n0\\n\", \"5\\n6\\n7\\n34\\n\", \"2\\n4\\n9\\n28\\n\", \"6\\n9\\n4\\n0\\n\", \"2\\n12\\n1\\n1\\n\", \"3\\n9\\n11\\n1\\n\", \"5\\n6\\n9\\n34\\n\", \"2\\n4\\n9\\n50\\n\", \"6\\n9\\n0\\n0\\n\", \"2\\n9\\n1\\n1\\n\", \"3\\n3\\n9\\n1\\n\", \"6\\n9\\n10\\n34\\n\", \"2\\n4\\n4\\n9\\n\", \"2\\n6\\n0\\n0\\n\", \"3\\n9\\n1\\n1\\n\", \"2\\n3\\n9\\n1\\n\", \"9\\n9\\n10\\n34\\n\", \"3\\n4\\n4\\n9\\n\", \"2\\n6\\n1\\n0\\n\", \"3\\n7\\n1\\n1\\n\", \"1000000000\\n0\\n0\", \"5\\n6\\n7\\n10\"]}", "source": "taco"} | Training is indispensable for achieving good results at ICPC. Rabbit wants to win at ICPC, so he decided to practice today as well.
Today's training is to perform a very large number of calculations to improve the calculation power and raise awareness. Exponentiation is an operation that easily produces large numbers.
There are N non-negative integers A1, A2, ..., AN. We would like to find the sorts B1, B2, ..., BN that maximize B1B2 ... BN -1BN. Of course, it is common sense for rabbits, but this calculation is performed in order from the upper right. We also promise that 00 = 1.
There may be multiple types of B1, B2, ..., and BN that satisfy the maximum conditions. In such a case, let's choose the smallest column in the dictionary order.
Input
N
A1
...
AN
Satisfy 1 ≤ N ≤ 100, 0 ≤ Ai ≤ 1,000,000,000.
Output
The output consists of N lines. Output Bi on line i.
Examples
Input
4
7
5
10
6
Output
5
6
7
10
Input
3
0
0
1000000000
Output
1000000000
0
0
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n2 3 3 1 2 1 2 1 3\\n3 2 2 1 1 1 3 3 2\", \"3\\n1 1 1 2 2 2 3 3 3\\n2 1 1 1 2 2 3 3 3\", \"3\\n1 1 1 2 2 2 3 3 3\\n1 1 1 2 3 2 3 3 2\", \"3\\n2 3 3 1 2 1 2 1 3\\n3 2 1 2 1 1 3 3 2\", \"3\\n2 3 1 1 3 2 2 1 3\\n1 2 1 3 1 2 3 2 3\", \"3\\n3 3 1 1 3 2 2 1 2\\n1 1 2 3 2 2 3 1 3\", \"3\\n2 3 3 1 1 1 3 2 2\\n3 2 2 1 1 1 3 3 2\", \"3\\n1 1 2 2 1 2 3 3 3\\n1 1 1 2 3 2 3 3 2\", \"3\\n1 1 1 2 2 2 3 3 3\\n1 1 1 2 3 2 2 3 3\", \"3\\n2 3 1 1 3 2 2 1 3\\n2 2 2 3 1 1 3 1 3\", \"3\\n2 3 3 2 1 1 1 2 3\\n3 2 2 1 1 1 3 3 2\", \"3\\n2 3 1 1 3 2 2 1 3\\n1 1 2 3 2 2 3 1 3\", \"3\\n2 3 3 1 1 1 2 2 3\\n3 1 2 1 2 1 3 3 2\", \"3\\n2 3 1 1 3 2 2 1 3\\n2 1 2 3 1 2 3 1 3\", \"8\\n3 6 7 5 4 8 4 1 1 3 8 7 3 8 2 4 7 5 2 2 6 5 6 1\\n7 5 8 1 3 6 7 5 4 8 1 3 3 8 2 4 2 6 5 6 1 4 7 2\", \"3\\n1 1 1 2 2 2 3 3 3\\n1 1 1 2 2 2 3 3 3\", \"3\\n2 3 3 1 1 1 2 2 3\\n3 2 2 1 1 1 3 3 2\", \"3\\n2 3 1 1 3 2 2 1 3\\n1 2 2 3 1 2 3 1 3\"], \"outputs\": [\"-1\\n\", \"1\\n\", \"4\\n\", \"5\\n\", \"7\\n\", \"6\\n\", \"-1\\n\", \"-1\\n\", \"4\\n\", \"-1\\n\", \"-1\\n\", \"4\\n\", \"6\\n\", \"4\\n\", \"7\", \"0\", \"-1\", \"4\"]}", "source": "taco"} | Given are integer sequences A and B of length 3N. Each of these two sequences contains three copies of each of 1, 2, \dots, N. In other words, A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).
Tak can perform the following operation to the sequence A arbitrarily many times:
* Pick a value from 1, 2, \dots, N and call it x. A contains exactly three copies of x. Remove the middle element of these three. After that, append x to the beginning or the end of A.
Check if he can turn A into B. If he can, print the minimum required number of operations to achieve that.
Constraints
* 1 \leq N \leq 33
* A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{3N}
B_1 B_2 ... B_{3N}
Output
If Tak can turn A into B, print the minimum required number of operations to achieve that. Otherwise, print -1.
Examples
Input
3
2 3 1 1 3 2 2 1 3
1 2 2 3 1 2 3 1 3
Output
4
Input
3
1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3
Output
0
Input
3
2 3 3 1 1 1 2 2 3
3 2 2 1 1 1 3 3 2
Output
-1
Input
8
3 6 7 5 4 8 4 1 1 3 8 7 3 8 2 4 7 5 2 2 6 5 6 1
7 5 8 1 3 6 7 5 4 8 1 3 3 8 2 4 2 6 5 6 1 4 7 2
Output
7
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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3\\n3\\n2 1 0\\n4\\n1 1000 101 1000\\n4\\n1 4 3 3\\n\", \"4\\n5\\n1 2 2 1 3\\n3\\n2 2 1\\n4\\n2 1000 100 1100\\n4\\n1 3 4 4\\n\", \"4\\n5\\n6 3 2 1 5\\n3\\n1 1 0\\n4\\n-1 1000 101 1000\\n4\\n0 2 3 4\\n\", \"1\\n5\\n1934658 10894 86 433 23442\\n\", \"4\\n5\\n2 1 2 2 3\\n3\\n1 1 1\\n4\\n1 1000 111 1100\\n4\\n1 2 8 3\\n\", \"4\\n5\\n1 2 2 0 3\\n3\\n2 2 1\\n4\\n2 1000 100 1100\\n4\\n1 3 4 4\\n\", \"4\\n5\\n1 2 2 1 3\\n3\\n1 1 1\\n4\\n1 1000 101 1000\\n4\\n1 2 3 4\\n\"], \"outputs\": [\"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 3\\n1 4\\n4 2\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n2 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 4\\n1 5\\n5 3\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 4\\n1 5\\n5 2\\n5 3\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 3\\n1 4\\n4 2\\n\", \"YES\\n1 3\\n1 4\\n1 5\\n5 2\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 5\\n5 3\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 4\\n1 5\\n5 3\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 3\\n1 4\\n4 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 5\\n5 2\\n5 3\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 4\\n1 5\\n5 2\\n5 3\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 4\\n1 5\\n5 2\\n5 3\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n2 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 3\\n1 4\\n1 5\\n5 2\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 5\\n5 3\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 5\\n5 2\\n5 3\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 2\\n1 3\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\n\", \"YES\\n1 2\\n1 5\\n5 3\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 4\\n1 5\\nYES\\n1 3\\n3 2\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\", \"YES\\n1 2\\n1 3\\n1 5\\n5 4\\nNO\\nYES\\n1 2\\n1 3\\n1 4\\nYES\\n1 2\\n1 3\\n1 4\\n\"]}", "source": "taco"} | There are $n$ districts in the town, the $i$-th district belongs to the $a_i$-th bandit gang. Initially, no districts are connected to each other.
You are the mayor of the city and want to build $n-1$ two-way roads to connect all districts (two districts can be connected directly or through other connected districts).
If two districts belonging to the same gang are connected directly with a road, this gang will revolt.
You don't want this so your task is to build $n-1$ two-way roads in such a way that all districts are reachable from each other (possibly, using intermediate districts) and each pair of directly connected districts belong to different gangs, or determine that it is impossible to build $n-1$ roads to satisfy all the conditions.
You have to answer $t$ independent test cases.
-----Input-----
The first line of the input contains one integer $t$ ($1 \le t \le 500$) — the number of test cases. Then $t$ test cases follow.
The first line of the test case contains one integer $n$ ($2 \le n \le 5000$) — the number of districts. The second line of the test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the gang the $i$-th district belongs to.
It is guaranteed that the sum of $n$ does not exceed $5000$ ($\sum n \le 5000$).
-----Output-----
For each test case, print:
NO on the only line if it is impossible to connect all districts satisfying the conditions from the problem statement. YES on the first line and $n-1$ roads on the next $n-1$ lines. Each road should be presented as a pair of integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le n; x_i \ne y_i$), where $x_i$ and $y_i$ are two districts the $i$-th road connects.
For each road $i$, the condition $a[x_i] \ne a[y_i]$ should be satisfied. Also, all districts should be reachable from each other (possibly, using intermediate districts).
-----Example-----
Input
4
5
1 2 2 1 3
3
1 1 1
4
1 1000 101 1000
4
1 2 3 4
Output
YES
1 3
3 5
5 4
1 2
NO
YES
1 2
2 3
3 4
YES
1 2
1 3
1 4
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3\\n101\\n3 3\\n3 2\\n3 1\\n\", \"4\\n1111\\n3 4\\n5 2\\n3 1\\n3 2\\n\", \"6\\n011100\\n5 3\\n5 5\\n2 4\\n3 5\\n4 2\\n1 5\\n\", \"1\\n0\\n1 5\\n\", \"20\\n00101101001100000010\\n1 1\\n5 3\\n3 3\\n4 5\\n1 4\\n5 2\\n4 2\\n4 4\\n5 1\\n1 1\\n5 3\\n2 4\\n2 4\\n1 2\\n2 3\\n1 4\\n1 5\\n1 3\\n3 4\\n4 3\\n\", \"50\\n10011111101111011010001011111110110011101111100111\\n2 1\\n4 3\\n3 4\\n1 4\\n3 2\\n5 3\\n5 5\\n3 5\\n5 5\\n4 4\\n1 1\\n1 2\\n1 4\\n1 5\\n1 1\\n4 1\\n2 4\\n3 1\\n1 1\\n1 3\\n1 5\\n2 3\\n3 1\\n5 5\\n5 4\\n4 4\\n1 4\\n2 1\\n2 2\\n2 5\\n1 5\\n2 1\\n5 4\\n1 2\\n4 5\\n5 5\\n5 1\\n1 4\\n4 2\\n4 4\\n2 5\\n1 2\\n3 4\\n5 4\\n4 3\\n3 3\\n3 3\\n3 2\\n5 3\\n5 1\\n\", \"70\\n0010011111011101101111000111101011010101000011000000010100010101010001\\n3 1\\n1 5\\n3 1\\n4 1\\n3 3\\n2 4\\n2 1\\n5 1\\n2 4\\n5 2\\n5 2\\n4 1\\n2 5\\n2 2\\n4 2\\n5 1\\n1 2\\n2 4\\n3 1\\n1 1\\n5 3\\n5 2\\n3 5\\n4 4\\n2 1\\n3 2\\n1 3\\n5 1\\n3 4\\n2 3\\n1 5\\n4 1\\n2 2\\n5 1\\n3 3\\n4 2\\n1 4\\n5 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\"7\\n0000111\\n3 3\\n2 7\\n5 3\\n1 5\\n3 2\\n4 4\\n5 4\\n\", \"6\\n011110\\n5 3\\n6 5\\n2 4\\n3 5\\n6 2\\n1 9\\n\", \"25\\n0101110011000110001100011\\n1 1\\n2 1\\n1 3\\n1 4\\n1 6\\n2 2\\n2 2\\n2 3\\n2 3\\n2 5\\n3 1\\n3 2\\n6 3\\n3 4\\n1 5\\n4 1\\n4 2\\n4 3\\n7 4\\n5 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n1 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n3 4\\n3 5\\n4 1\\n4 3\\n4 5\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n\", \"7\\n0000111\\n3 3\\n2 7\\n5 3\\n1 5\\n3 2\\n4 8\\n5 4\\n\", \"6\\n011110\\n5 3\\n6 5\\n2 4\\n3 5\\n4 2\\n1 9\\n\", \"25\\n0101110011000110001100011\\n1 1\\n2 1\\n1 3\\n1 4\\n1 6\\n2 2\\n2 2\\n2 3\\n2 5\\n2 5\\n3 1\\n3 2\\n6 3\\n3 4\\n1 5\\n4 1\\n4 2\\n4 3\\n7 4\\n5 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n1 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n3 4\\n3 5\\n5 1\\n4 3\\n4 5\\n4 4\\n4 5\\n5 1\\n5 2\\n5 3\\n5 4\\n5 5\\n\", 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4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n3 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n3 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n3 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n5 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n3 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n3 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 3\\n2 4\\n4 5\\n3 1\\n5 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 2\\n2 4\\n4 5\\n3 1\\n5 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 2\\n2 4\\n4 5\\n4 1\\n5 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n4 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 2\\n2 4\\n4 5\\n4 1\\n5 2\\n3 2\\n2 4\\n5 10\\n5 1\\n4 4\\n1 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 2\\n2 4\\n4 5\\n4 1\\n5 2\\n2 2\\n2 4\\n5 10\\n5 1\\n4 4\\n1 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"25\\n1111111110111111111111111\\n1 4\\n1 2\\n1 3\\n4 4\\n1 5\\n1 1\\n4 2\\n2 2\\n2 4\\n4 5\\n4 1\\n5 2\\n2 2\\n2 4\\n5 10\\n3 1\\n4 4\\n1 5\\n4 4\\n4 5\\n5 1\\n1 2\\n5 3\\n1 4\\n5 5\\n\", \"4\\n1111\\n3 4\\n5 2\\n3 1\\n3 2\\n\", \"3\\n101\\n3 3\\n3 2\\n3 1\\n\", \"6\\n011100\\n5 3\\n5 5\\n2 4\\n3 5\\n4 2\\n1 5\\n\"], \"outputs\": [\"2\\n\", \"4\\n\", \"6\\n\", \"1\\n\", \"15\\n\", \"37\\n\", \"46\\n\", \"1\\n\", \"7\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"2\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"1\\n\", \"15\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"25\\n\", \"46\\n\", \"7\\n\", \"2\\n\", \"37\\n\", \"1\\n\", \"25\\n\", \"25\", \"1\", \"15\", \"24\", \"45\", \"7\", \"2\", \"38\", \"4\", \"3\", \"6\", \"23\", \"5\", \"22\", \"25\", \"25\", \"24\", \"25\", \"1\", \"25\", \"25\", \"24\", \"25\", \"24\", \"7\", \"25\", \"4\", \"3\", \"6\", \"25\", \"24\", \"23\", \"24\", \"24\", \"7\", \"25\", \"3\", \"25\", \"25\", \"23\", \"24\", \"7\", \"24\", \"5\", \"24\", \"24\", \"23\", \"24\", \"7\", \"25\", \"5\", \"23\", \"24\", \"7\", \"5\", \"24\", \"7\", \"5\", \"22\", \"24\", \"7\", \"5\", \"23\", \"24\", \"7\", \"6\", \"24\", \"24\", \"6\", \"5\", \"24\", \"24\", \"5\", \"5\", \"23\", \"24\", \"6\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"24\", \"4\\n\", \"2\\n\", \"6\\n\"]}", "source": "taco"} | It is a holiday season, and Koala is decorating his house with cool lights! He owns $n$ lights, all of which flash periodically.
After taking a quick glance at them, Koala realizes that each of his lights can be described with two parameters $a_i$ and $b_i$. Light with parameters $a_i$ and $b_i$ will toggle (on to off, or off to on) every $a_i$ seconds starting from the $b_i$-th second. In other words, it will toggle at the moments $b_i$, $b_i + a_i$, $b_i + 2 \cdot a_i$ and so on.
You know for each light whether it's initially on or off and its corresponding parameters $a_i$ and $b_i$. Koala is wondering what is the maximum number of lights that will ever be on at the same time. So you need to find that out.
[Image] Here is a graphic for the first example.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 100$), the number of lights.
The next line contains a string $s$ of $n$ characters. The $i$-th character is "1", if the $i$-th lamp is initially on. Otherwise, $i$-th character is "0".
The $i$-th of the following $n$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le 5$) — the parameters of the $i$-th light.
-----Output-----
Print a single integer — the maximum number of lights that will ever be on at the same time.
-----Examples-----
Input
3
101
3 3
3 2
3 1
Output
2
Input
4
1111
3 4
5 2
3 1
3 2
Output
4
Input
6
011100
5 3
5 5
2 4
3 5
4 2
1 5
Output
6
-----Note-----
For first example, the lamps' states are shown in the picture above. The largest number of simultaneously on lamps is $2$ (e.g. at the moment $2$).
In the second example, all lights are initially on. So the answer is $4$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"27 29\\n12 11\\n21 20\\n19 26\\n16 24\\n22 4\\n1 3\\n23 5\\n9 1\\n4 3\\n21 23\\n22 8\\n14 6\\n25 13\\n7 20\\n9 16\\n3 20\\n23 19\\n17 10\\n13 18\\n8 14\\n23 25\\n25 27\\n19 15\\n19 15\\n17 24\\n12 27\\n18 11\\n25 5\\n22 17\\n\", \"15 29\\n6 11\\n14 3\\n10 4\\n14 7\\n6 14\\n7 15\\n13 8\\n10 13\\n4 14\\n15 8\\n12 7\\n3 5\\n6 7\\n8 1\\n4 5\\n11 5\\n10 6\\n11 3\\n13 14\\n7 10\\n3 12\\n7 14\\n8 11\\n7 15\\n15 8\\n12 7\\n4 3\\n9 4\\n8 10\\n\", \"34 27\\n19 10\\n8 31\\n26 22\\n2 30\\n32 26\\n30 4\\n34 1\\n2 31\\n4 18\\n33 11\\n10 13\\n20 23\\n4 32\\n23 27\\n30 7\\n10 17\\n29 9\\n18 10\\n2 28\\n3 12\\n31 8\\n3 25\\n5 22\\n3 16\\n21 1\\n10 30\\n5 3\\n\", \"2 40\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n1 2\\n\", \"27 28\\n20 14\\n21 5\\n11 17\\n14 9\\n17 13\\n7 19\\n24 27\\n16 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\"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n3\\n7\\n7\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n3\\n7\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n3\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n3\\n7\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n3\\n7\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n3\\n7\", \"0\\n0\\n0\\n0\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n7\\n7\\n15\\n15\", \"0\\n0\\n0\\n0\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n7\\n7\\n15\\n15\", \"0\\n0\\n1\\n3\\n\"]}", "source": "taco"} | A ski base is planned to be built in Walrusland. Recently, however, the project is still in the constructing phase. A large land lot was chosen for the construction. It contains n ski junctions, numbered from 1 to n. Initially the junctions aren't connected in any way.
In the constructing process m bidirectional ski roads will be built. The roads are built one after another: first the road number 1 will be built, then the road number 2, and so on. The i-th road connects the junctions with numbers ai and bi.
Track is the route with the following properties:
* The route is closed, that is, it begins and ends in one and the same junction.
* The route contains at least one road.
* The route doesn't go on one road more than once, however it can visit any junction any number of times.
Let's consider the ski base as a non-empty set of roads that can be divided into one or more tracks so that exactly one track went along each road of the chosen set. Besides, each track can consist only of roads from the chosen set. Ski base doesn't have to be connected.
Two ski bases are considered different if they consist of different road sets.
After building each new road the Walrusland government wants to know the number of variants of choosing a ski base based on some subset of the already built roads. The government asks you to help them solve the given problem.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105). They represent the number of junctions and the number of roads correspondingly. Then on m lines follows the description of the roads in the order in which they were built. Each road is described by a pair of integers ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — the numbers of the connected junctions. There could be more than one road between a pair of junctions.
Output
Print m lines: the i-th line should represent the number of ways to build a ski base after the end of construction of the road number i. The numbers should be printed modulo 1000000009 (109 + 9).
Examples
Input
3 4
1 3
2 3
1 2
1 2
Output
0
0
1
3
Note
Let us have 3 junctions and 4 roads between the junctions have already been built (as after building all the roads in the sample): 1 and 3, 2 and 3, 2 roads between junctions 1 and 2. The land lot for the construction will look like this:
<image>
The land lot for the construction will look in the following way:
<image>
We can choose a subset of roads in three ways:
<image>
In the first and the second ways you can choose one path, for example, 1 - 2 - 3 - 1. In the first case you can choose one path 1 - 2 - 1.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.75 |
{"tests": "{\"inputs\": [[0], [1], [5], [43], [91], [101], [239]], \"outputs\": [[{}], [{\"P\": 1}], [{\"N\": 1}], [{\"Q\": 1, \"D\": 1, \"N\": 1, \"P\": 3}], [{\"H\": 1, \"Q\": 1, \"D\": 1, \"N\": 1, \"P\": 1}], [{\"H\": 2, \"P\": 1}], [{\"H\": 4, \"Q\": 1, \"D\": 1, \"P\": 4}]]}", "source": "taco"} | # Making Change
Complete the method that will determine the minimum number of coins needed to make change for a given amount in American currency.
Coins used will be half-dollars, quarters, dimes, nickels, and pennies, worth 50¢, 25¢, 10¢, 5¢ and 1¢, respectively. They'll be represented by the symbols `H`, `Q`, `D`, `N` and `P` (symbols in Ruby, strings in in other languages)
The argument passed in will be an integer representing the value in cents. The return value should be a hash/dictionary/object with the symbols as keys, and the numbers of coins as values. Coins that are not used should not be included in the hash. If the argument passed in is 0, then the method should return an empty hash.
## Examples
```python
make_change(0) #--> {}
make_change(1) #--> {"P":1}
make_change(43) #--> {"Q":1, "D":1, "N":1, "P":3}
make_change(91) #--> {"H":1, "Q":1, "D":1, "N":1, "P":1}
```
#### **If you liked this kata, check out [Part 2](https://www.codewars.com/kata/making-change-part-2/ruby).**
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"437\\n\", \"425\\n\", \"Never\\n\", \"449\\n\", \"3212\\n\", \"336\\n\", \"407\\n\", \"708\\n\", \"145\\n\", \"708\\n\", \"413\\n\", \"145\\n\", \"145\\n\", \"437\\n\", \"425\\n\", \"135\\n\", \"437\\n\", \"Never\\n\", \"437\\n\", \"425\\n\", \"14\\n\", \"42\\n\", \"Never\\n\"]}", "source": "taco"} | Joe has been hurt on the Internet. Now he is storming around the house, destroying everything in his path.
Joe's house has n floors, each floor is a segment of m cells. Each cell either contains nothing (it is an empty cell), or has a brick or a concrete wall (always something one of three). It is believed that each floor is surrounded by a concrete wall on the left and on the right.
Now Joe is on the n-th floor and in the first cell, counting from left to right. At each moment of time, Joe has the direction of his gaze, to the right or to the left (always one direction of the two). Initially, Joe looks to the right.
Joe moves by a particular algorithm. Every second he makes one of the following actions: If the cell directly under Joe is empty, then Joe falls down. That is, he moves to this cell, the gaze direction is preserved. Otherwise consider the next cell in the current direction of the gaze. If the cell is empty, then Joe moves into it, the gaze direction is preserved. If this cell has bricks, then Joe breaks them with his forehead (the cell becomes empty), and changes the direction of his gaze to the opposite. If this cell has a concrete wall, then Joe just changes the direction of his gaze to the opposite (concrete can withstand any number of forehead hits).
Joe calms down as soon as he reaches any cell of the first floor.
The figure below shows an example Joe's movements around the house.
[Image]
Determine how many seconds Joe will need to calm down.
-----Input-----
The first line contains two integers n and m (2 ≤ n ≤ 100, 1 ≤ m ≤ 10^4).
Next n lines contain the description of Joe's house. The i-th of these lines contains the description of the (n - i + 1)-th floor of the house — a line that consists of m characters: "." means an empty cell, "+" means bricks and "#" means a concrete wall.
It is guaranteed that the first cell of the n-th floor is empty.
-----Output-----
Print a single number — the number of seconds Joe needs to reach the first floor; or else, print word "Never" (without the quotes), if it can never happen.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
-----Examples-----
Input
3 5
..+.#
#+..+
+.#+.
Output
14
Input
4 10
...+.##+.+
+#++..+++#
++.#++++..
.+##.++#.+
Output
42
Input
2 2
..
++
Output
Never
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [[0], [3], [16], [32], [49], [89], [327], [363], [366], [512], [656], [1038], [1052], [1222], [1235], [1302], [1735], [1757], [1974], [2048]], \"outputs\": [[0], [7], [171], [683], [1215], [3715], [52239], [60195], [62063], [174763], [209095], [699451], [700379], [757295], [762019], [832559], [1398915], [1443119], [2038207], [2796203]]}", "source": "taco"} | Introduction
It's been more than 20 minutes since the negligent waiter has taken your order for the house special prime tofu steak with a side of chili fries.
Out of boredom, you start fiddling around with the condiments tray. To be efficient, you want to be familiar with the choice of sauces and spices before your order is finally served.
You also examine the toothpick holder and try to analyze its inner workings when - yikes - the holder's lid falls off and all 23 picks lay scattered on the table.
Being a good and hygiene oriented citizen, you decide not to just put them back in the holder. Instead of letting all the good wood go to waste, you start playing around with the picks.
In the first "round", you lay down one toothpick vertically. You've used a total of one toothpick.
In the second "round", at each end of the first toothpick, you add a perpendicular toothpick at its center point. You added two additional toothpicks for a total of three toothpicks.
In the next rounds, you continue to add perpendicular toothpicks to each free end of toothpicks already on the table.
With your 23 toothpicks, you can complete a total of six rounds:
You wonder if you'd be able to implement this sequence in your favorite programming language. Because your food still hasn't arrived, you decide to take out your laptop and start implementing...
Challenge
Implement a script that returns the amount of toothpicks needed to complete n amount of rounds of the toothpick sequence.
```
0 <= n <= 5000
```
Hint
You can attempt this brute force or get some inspiration from the math department.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"417465899\\n\", \"367539989\\n\", \"275404739\\n\", \"278436471\\n\", \"337306079\\n\", \"337306479\\n\", \"336343153\\n\", \"298175205\\n\", \"386985051\\n\", \"327347767\\n\", \"339488833\\n\", \"340251327\\n\", \"326789147\\n\", \"319752713\\n\", \"365073087\\n\", \"362583391\\n\", \"248125785\\n\", \"283655137\\n\", \"320759913\\n\", \"320129205\\n\", \"201012992\\n\", \"201452132\\n\", \"217771906\\n\", \"217771546\\n\", \"191520546\\n\", \"179147484\\n\", \"128119622\\n\", \"136097906\\n\", \"156698006\\n\", \"204712424\\n\", \"226099620\\n\", \"161057046\\n\", \"157855566\\n\", \"224934246\\n\", \"224913710\\n\", \"224423194\\n\", \"224429562\\n\", \"224451482\\n\", \"224444090\\n\", \"227316298\\n\", \"419743139\\n\", \"420801469\\n\", \"373935249\\n\", \"318946085\\n\", \"333751227\\n\", \"388605779\\n\", \"386924789\\n\", \"351993115\\n\", \"403137589\\n\", \"345677191\\n\", \"470567303\\n\", \"479516563\\n\", \"391521047\\n\", \"493777691\\n\", \"349697259\\n\", \"299531421\\n\", \"340424455\\n\", \"359842645\\n\", \"350387205\\n\", \"267758043\\n\", \"15258\\n\", \"251918921\\n\", \"188723084\\n\", \"1629\\n\", \"1648\\n\", \"599598800\\n\", \"3469\\n\", \"\\n1574\\n\", \"\\n24\\n\", \"\\n0\\n\", \"\\n667387032\\n\"]}", "source": "taco"} | You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s.
Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order.
A merge z is produced from a sequence a by the following rules:
* if a_i=0, then remove a letter from the beginning of x and append it to the end of z;
* if a_i=1, then remove a letter from the beginning of y and append it to the end of z.
Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i.
Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i.
Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive.
Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered.
Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353.
Input
The first line contains a string x (1 ≤ |x| ≤ 1000).
The second line contains a string y (1 ≤ |y| ≤ 1000).
Both strings consist only of lowercase Latin letters.
Output
Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353.
Examples
Input
aaa
bb
Output
24
Input
code
forces
Output
1574
Input
aaaaa
aaa
Output
0
Input
justamassivetesttocheck
howwellyouhandlemodulooperations
Output
667387032
Note
In the first example there are:
* 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10";
* 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101";
* 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010";
* 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010";
* 2 pairs of substrings "aaa" and "b", each with no valid merging sequences;
* 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010";
Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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\"||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|=|||\\n\", \"|+|=||||\\n\", \"|+||=|\\n\", \"|+||||||=|||||\\n\", \"|+|||=||\\n\", \"|+||||=|||\\n\", \"|+|||||=||||\\n\", \"||+||=||\\n\", \"||+|||=|||\\n\", \"|||||+||=||||||||||\\n\", \"|||+|||=||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||+|||||=||||||||||||\\n\", \"||+|||||||=|||||||\\n\", \"||||+||||=||||||\\n\", \"||||+|||=|||||\\n\", \"||+|||=|||||||\\n\", \"||+|=|\\n\", \"|||+|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||+|=||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+||||||=|||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|=||||\\n\", \"||||||||||||||||||+||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||+|||=||||\\n\", \"|||||+|||||=||||||||||||\\n\", \"||||||||||||+|||||||||||=||||||||||||||||||||||\\n\", \"||+|=||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|||||=||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||||=|\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+|=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|\\n\", \"||+|||=|||\\n\", \"||+||=||\\n\", \"|+||=|\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||=|||||||||||||||||||||||||\\n\", \"|||||+||=||||||||||\\n\", \"||+|||=|||||||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|||=||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||||||||||=|\\n\", \"|+||||=|||\\n\", \"|||+|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|=|||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||+|=|\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||+|||=|||||\\n\", \"||+|||||||=|||||||\\n\", \"|+|=||\\n\", \"||+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||+|=|\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||=|\\n\", \"||||+||||=||||||\\n\", \"|+|=|\\n\", \"||||+|||||||=|||\\n\", \"|+||=|||\\n\", \"|+|||||||||=\\n\", \"|||+||||=||||||||||\\n\", \"||+||||||||=\\n\", \"|||||||+|||=\\n\", \"|||||+||=|}\\n\", \"||||+|||||||=||}\\n\", \"||||+||||||=\\n\", \"|||+|||||||=\\n\", \"|{|+|||||||=\\n\", \"|+=|||||||||||\\n\", \"|||||+|=||\\n\", \"|||||+|=||}\\n\", \"|||+||||||}=\\n\", \"||||||||||||||||||+||||||=||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||||+||=\\n\", \"|}|+|||||||=\\n\", \"|+|=||||||||||\\n\", \"|||||+|=||~\\n\", \"|}||||||+||=\\n\", \"|||+=|||||||\\n\", \"|+|||=|\\n\", \"||+||||||{|=\\n\", \"|+|||||=\\n\", \"+||||||=||\\n\", \"|+{||||=\\n\", \"||+||=|\\n\", \"|}+||||||||=\\n\", \"|}|+||||||}=\\n\", \"||+|=||\\n\", \"|||+||=\\n\", \"||+|}||||||=\\n\", \"||||+|||||{=\\n\", \"}||+|||||||=\\n\", \"||||||||||+=\\n\", \"|}|+|||||}}=\\n\", \"|~|+|||||}}=\\n\", \"||+|||=||||\\n\", \"||||||+|=||||||||||\\n\", \"|+|=||||||\\n\", \"|||||+||=||\\n\", \"||+|=|||||\\n\", \"||||+||=||||||\\n\"], \"outputs\": [\"|||+|=||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"||||+||=||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+|=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|=||\\n\", \"|+|=||\\n\", \"|+|=||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"||+|=|||\\n\", \"|+|=||\\n\", \"|+|||||=||||||\\n\", \"|+||=|||\\n\", \"|+|||=||||\\n\", \"|+||||=|||||\\n\", \"|+||=|||\\n\", \"|+|||=||||\\n\", \"Impossible\\n\", \"||+|||=|||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"||||||+|||||=|||||||||||\\n\", \"|+|||||||=||||||||\\n\", \"|||+||||=|||||||\\n\", \"|||+|||=||||||\\n\", \"|||+|||=||||||\\n\", \"|+|=||\\n\", \"||+|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|+|||||=||||||\\n\", \"Impossible\\n\", \"||+|=|||\\n\", \"Impossible\\n\", \"||+|||=|||||\\n\", \"||||||+|||||=|||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|+||||=|||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||+||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+|=||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"|+|||=||||\\n\", \"|+||=|||\\n\", \"|+|=||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||+|||=||||||\\n\", \"Impossible\\n\", \"|+||=|||\\n\", \"||||||||||||||||||||||||||||||||||||||||||||||||||+|||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"|+|||=||||\\n\", \"||+|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||+||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"|+|=||\\n\", \"Impossible\\n\", \"|||+|||=||||||\\n\", \"|+|||||||=||||||||\\n\", \"|+|=||\\n\", \"|+||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||=|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||+||||=|||||||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|+||=|||\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"|||+|=||||\\n\", \"||||+||=||||||\\n\"]}", "source": "taco"} | When new students come to the Specialized Educational and Scientific Centre (SESC) they need to start many things from the beginning. Sometimes the teachers say (not always unfairly) that we cannot even count. So our teachers decided to teach us arithmetics from the start. And what is the best way to teach students add and subtract? — That's right, using counting sticks! An here's our new task:
An expression of counting sticks is an expression of type:[ A sticks][sign +][B sticks][sign =][C sticks] (1 ≤ A, B, C).
Sign + consists of two crossed sticks: one vertical and one horizontal. Sign = consists of two horizontal sticks. The expression is arithmetically correct if A + B = C.
We've got an expression that looks like A + B = C given by counting sticks. Our task is to shift at most one stick (or we can shift nothing) so that the expression became arithmetically correct. Note that we cannot remove the sticks from the expression, also we cannot shift the sticks from the signs + and =.
We really aren't fabulous at arithmetics. Can you help us?
-----Input-----
The single line contains the initial expression. It is guaranteed that the expression looks like A + B = C, where 1 ≤ A, B, C ≤ 100.
-----Output-----
If there isn't a way to shift the stick so the expression becomes correct, print on a single line "Impossible" (without the quotes). If there is a way, print the resulting expression. Follow the format of the output from the test samples. Don't print extra space characters.
If there are multiple correct answers, print any of them. For clarifications, you are recommended to see the test samples.
-----Examples-----
Input
||+|=|||||
Output
|||+|=||||
Input
|||||+||=||
Output
Impossible
Input
|+|=||||||
Output
Impossible
Input
||||+||=||||||
Output
||||+||=||||||
-----Note-----
In the first sample we can shift stick from the third group of sticks to the first one.
In the second sample we cannot shift vertical stick from + sign to the second group of sticks. So we cannot make a - sign.
There is no answer in the third sample because we cannot remove sticks from the expression.
In the forth sample the initial expression is already arithmetically correct and that is why we don't have to shift sticks.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"-957757861 308710346 45337024\\n\", \"1 2000000000 -1\\n\", \"999999999 -1000000000 500000000\\n\", \"427055698 738296578 -52640953\\n\", \"592707810 829317963 -753392742\\n\", \"-1548994394 -1586527767 -1203252104\\n\", \"1000000013 -1 135\\n\", \"546348890 -29226055 -341135185\\n\", \"701408733 1134903170 1836311903\\n\", \"610684570 628836350 933504357\\n\", \"-3416750 528845750 -93743375\\n\", \"1999999993 1999999991 -1\\n\", \"1300000013 0 -800000008\\n\", \"931480234 -1767614767 -320146190\\n\", \"0 -1 -2\\n\", \"-1516373701 -584304312 -746376800\\n\", \"1663473197 -1943214909 -399995353\\n\", \"-1 1 -2\\n\", \"12453630 -163142553 -74721780\\n\", \"3162 56 674\\n\", \"0 15 -17\\n\", \"999999993 -999999997 1\\n\", \"-2000000000 1 2000000000\\n\", \"-1638453107 317016895 -430897103\\n\", \"-13 0 0\\n\", \"853072 -269205 -1778980\\n\", \"999999999 -2 1\\n\", \"-1183748658 875864960 -1315510852\\n\", \"0 2 3\\n\", \"1999999 -2000000 1000000\\n\", \"1233978557 804808375 539283626\\n\", \"1880586355 -177315705 -478540057\\n\", \"-1061610169 583743042 1503847115\\n\", \"200000003 200000001 1\\n\", \"296038088 887120955 1338330394\\n\", \"7 5 -17\\n\", \"532430220 -2899704 -328786059\\n\", \"-1000 0 -6\\n\", \"2000000000 -2000000000 2000000000\\n\", \"1044910887 -700497854 -1772517851\\n\", \"19 -5 115\\n\", \"1906842444 749552572 -1693767003\\n\", \"1999999993 1999999991 -1999999997\\n\", \"999999993 999999991 1\\n\", \"19999 -20000 10000\\n\", \"827797728 -613880705 854959653\\n\", \"10273743 174653631 -628469658\\n\", \"-860498206 308710346 45337024\\n\", \"1 706624180 -1\\n\", \"999999999 -1000000000 36822547\\n\", \"427055698 738296578 -28669090\\n\", \"592707810 829317963 -88100968\\n\", \"1000000013 -1 268\\n\", \"129141401 -29226055 -341135185\\n\", \"610684570 628836350 913439180\\n\", \"-3416750 501473395 -93743375\\n\", \"1024765849 1999999991 -1\\n\", \"1475040178 -1767614767 -320146190\\n\", \"0 -2 -2\\n\", \"-434692199 -584304312 -746376800\\n\", \"1663473197 -1943214909 -136578584\\n\", \"-1 1 -4\\n\", \"3162 56 1094\\n\", \"764330811 -999999997 1\\n\", \"-2000000000 1 1809865499\\n\", \"-1638453107 317016895 -737495309\\n\", \"-23 0 0\\n\", \"853072 -135844 -1778980\\n\", \"999999999 -2 2\\n\", \"-1183748658 1287471572 -1315510852\\n\", \"1999999 -2000000 1100000\\n\", \"304462943 200000001 1\\n\", \"296038088 1099148071 1338330394\\n\", \"14 5 -17\\n\", \"-1000 1 -6\\n\", \"1044910887 -974454817 -1772517851\\n\", \"19 -5 207\\n\", \"999999993 1318483765 1\\n\", \"19999 -20000 11000\\n\", \"334520869 -613880705 854959653\\n\", \"10273743 26000103 -628469658\\n\", \"2 5 4\\n\", \"-860498206 528675880 45337024\\n\", \"1 706624180 -2\\n\", \"999999999 -1751388536 36822547\\n\", \"427055698 294461918 -28669090\\n\", \"249456932 829317963 -88100968\\n\", \"129141401 -29226055 -113041200\\n\", \"610684570 460815995 913439180\\n\", \"-6813467 501473395 -93743375\\n\", \"662278544 1 -800000008\\n\", \"0 -2 -4\\n\", \"-403663559 -584304312 -746376800\\n\", \"1663473197 -1071516189 -136578584\\n\", \"-1 1 -1\\n\", \"2681498 -163142553 -5717903\\n\", \"1 15 -8\\n\", \"764330811 -999999997 2\\n\", \"-2000000000 1 35409503\\n\", \"-1638453107 317016895 -1096030418\\n\", \"853072 -91270 -1778980\\n\", \"1636883485 -2 2\\n\", \"1999999 -3814657 1100000\\n\", \"346834837 200000001 1\\n\", \"296038088 1099148071 1867823007\\n\", \"26 5 -17\\n\", \"1044910887 -1931439490 -1772517851\\n\", \"19 -3 207\\n\", \"19999 -19548 11000\\n\", \"4 5 4\\n\", \"-1463207204 528675880 45337024\\n\", \"999999999 -1751388536 37862991\\n\", \"253738138 -29226055 -113041200\\n\", \"610684570 136607671 913439180\\n\", \"-6813467 501473395 -47372138\\n\", \"662278544 1 -906117615\\n\", \"-403663559 -584304312 -359051810\\n\", \"1663473197 -1547763704 -136578584\\n\", \"2681498 -163142553 -8657794\\n\", \"662278544 0 -800000008\\n\", \"12453630 -163142553 -5717903\\n\", \"0 15 -8\\n\", \"0 2 2\\n\", \"1880586355 -177315705 -900907112\\n\", \"-1061610169 583743042 1999520508\\n\", \"532430220 -3138556 -328786059\\n\", \"1906842444 749552572 -2618628981\\n\", \"839898762 -1 268\\n\", \"1412 56 1094\\n\", \"-24 0 0\\n\", \"0 2 4\\n\", \"-1718610591 583743042 1999520508\\n\", \"77932992 -3138556 -328786059\\n\", \"-1630 0 -6\\n\", \"1906842444 489184116 -2618628981\\n\", \"999999993 651547581 1\\n\", \"65614050 -613880705 854959653\\n\", \"10273743 26000103 -802752593\\n\", \"2 706624180 -2\\n\", \"427055698 294461918 -3156827\\n\", \"66403239 829317963 -88100968\\n\", \"715252896 -1 268\\n\", \"0 -2 -1\\n\", \"-2 1 -1\\n\", \"1412 56 2065\\n\", \"1 13 -8\\n\", \"2 5 3\\n\"], \"outputs\": [\"587450634832960 1822535171726016\\n\", \"1 0\\n\", \"500000000 500000000\\n\", \"-1\\n\\n\", \"-15849808632976 11327748563154\\n\", \"-878123061596147680 857348814150663048\\n\", \"0 135\\n\", \"50549411713300 944965544604433\\n\", \"-796030994547383611 491974210728665288\\n\", \"-1\\n\\n\", \"-1\\n\\n\", \"-999999995 999999996\\n\", \"-1\\n\\n\", \"-98880374013340920 -52107006370101410\\n\", \"0 -2\\n\", \"202167007852295200 -524659372900676000\\n\", \"90913128604458086 77825438652462521\\n\", \"0 2\\n\", \"-780 -60\\n\", \"-4381 247358\\n\", \"-1\\n\\n\", \"-249999999 -249999998\\n\", \"0 -2000000000\\n\", \"-23538272620589909 -121653945000687008\\n\", \"0 0\\n\", \"7238140 22936620\\n\", \"-1 -499999999\\n\", \"-97498198168399474 -131770725522871624\\n\", \"-1\\n\\n\", \"1000000 1000000\\n\", \"3168196851074932 -4857661898189602\\n\", \"-1\\n\\n\", \"-333340893817405 -606222356685680\\n\", \"100000000 -100000001\\n\", \"2114412129515872 -705593211994286\\n\", \"-34 51\\n\", \"-1\\n\\n\", \"-1\\n\\n\", \"0 1\\n\", \"572270531415215165 853638173436907976\\n\", \"115 460\\n\", \"-1\\n\\n\", \"-1999999987000000015 1999999989000000012\\n\", \"499999995 -499999996\\n\", \"10000 10000\\n\", \"60828197453915544 82024802605070757\\n\", \"-1\\n\\n\", \"-1622334467693536 -4522089774672640\", \"1 0\", \"36822547 36822547\", \"-1951616794420090 1128881126101595\", \"-1\", \"0 268\", \"-83267346171465 -367934082863230\", \"-2101140117985524 2040489309280130\", \"-401974966761500 -2738825192675\", \"-328896275 168520836\", \"220704317026503310 184173464235457970\", \"0 -1\", \"171923137727900000 -127901925868246400\", \"31042326563745808 26573529243806488\", \"0 4\", \"-7111 401498\", \"442957327 338565934\", \"0 -1809865499\", \"-40286568460981727 -208214938403405024\", \"0 0\", \"1877268645 11788855715\", \"-2 -999999998\", \"-64366736376131586 -59181141908029288\", \"1100000 1100000\", \"-60554816 92183487\", \"-472229391032306190 127187491573742906\", \"-17 51\", \"0 6\", \"-689015726916782460 -738833675825079263\", \"207 828\", \"-201043462 152480801\", \"11000 11000\", \"-195923878413982497 -106764434084788128\", \"-296949609016254 117337380047460\", \"8 -4\", \"198226775344544 322643402163808\", \"2 0\", \"5279259794266835 3014328163323992\", \"-276805310393470 401448465197425\", \"-29381296636866640 8837826315375096\", \"-27592113466800 -121921490589600\", \"-4774778607411720 6327652799274956\", \"-12036777122220125 -163542442184000\", \"0 800000008\", \"0 -2\", \"26247929208207200 -18133243761796800\", \"-66137919802690400 -102675683322887256\", \"0 1\", \"439389334186567 7222037409471\", \"8 0\", \"885914654 677131868\", \"0 -35409503\", \"-59871980107842854 -309439128882822848\", \"14988795990 140095564490\", \"-2 -1636883484\", \"-1910409600000 -1001614900000\", \"-96934228 168100835\", \"-659060666264552445 177507530299768143\", \"17 -85\", \"271017133926885073 146620567338477310\", \"-207 -1242\", \"-15257000 -15609000\", \"4 -4\", \"691111144664336 1912776511834704\", \"5428428567882255 3099499883019576\", \"1361948863982400 11824324863486000\", \"47808013686450500 -213718717748025580\", \"-6082647087424094 -82644295023488\", \"0 906117615\", \"12626821319953490 -8723173059297060\", \"22489928465101304 24171256314809776\", \"665303755797266 10935287316258\", \"-1\", \"-1\", \"-1\", \"0 -1\", \"-1\", \"-1\", \"-1\", \"-1\", \"0 268\", \"-1\", \"0 0\", \"0 -2\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\", \"-1\", \"1 0\", \"-1\", \"-1\", \"0 268\", \"-1\", \"0 1\", \"-1\", \"8 0\", \"6 -3\\n\"]}", "source": "taco"} | A line on the plane is described by an equation Ax + By + C = 0. You are to find any point on this line, whose coordinates are integer numbers from - 5·1018 to 5·1018 inclusive, or to find out that such points do not exist.
Input
The first line contains three integers A, B and C ( - 2·109 ≤ A, B, C ≤ 2·109) — corresponding coefficients of the line equation. It is guaranteed that A2 + B2 > 0.
Output
If the required point exists, output its coordinates, otherwise output -1.
Examples
Input
2 5 3
Output
6 -3
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.375 |
{"tests": "{\"inputs\": [\"1 1 1\\n\", \"3 1 4\\n\", \"1000 123456 654321\\n\", \"305 337309 378395\\n\", \"108 531040 908573\\n\", \"575 39377 68346\\n\", \"66 199449 266025\\n\", \"781 817338 452871\\n\", \"99 534023 117289\\n\", \"156 78149 46740\\n\", \"57 339480 774350\\n\", \"270 967166 795005\\n\", \"628 446579 365440\\n\", \"97 119368 2062\\n\", \"757 869978 224540\\n\", \"892 777143 664073\\n\", \"177 2501 570142\\n\", \"908 879494 944888\\n\", \"734 32585 49636\\n\", \"38 592277 400426\\n\", \"192 42070 61266\\n\", \"78 535199 331023\\n\", \"842 171735 282219\\n\", \"1000 1000000 1\\n\", \"734 32585 49636\\n\", \"270 967166 795005\\n\", \"99 534023 117289\\n\", \"892 777143 664073\\n\", \"192 42070 61266\\n\", \"38 592277 400426\\n\", \"97 119368 2062\\n\", \"757 869978 224540\\n\", \"78 535199 331023\\n\", \"842 171735 282219\\n\", \"57 339480 774350\\n\", \"66 199449 266025\\n\", \"628 446579 365440\\n\", \"156 78149 46740\\n\", \"305 337309 378395\\n\", \"1000 123456 654321\\n\", \"108 531040 908573\\n\", \"1000 1000000 1\\n\", \"781 817338 452871\\n\", \"177 2501 570142\\n\", \"908 879494 944888\\n\", \"575 39377 68346\\n\", \"734 32585 16425\\n\", \"270 967166 652936\\n\", \"99 534023 17265\\n\", \"565 777143 664073\\n\", \"115 42070 61266\\n\", \"38 592277 38230\\n\", \"97 190473 2062\\n\", \"757 848627 224540\\n\", \"78 535199 192416\\n\", \"808 171735 282219\\n\", \"48 339480 774350\\n\", \"2 199449 266025\\n\", \"825 446579 365440\\n\", \"4 78149 46740\\n\", \"305 337309 460205\\n\", \"108 44604 908573\\n\", \"238 817338 452871\\n\", \"252 2501 570142\\n\", \"908 879494 453030\\n\", \"575 75790 68346\\n\", \"1 1 2\\n\", \"3 1 2\\n\", \"734 32585 1522\\n\", \"41 967166 652936\\n\", \"171 534023 17265\\n\", \"855 777143 664073\\n\", \"115 42070 96429\\n\", \"38 1061692 38230\\n\", \"97 105162 2062\\n\", \"757 848627 229764\\n\", \"78 475789 192416\\n\", \"808 170805 282219\\n\", \"9 339480 774350\\n\", \"3 199449 266025\\n\", \"825 131202 365440\\n\", \"7 78149 46740\\n\", \"305 337309 548997\\n\", \"108 44604 705326\\n\", \"341 817338 452871\\n\", \"252 2501 734474\\n\", \"133 879494 453030\\n\", \"422 75790 68346\\n\", \"3 1 1\\n\", \"734 32585 411\\n\", \"1 1 1\\n\", \"3 1 4\\n\"], \"outputs\": [\"2\\n\", \"370000006\\n\", \"977760856\\n\", \"174667130\\n\", \"145579983\\n\", \"899189133\\n\", \"27912582\\n\", \"711597307\\n\", \"29694885\\n\", \"114906561\\n\", \"622654301\\n\", \"530539317\\n\", \"214808787\\n\", \"2436614\\n\", \"921904658\\n\", \"527873013\\n\", \"779148936\\n\", \"114377456\\n\", \"684730644\\n\", \"499077928\\n\", \"904814024\\n\", \"684367478\\n\", \"948183028\\n\", \"478180868\\n\", \"684730644\\n\", \"530539317\\n\", \"29694885\\n\", \"527873013\\n\", \"904814024\\n\", \"499077928\\n\", \"2436614\\n\", \"921904658\\n\", \"684367478\\n\", \"948183028\\n\", \"622654301\\n\", \"27912582\\n\", \"214808787\\n\", \"114906561\\n\", \"174667130\\n\", \"977760856\\n\", \"145579983\\n\", \"478180868\\n\", \"711597307\\n\", \"779148936\\n\", \"114377456\\n\", \"899189133\\n\", \"792067890\", \"842909942\", \"605153756\", \"454582741\", \"272189032\", \"471289873\", \"42102296\", \"745709873\", \"893905950\", \"873936138\", \"42513590\", \"243371868\", \"425023285\", \"604608981\", \"735340251\", \"702489388\", \"895934805\", \"547586588\", \"644299130\", \"696523617\", \"500000005\", \"722222231\", \"78627061\", \"298411581\", \"77583596\", \"572411130\", \"514584535\", \"145343573\", \"880090513\", \"284492455\", \"219324062\", \"827469392\", \"904180032\", \"619776867\", \"565939447\", \"556254979\", \"640996099\", \"565342873\", \"720603868\", \"956999535\", \"711277983\", \"827910507\", \"250000006\", \"591169223\", \"2\\n\", \"370000006\\n\"]}", "source": "taco"} | You are given three integers k, p_{a} and p_{b}.
You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability p_{a} / (p_{a} + p_{b}), add 'a' to the end of the sequence. Otherwise (with probability p_{b} / (p_{a} + p_{b})), add 'b' to the end of the sequence.
You stop once there are at least k subsequences that form 'ab'. Determine the expected number of times 'ab' is a subsequence in the resulting sequence. It can be shown that this can be represented by P / Q, where P and Q are coprime integers, and $Q \neq 0 \operatorname{mod}(10^{9} + 7)$. Print the value of $P \cdot Q^{-1} \operatorname{mod}(10^{9} + 7)$.
-----Input-----
The first line will contain three integers integer k, p_{a}, p_{b} (1 ≤ k ≤ 1 000, 1 ≤ p_{a}, p_{b} ≤ 1 000 000).
-----Output-----
Print a single integer, the answer to the problem.
-----Examples-----
Input
1 1 1
Output
2
Input
3 1 4
Output
370000006
-----Note-----
The first sample, we will keep appending to our sequence until we get the subsequence 'ab' at least once. For instance, we get the sequence 'ab' with probability 1/4, 'bbab' with probability 1/16, and 'aab' with probability 1/8. Note, it's impossible for us to end with a sequence like 'aabab', since we would have stopped our algorithm once we had the prefix 'aab'.
The expected amount of times that 'ab' will occur across all valid sequences is 2.
For the second sample, the answer is equal to $\frac{341}{100}$.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
{"tests": "{\"inputs\": [\"3 6 3\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n3 5\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n1 2\\n2 3\\n3 4\\n\", \"1 1 1\\n1\\n1\\n1 1\\n\", \"1 1 1\\n1\\n1\\n1 1\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 2\\n2 3\\n3 4\\n\", \"3 6 3\\n2 1 3\\n1 1 3 1 2 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 3\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n3 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n3 5\\n\", \"2 4 3\\n2 1\\n1 2 2 2\\n2 2\\n2 3\\n3 4\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 1 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n0 5\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 1\\n1 3\\n1 6\\n0 5\\n\", \"2 4 3\\n2 1\\n1 1 1 2\\n2 2\\n1 3\\n3 4\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 3\\n1 3\\n2 4\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 2\\n1 3\\n3 4\\n\", \"3 6 3\\n2 1 3\\n1 1 3 1 3 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 3 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n2 6\\n3 5\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 3\\n1 3\\n3 4\\n\", \"3 6 3\\n2 1 3\\n1 1 3 1 2 3\\n1 4\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 1 3\\n1 5\\n2 6\\n5 5\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n0 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 1 3\\n1 5\\n2 6\\n5 9\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 1\\n1 5\\n1 6\\n0 5\\n\", \"2 4 3\\n2 1\\n1 2 2 2\\n1 2\\n2 3\\n3 4\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n1 5\\n\", \"3 6 3\\n2 1 3\\n1 1 3 2 3 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 1 1 3 3\\n1 5\\n1 6\\n3 5\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n0 0\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n1 6\\n1 5\\n\", \"3 6 1\\n2 1 3\\n1 2 1 1 3 3\\n1 2\\n1 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n1 6\\n1 8\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 2\\n3 3\\n3 4\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n3 8\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 3\\n1 2\\n3 4\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n3 6\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 12\\n0 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 1 3\\n1 5\\n2 1\\n5 9\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 3\\n1 5\\n1 6\\n0 6\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 3 1\\n2 5\\n1 6\\n0 5\\n\", \"3 6 3\\n2 1 3\\n1 1 3 2 3 3\\n1 4\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 3 1 1 3 3\\n1 5\\n1 6\\n3 5\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n2 2\\n3 3\\n4 4\\n\", \"3 6 2\\n2 1 3\\n1 2 2 1 1 3\\n1 5\\n1 6\\n0 6\\n\", \"3 6 3\\n2 1 3\\n1 2 3 2 2 3\\n1 5\\n2 6\\n3 5\\n\", \"3 6 3\\n2 1 3\\n1 1 3 1 2 3\\n1 5\\n2 3\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n3 7\\n\", \"3 6 1\\n2 1 3\\n1 2 3 1 1 3\\n2 5\\n2 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 2 1 3 1\\n1 5\\n1 6\\n3 5\\n\", \"3 6 1\\n2 1 3\\n1 2 3 2 1 3\\n1 5\\n2 6\\n5 5\\n\", \"3 6 2\\n2 1 3\\n1 2 3 1 1 3\\n1 5\\n2 6\\n5 9\\n\", \"2 4 3\\n2 1\\n1 2 2 2\\n1 2\\n2 4\\n3 4\\n\", \"3 6 3\\n2 1 3\\n1 2 3 1 2 3\\n1 5\\n2 6\\n3 5\\n\", \"2 4 3\\n2 1\\n1 1 2 2\\n1 2\\n2 3\\n3 4\\n\"], \"outputs\": [\"110\\n\", \"010\\n\", \"1\\n\", \"1\\n\", \"010\\n\", \"110\\n\", \"100\\n\", \"1\\n\", \"000\\n\", \"0\\n\", \"11\\n\", \"01\\n\", \"001\\n\", \"111\\n\", \"010\\n\", \"000\\n\", \"1\\n\", \"1\\n\", \"110\\n\", \"010\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"11\\n\", \"100\\n\", \"1\\n\", \"110\\n\", \"11\\n\", \"1\\n\", \"11\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"000\\n\", \"1\\n\", \"100\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"11\\n\", \"11\\n\", \"110\\n\", \"0\\n\", \"000\\n\", \"01\\n\", \"100\\n\", \"100\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"01\\n\", \"100\\n\", \"110\\n\", \"010\\n\"]}", "source": "taco"} | Recently Lynyrd and Skynyrd went to a shop where Lynyrd bought a permutation $p$ of length $n$, and Skynyrd bought an array $a$ of length $m$, consisting of integers from $1$ to $n$.
Lynyrd and Skynyrd became bored, so they asked you $q$ queries, each of which has the following form: "does the subsegment of $a$ from the $l$-th to the $r$-th positions, inclusive, have a subsequence that is a cyclic shift of $p$?" Please answer the queries.
A permutation of length $n$ is a sequence of $n$ integers such that each integer from $1$ to $n$ appears exactly once in it.
A cyclic shift of a permutation $(p_1, p_2, \ldots, p_n)$ is a permutation $(p_i, p_{i + 1}, \ldots, p_{n}, p_1, p_2, \ldots, p_{i - 1})$ for some $i$ from $1$ to $n$. For example, a permutation $(2, 1, 3)$ has three distinct cyclic shifts: $(2, 1, 3)$, $(1, 3, 2)$, $(3, 2, 1)$.
A subsequence of a subsegment of array $a$ from the $l$-th to the $r$-th positions, inclusive, is a sequence $a_{i_1}, a_{i_2}, \ldots, a_{i_k}$ for some $i_1, i_2, \ldots, i_k$ such that $l \leq i_1 < i_2 < \ldots < i_k \leq r$.
-----Input-----
The first line contains three integers $n$, $m$, $q$ ($1 \le n, m, q \le 2 \cdot 10^5$) — the length of the permutation $p$, the length of the array $a$ and the number of queries.
The next line contains $n$ integers from $1$ to $n$, where the $i$-th of them is the $i$-th element of the permutation. Each integer from $1$ to $n$ appears exactly once.
The next line contains $m$ integers from $1$ to $n$, the $i$-th of them is the $i$-th element of the array $a$.
The next $q$ lines describe queries. The $i$-th of these lines contains two integers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le m$), meaning that the $i$-th query is about the subsegment of the array from the $l_i$-th to the $r_i$-th positions, inclusive.
-----Output-----
Print a single string of length $q$, consisting of $0$ and $1$, the digit on the $i$-th positions should be $1$, if the subsegment of array $a$ from the $l_i$-th to the $r_i$-th positions, inclusive, contains a subsequence that is a cyclic shift of $p$, and $0$ otherwise.
-----Examples-----
Input
3 6 3
2 1 3
1 2 3 1 2 3
1 5
2 6
3 5
Output
110
Input
2 4 3
2 1
1 1 2 2
1 2
2 3
3 4
Output
010
-----Note-----
In the first example the segment from the $1$-st to the $5$-th positions is $1, 2, 3, 1, 2$. There is a subsequence $1, 3, 2$ that is a cyclic shift of the permutation. The subsegment from the $2$-nd to the $6$-th positions also contains a subsequence $2, 1, 3$ that is equal to the permutation. The subsegment from the $3$-rd to the $5$-th positions is $3, 1, 2$, there is only one subsequence of length $3$ ($3, 1, 2$), but it is not a cyclic shift of the permutation.
In the second example the possible cyclic shifts are $1, 2$ and $2, 1$. The subsegment from the $1$-st to the $2$-nd positions is $1, 1$, its subsequences are not cyclic shifts of the permutation. The subsegment from the $2$-nd to the $3$-rd positions is $1, 2$, it coincides with the permutation. The subsegment from the $3$ to the $4$ positions is $2, 2$, its subsequences are not cyclic shifts of the permutation.
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0.5 |
{"tests": "{\"inputs\": [[\"abcdefg\", \"abcqetg\"], [\"Hello World!\", \"hello world.\"], [\"FixedGrey\", \"FixedGrey\"], [\"HACKER\", \"H4CK3R\"], [\"This is a really long sentence.\", \"That is a_really long sentence,\"], [\"\", \"\"], [\"abcdefghijklmnopqrstuvwxyz\", \"zyxwvutsrqponmlkjihgfedcba\"], [\"YOLO lol\", \"ROLO mom\"], [\"www.youtube.com/zedaphplays\", \"www.twitter.com/zedaphplays\"], [\"Congratulations! You did it!\", \"Conglaturations! U did this!\"]], \"outputs\": [[[3, 5]], [[0, 6, 11]], [[]], [[1, 4]], [[2, 3, 9, 30]], [[]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]], [[0, 5, 7]], [[4, 5, 6, 8, 9, 10]], [[4, 8, 17, 18, 19, 20, 22, 23, 24, 26]]]}", "source": "taco"} | This kata is part of the collection [Mary's Puzzle Books](https://www.codewars.com/collections/marys-puzzle-books).
Mary brought home a "spot the differences" book. The book is full of a bunch of problems, and each problem consists of two strings that are similar. However, in each string there are a few characters that are different. An example puzzle from her book is:
```
String 1: "abcdefg"
String 2: "abcqetg"
```
Notice how the "d" from String 1 has become a "q" in String 2, and "f" from String 1 has become a "t" in String 2.
It's your job to help Mary solve the puzzles. Write a program `spot_diff`/`Spot` that will compare the two strings and return a list with the positions where the two strings differ. In the example above, your program should return `[3, 5]` because String 1 is different from String 2 at positions 3 and 5.
NOTES:
```if-not:csharp
• If both strings are the same, return `[]`
```
```if:csharp
• If both strings are the same, return `new List()`
```
• Both strings will always be the same length
• Capitalization and punctuation matter
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters. | 0 |
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