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Solve the programming task below in a Python markdown code block.
Write a function named `first_non_repeating_letter` that takes a string input, and returns the first character that is not repeated anywhere in the string.
For example, if given the input `'stress'`, the function should return `'t'`, since the letter *t* only occurs once in the string, and occurs first in the string.
As an added challenge, upper- and lowercase letters are considered the **same character**, but the function should return the correct case for the initial letter. For example, the input `'sTreSS'` should return `'T'`.
If a string contains *all repeating characters*, it should return an empty string (`""`) or `None` -- see sample tests.
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.
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Solve the programming task below in a Python markdown code block.
Vasya has got a robot which is situated on an infinite Cartesian plane, initially in the cell $(0, 0)$. Robot can perform the following four kinds of operations: U — move from $(x, y)$ to $(x, y + 1)$; D — move from $(x, y)$ to $(x, y - 1)$; L — move from $(x, y)$ to $(x - 1, y)$; R — move from $(x, y)$ to $(x + 1, y)$.
Vasya also has got a sequence of $n$ operations. Vasya wants to modify this sequence so after performing it the robot will end up in $(x, y)$.
Vasya wants to change the sequence so the length of changed subsegment is minimum possible. This length can be calculated as follows: $maxID - minID + 1$, where $maxID$ is the maximum index of a changed operation, and $minID$ is the minimum index of a changed operation. For example, if Vasya changes RRRRRRR to RLRRLRL, then the operations with indices $2$, $5$ and $7$ are changed, so the length of changed subsegment is $7 - 2 + 1 = 6$. Another example: if Vasya changes DDDD to DDRD, then the length of changed subsegment is $1$.
If there are no changes, then the length of changed subsegment is $0$. Changing an operation means replacing it with some operation (possibly the same); Vasya can't insert new operations into the sequence or remove them.
Help Vasya! Tell him the minimum length of subsegment that he needs to change so that the robot will go from $(0, 0)$ to $(x, y)$, or tell him that it's impossible.
-----Input-----
The first line contains one integer number $n~(1 \le n \le 2 \cdot 10^5)$ — the number of operations.
The second line contains the sequence of operations — a string of $n$ characters. Each character is either U, D, L or R.
The third line contains two integers $x, y~(-10^9 \le x, y \le 10^9)$ — the coordinates of the cell where the robot should end its path.
-----Output-----
Print one integer — the minimum possible length of subsegment that can be changed so the resulting sequence of operations moves the robot from $(0, 0)$ to $(x, y)$. If this change is impossible, print $-1$.
-----Examples-----
Input
5
RURUU
-2 3
Output
3
Input
4
RULR
1 1
Output
0
Input
3
UUU
100 100
Output
-1
-----Note-----
In the first example the sequence can be changed to LULUU. So the length of the changed subsegment is $3 - 1 + 1 = 3$.
In the second example the given sequence already leads the robot to $(x, y)$, so the length of the changed subsegment is $0$.
In the third example the robot can't end his path in the cell $(x, y)$.
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.
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Solve the programming task below in a Python markdown code block.
In some country live wizards. They love playing with numbers.
The blackboard has two numbers written on it — a and b. The order of the numbers is not important. Let's consider a ≤ b for the sake of definiteness. The players can cast one of the two spells in turns:
* Replace b with b - ak. Number k can be chosen by the player, considering the limitations that k > 0 and b - ak ≥ 0. Number k is chosen independently each time an active player casts a spell.
* Replace b with b mod a.
If a > b, similar moves are possible.
If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses.
To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second.
Input
The first line contains a single integer t — the number of input data sets (1 ≤ t ≤ 104). Each of the next t lines contains two integers a, b (0 ≤ a, b ≤ 1018). The numbers are separated by a space.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.
Output
For any of the t input sets print "First" (without the quotes) if the player who moves first wins. Print "Second" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input.
Examples
Input
4
10 21
31 10
0 1
10 30
Output
First
Second
Second
First
Note
In the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win.
In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win.
In the third sample, the first player has no moves.
In the fourth sample, the first player wins in one move, taking 30 modulo 10.
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.
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Solve the programming task below in a Python markdown code block.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
-----Constraints-----
- N is an integer between 1 and 10 \ 000 (inclusive).
- a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
-----Output-----
Print the maximum number of operations that Snuke can perform.
-----Sample Input-----
3
5 2 4
-----Sample Output-----
3
The sequence is initially {5, 2, 4}. Three operations can be performed as follows:
- First, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {15, 6, 2}.
- Next, multiply a_1 by 3, divide a_2 by 2 and multiply a_3 by 3. The sequence is now {45, 3, 6}.
- Finally, multiply a_1 by 3, multiply a_2 by 3 and divide a_3 by 2. The sequence is now {135, 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.
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Solve the programming task below in a Python markdown code block.
Four players participate in the playoff tournament. The tournament is held according to the following scheme: the first player will play with the second, and the third player with the fourth, then the winners of the pairs will play in the finals of the tournament.
It is known that in a match between two players, the one whose skill is greater will win. The skill of the $i$-th player is equal to $s_i$ and all skill levels are pairwise different (i. e. there are no two identical values in the array $s$).
The tournament is called fair if the two players with the highest skills meet in the finals.
Determine whether the given tournament is fair.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
A single line of test case contains four integers $s_1, s_2, s_3, s_4$ ($1 \le s_i \le 100$) — skill of the players. It is guaranteed that all the numbers in the array are different.
-----Output-----
For each testcase, output YES if the tournament is fair, or NO otherwise.
-----Examples-----
Input
4
3 7 9 5
4 5 6 9
5 3 8 1
6 5 3 2
Output
YES
NO
YES
NO
-----Note-----
Consider the example:
in the first test case, players $2$ and $3$ with skills $7$ and $9$ advance to the finals;
in the second test case, players $2$ and $4$ with skills $5$ and $9$ advance to the finals. The player with skill $6$ does not advance, but the player with skill $5$ advances to the finals, so the tournament is not fair;
in the third test case, players $1$ and $3$ with skills $5$ and $8$ advance to the finals;
in the fourth test case, players $1$ and $3$ with skills $6$ and $3$ advance to the finals. The player with skill $5$ does not advance, but the player with skill $3$ advances to the finals, so the tournament is not fair.
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.
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Solve the programming task below in a Python markdown code block.
For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.
For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.
Write a program that will perform the k-rounding of n.
-----Input-----
The only line contains two integers n and k (1 ≤ n ≤ 10^9, 0 ≤ k ≤ 8).
-----Output-----
Print the k-rounding of n.
-----Examples-----
Input
375 4
Output
30000
Input
10000 1
Output
10000
Input
38101 0
Output
38101
Input
123456789 8
Output
12345678900000000
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.
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Solve the programming task below in a Python markdown code block.
You are fed up with your messy room, so you decided to clean it up.
Your room is a bracket sequence $s=s_{1}s_{2}\dots s_{n}$ of length $n$. Each character of this string is either an opening bracket '(' or a closing bracket ')'.
In one operation you can choose any consecutive substring of $s$ and reverse it. In other words, you can choose any substring $s[l \dots r]=s_l, s_{l+1}, \dots, s_r$ and change the order of elements in it into $s_r, s_{r-1}, \dots, s_{l}$.
For example, if you will decide to reverse substring $s[2 \dots 4]$ of string $s=$"((()))" it will be equal to $s=$"()(())".
A regular (aka balanced) bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
A prefix of a string $s$ is a substring that starts at position $1$. For example, for $s=$"(())()" there are $6$ prefixes: "(", "((", "(()", "(())", "(())(" and "(())()".
In your opinion, a neat and clean room $s$ is a bracket sequence that:
the whole string $s$ is a regular bracket sequence; and there are exactly $k$ prefixes of this sequence which are regular (including whole $s$ itself).
For example, if $k = 2$, then "(())()" is a neat and clean room.
You want to use at most $n$ operations to make your room neat and clean. Operations are applied one after another sequentially.
It is guaranteed that the answer exists. Note that you do not need to minimize the number of operations: find any way to achieve the desired configuration in $n$ or less operations.
-----Input-----
The first line contains integer number $t$ ($1 \le t \le 100$) — the number of test cases in the input. Then $t$ test cases follow.
The first line of a test case contains two integers $n$ and $k$ ($1 \le k \le \frac{n}{2}, 2 \le n \le 2000$, $n$ is even) — length of $s$ and required number of regular prefixes.
The second line of a test case contains $s$ of length $n$ — the given bracket sequence. It contains only '(' and ')'.
It is guaranteed that there are exactly $\frac{n}{2}$ characters '(' and exactly $\frac{n}{2}$ characters ')' in the given string.
The sum of all values $n$ over all the test cases in the input doesn't exceed $2000$.
-----Output-----
For each test case print an answer.
In the first line print integer $m$ ($0 \le m \le n$) — the number of operations. You do not need to minimize $m$, any value is suitable.
In the following $m$ lines print description of the operations, each line should contain two integers $l,r$ ($1 \le l \le r \le n$), representing single reverse operation of $s[l \dots r]=s_{l}s_{l+1}\dots s_{r}$. Operations are applied one after another sequentially.
The final $s$ after all operations should be a regular, also it should be exactly $k$ prefixes (including $s$) which are regular.
It is guaranteed that the answer exists. If there are several possible answers you can print any.
-----Example-----
Input
4
8 2
()(())()
10 3
))()()()((
2 1
()
2 1
)(
Output
4
3 4
1 1
5 8
2 2
3
4 10
1 4
6 7
0
1
1 2
-----Note-----
In the first example, the final sequence is "()(()())", where two prefixes are regular, "()" and "()(()())". Note, that all the operations except "5 8" in the example output are useless (they do not change $s$).
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.
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Solve the programming task below in a Python markdown code block.
You are given the string s of length n and the numbers p, q. Split the string s to pieces of length p and q.
For example, the string "Hello" for p = 2, q = 3 can be split to the two strings "Hel" and "lo" or to the two strings "He" and "llo".
Note it is allowed to split the string s to the strings only of length p or to the strings only of length q (see the second sample test).
-----Input-----
The first line contains three positive integers n, p, q (1 ≤ p, q ≤ n ≤ 100).
The second line contains the string s consists of lowercase and uppercase latin letters and digits.
-----Output-----
If it's impossible to split the string s to the strings of length p and q print the only number "-1".
Otherwise in the first line print integer k — the number of strings in partition of s.
Each of the next k lines should contain the strings in partition. Each string should be of the length p or q. The string should be in order of their appearing in string s — from left to right.
If there are several solutions print any of them.
-----Examples-----
Input
5 2 3
Hello
Output
2
He
llo
Input
10 9 5
Codeforces
Output
2
Codef
orces
Input
6 4 5
Privet
Output
-1
Input
8 1 1
abacabac
Output
8
a
b
a
c
a
b
a
c
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.
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Solve the programming task below in a Python markdown code block.
In this problem you have to solve a simple classification task: given an image, determine whether it depicts a Fourier doodle.
You are given a set of 50 images with ids 1 through 50. You are also given a text file labels.txt containing the labels for images with ids 1 through 20, which comprise the learning data set.
You have to output the classification results for images with ids 21 through 50 in the same format.
Input
[Download the images and the training labels](http://tc-alchemy.progopedia.com/fourier-doodles.zip)
Each line of the file labels.txt contains a single integer 0 or 1. Line i (1-based) contains the label of the image {i}.png. Label 1 means that the image depicts a Fourier doodle, label 0 - that it does not.
Output
Output 30 lines, one line per image 21 through 50. Line i (1-based) should contain the classification result for the image {i + 20}.png.
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.
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Solve the programming task below in a Python markdown code block.
A substring of some string is called the most frequent, if the number of its occurrences is not less than number of occurrences of any other substring.
You are given a set of strings. A string (not necessarily from this set) is called good if all elements of the set are the most frequent substrings of this string. Restore the non-empty good string with minimum length. If several such strings exist, restore lexicographically minimum string. If there are no good strings, print "NO" (without quotes).
A substring of a string is a contiguous subsequence of letters in the string. For example, "ab", "c", "abc" are substrings of string "abc", while "ac" is not a substring of that string.
The number of occurrences of a substring in a string is the number of starting positions in the string where the substring occurs. These occurrences could overlap.
String a is lexicographically smaller than string b, if a is a prefix of b, or a has a smaller letter at the first position where a and b differ.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of strings in the set.
Each of the next n lines contains a non-empty string consisting of lowercase English letters. It is guaranteed that the strings are distinct.
The total length of the strings doesn't exceed 105.
Output
Print the non-empty good string with minimum length. If several good strings exist, print lexicographically minimum among them. Print "NO" (without quotes) if there are no good strings.
Examples
Input
4
mail
ai
lru
cf
Output
cfmailru
Input
3
kek
preceq
cheburek
Output
NO
Note
One can show that in the first sample only two good strings with minimum length exist: "cfmailru" and "mailrucf". The first string is lexicographically minimum.
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.
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Solve the programming task below in a Python markdown code block.
You are given a permutation $p_1, p_2, \ldots, p_n$.
In one move you can swap two adjacent values.
You want to perform a minimum number of moves, such that in the end there will exist a subsegment $1,2,\ldots, k$, in other words in the end there should be an integer $i$, $1 \leq i \leq n-k+1$ such that $p_i = 1, p_{i+1} = 2, \ldots, p_{i+k-1}=k$.
Let $f(k)$ be the minimum number of moves that you need to make a subsegment with values $1,2,\ldots,k$ appear in the permutation.
You need to find $f(1), f(2), \ldots, f(n)$.
-----Input-----
The first line of input contains one integer $n$ ($1 \leq n \leq 200\,000$): the number of elements in the permutation.
The next line of input contains $n$ integers $p_1, p_2, \ldots, p_n$: given permutation ($1 \leq p_i \leq n$).
-----Output-----
Print $n$ integers, the minimum number of moves that you need to make a subsegment with values $1,2,\ldots,k$ appear in the permutation, for $k=1, 2, \ldots, n$.
-----Examples-----
Input
5
5 4 3 2 1
Output
0 1 3 6 10
Input
3
1 2 3
Output
0 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.
|
Solve the programming task below in a Python markdown code block.
Write a function which outputs the positions of matching bracket pairs. The output should be a dictionary with keys the positions of the open brackets '(' and values the corresponding positions of the closing brackets ')'.
For example: input = "(first)and(second)" should return {0:6, 10:17}
If brackets cannot be paired or if the order is invalid (e.g. ')(') return False. In this kata we care only about the positions of round brackets '()', other types of brackets should be ignored.
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.
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Solve the programming task below in a Python markdown code block.
Addition of Big Integers
Given two integers $A$ and $B$, compute the sum, $A + B$.
Input
Two integers $A$ and $B$ separated by a space character are given in a line.
Output
Print the sum in a line.
Constraints
* $-1 \times 10^{100000} \leq A, B \leq 10^{100000}$
Sample Input 1
5 8
Sample Output 1
13
Sample Input 2
100 25
Sample Output 2
125
Sample Input 3
-1 1
Sample Output 3
0
Sample Input 4
12 -3
Sample Output 4
9
Example
Input
5 8
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.
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Solve the programming task below in a Python markdown code block.
Celebrating the new year, many people post videos of falling dominoes; Here's a list of them: https://www.youtube.com/results?search_query=New+Years+Dominos
User ainta, who lives in a 2D world, is going to post a video as well.
There are n dominoes on a 2D Cartesian plane. i-th domino (1 ≤ i ≤ n) can be represented as a line segment which is parallel to the y-axis and whose length is li. The lower point of the domino is on the x-axis. Let's denote the x-coordinate of the i-th domino as pi. Dominoes are placed one after another, so p1 < p2 < ... < pn - 1 < pn holds.
User ainta wants to take a video of falling dominoes. To make dominoes fall, he can push a single domino to the right. Then, the domino will fall down drawing a circle-shaped orbit until the line segment totally overlaps with the x-axis.
<image>
Also, if the s-th domino touches the t-th domino while falling down, the t-th domino will also fall down towards the right, following the same procedure above. Domino s touches domino t if and only if the segment representing s and t intersects.
<image>
See the picture above. If he pushes the leftmost domino to the right, it falls down, touching dominoes (A), (B) and (C). As a result, dominoes (A), (B), (C) will also fall towards the right. However, domino (D) won't be affected by pushing the leftmost domino, but eventually it will fall because it is touched by domino (C) for the first time.
<image>
The picture above is an example of falling dominoes. Each red circle denotes a touch of two dominoes.
User ainta has q plans of posting the video. j-th of them starts with pushing the xj-th domino, and lasts until the yj-th domino falls. But sometimes, it could be impossible to achieve such plan, so he has to lengthen some dominoes. It costs one dollar to increase the length of a single domino by 1. User ainta wants to know, for each plan, the minimum cost needed to achieve it. Plans are processed independently, i. e. if domino's length is increased in some plan, it doesn't affect its length in other plans. Set of dominos that will fall except xj-th domino and yj-th domino doesn't matter, but the initial push should be on domino xj.
Input
The first line contains an integer n (2 ≤ n ≤ 2 × 105)— the number of dominoes.
Next n lines describe the dominoes. The i-th line (1 ≤ i ≤ n) contains two space-separated integers pi, li (1 ≤ pi, li ≤ 109)— the x-coordinate and the length of the i-th domino. It is guaranteed that p1 < p2 < ... < pn - 1 < pn.
The next line contains an integer q (1 ≤ q ≤ 2 × 105) — the number of plans.
Next q lines describe the plans. The j-th line (1 ≤ j ≤ q) contains two space-separated integers xj, yj (1 ≤ xj < yj ≤ n). It means the j-th plan is, to push the xj-th domino, and shoot a video until the yj-th domino falls.
Output
For each plan, print a line containing the minimum cost needed to achieve it. If no cost is needed, print 0.
Examples
Input
6
1 5
3 3
4 4
9 2
10 1
12 1
4
1 2
2 4
2 5
2 6
Output
0
1
1
2
Note
Consider the example. The dominoes are set like the picture below.
<image>
Let's take a look at the 4th plan. To make the 6th domino fall by pushing the 2nd domino, the length of the 3rd domino (whose x-coordinate is 4) should be increased by 1, and the 5th domino (whose x-coordinate is 9) should be increased by 1 (other option is to increase 4th domino instead of 5th also by 1). Then, the dominoes will fall like in the picture below. Each cross denotes a touch between two dominoes.
<image> <image> <image> <image> <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.
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Solve the programming task below in a Python markdown code block.
George has recently entered the BSUCP (Berland State University for Cool Programmers). George has a friend Alex who has also entered the university. Now they are moving into a dormitory.
George and Alex want to live in the same room. The dormitory has n rooms in total. At the moment the i-th room has p_{i} people living in it and the room can accommodate q_{i} people in total (p_{i} ≤ q_{i}). Your task is to count how many rooms has free place for both George and Alex.
-----Input-----
The first line contains a single integer n (1 ≤ n ≤ 100) — the number of rooms.
The i-th of the next n lines contains two integers p_{i} and q_{i} (0 ≤ p_{i} ≤ q_{i} ≤ 100) — the number of people who already live in the i-th room and the room's capacity.
-----Output-----
Print a single integer — the number of rooms where George and Alex can move in.
-----Examples-----
Input
3
1 1
2 2
3 3
Output
0
Input
3
1 10
0 10
10 10
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.
|
Solve the programming task below in a Python markdown code block.
Your friend Jeff Zebos has been trying to run his new online company, but it's not going very well. He's not getting a lot of sales on his website which he decided to call Azamon. His big problem, you think, is that he's not ranking high enough on the search engines. If only he could rename his products to have better names than his competitors, then he'll be at the top of the search results and will be a millionaire.
After doing some research, you find out that search engines only sort their results lexicographically. If your friend could rename his products to lexicographically smaller strings than his competitor's, then he'll be at the top of the rankings!
To make your strategy less obvious to his competitors, you decide to swap no more than two letters of the product names.
Please help Jeff to find improved names for his products that are lexicographically smaller than his competitor's!
Given the string $s$ representing Jeff's product name and the string $c$ representing his competitor's product name, find a way to swap at most one pair of characters in $s$ (that is, find two distinct indices $i$ and $j$ and swap $s_i$ and $s_j$) such that the resulting new name becomes strictly lexicographically smaller than $c$, or determine that it is impossible.
Note: String $a$ is strictly lexicographically smaller than string $b$ if and only if one of the following holds: $a$ is a proper prefix of $b$, that is, $a$ is a prefix of $b$ such that $a \neq b$; There exists an integer $1 \le i \le \min{(|a|, |b|)}$ such that $a_i < b_i$ and $a_j = b_j$ for $1 \le j < i$.
-----Input-----
The first line of input contains a single integer $t$ ($1 \le t \le 1500$) denoting the number of test cases. The next lines contain descriptions of the test cases.
Each test case consists of a single line containing two space-separated strings $s$ and $c$ ($2 \le |s| \le 5000, 1 \le |c| \le 5000$). The strings $s$ and $c$ consists of uppercase English letters.
It is guaranteed that the sum of $|s|$ in the input is at most $5000$ and the sum of the $|c|$ in the input is at most $5000$.
-----Output-----
For each test case, output a single line containing a single string, which is either the new name which is obtained after swapping no more than one pair of characters that is strictly lexicographically smaller than $c$. In case there are many possible such strings, you can output any of them; three dashes (the string "---" without quotes) if it is impossible.
-----Example-----
Input
3
AZAMON APPLE
AZAMON AAAAAAAAAAALIBABA
APPLE BANANA
Output
AMAZON
---
APPLE
-----Note-----
In the first test case, it is possible to swap the second and the fourth letters of the string and the resulting string "AMAZON" is lexicographically smaller than "APPLE".
It is impossible to improve the product's name in the second test case and satisfy all conditions.
In the third test case, it is possible not to swap a pair of characters. The name "APPLE" is lexicographically smaller than "BANANA". Note that there are other valid answers, e.g., "APPEL".
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.
|
Solve the programming task below in a Python markdown code block.
Bob is preparing to pass IQ test. The most frequent task in this test is `to find out which one of the given numbers differs from the others`. Bob observed that one number usually differs from the others in **evenness**. Help Bob — to check his answers, he needs a program that among the given numbers finds one that is different in evenness, and return a position of this number.
`!` Keep in mind that your task is to help Bob solve a `real IQ test`, which means indexes of the elements start from `1 (not 0)`
##Examples :
```python
iq_test("2 4 7 8 10") => 3 // Third number is odd, while the rest of the numbers are even
iq_test("1 2 1 1") => 2 // Second number is even, while the rest of the numbers are odd
```
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.
|
Solve the programming task below in a Python markdown code block.
Kate has a set $S$ of $n$ integers $\{1, \dots, n\} $.
She thinks that imperfection of a subset $M \subseteq S$ is equal to the maximum of $gcd(a, b)$ over all pairs $(a, b)$ such that both $a$ and $b$ are in $M$ and $a \neq b$.
Kate is a very neat girl and for each $k \in \{2, \dots, n\}$ she wants to find a subset that has the smallest imperfection among all subsets in $S$ of size $k$. There can be more than one subset with the smallest imperfection and the same size, but you don't need to worry about it. Kate wants to find all the subsets herself, but she needs your help to find the smallest possible imperfection for each size $k$, will name it $I_k$.
Please, help Kate to find $I_2$, $I_3$, ..., $I_n$.
-----Input-----
The first and only line in the input consists of only one integer $n$ ($2\le n \le 5 \cdot 10^5$) — the size of the given set $S$.
-----Output-----
Output contains only one line that includes $n - 1$ integers: $I_2$, $I_3$, ..., $I_n$.
-----Examples-----
Input
2
Output
1
Input
3
Output
1 1
-----Note-----
First sample: answer is 1, because $gcd(1, 2) = 1$.
Second sample: there are subsets of $S$ with sizes $2, 3$ with imperfection equal to 1. For example, $\{2,3\}$ and $\{1, 2, 3\}$.
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.
|
Solve the programming task below in a Python markdown code block.
Chef is fan of pairs and he likes all things that come in pairs. He even has a doll collection in which the dolls come in pairs. One day while going through his collection he found that there are odd number of dolls. Someone had stolen a doll!!!
Help chef find which type of doll is missing..
------ Input ------
The first line contains an integer T, the number of test cases.
The first line of each test case contains an integer N, the number of dolls.
The next N lines are the types of dolls that are left.
------ Output ------
For each test case, display the type of doll that doesn't have a pair, in a new line.
------ Constraints ------
1≤T≤10
1≤N≤100000 (10^{5})
0≤type≤100000
----- Sample Input 1 ------
1
3
1
2
1
----- Sample Output 1 ------
2
----- explanation 1 ------
----- Sample Input 2 ------
1
5
1
1
2
2
3
----- Sample Output 2 ------
3
----- explanation 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.
|
Solve the programming task below in a Python markdown code block.
A string is called palindrome if it reads the same from left to right and from right to left. For example "kazak", "oo", "r" and "mikhailrubinchikkihcniburliahkim" are palindroms, but strings "abb" and "ij" are not.
You are given string s consisting of lowercase Latin letters. At once you can choose any position in the string and change letter in that position to any other lowercase letter. So after each changing the length of the string doesn't change. At first you can change some letters in s. Then you can permute the order of letters as you want. Permutation doesn't count as changes.
You should obtain palindrome with the minimal number of changes. If there are several ways to do that you should get the lexicographically (alphabetically) smallest palindrome. So firstly you should minimize the number of changes and then minimize the palindrome lexicographically.
-----Input-----
The only line contains string s (1 ≤ |s| ≤ 2·10^5) consisting of only lowercase Latin letters.
-----Output-----
Print the lexicographically smallest palindrome that can be obtained with the minimal number of changes.
-----Examples-----
Input
aabc
Output
abba
Input
aabcd
Output
abcba
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.
|
Solve the programming task below in a Python markdown code block.
You might have heard about our new goodie distribution program aka the "Laddu Accrual System". This problem is designed to give you a glimpse of its rules. You can read the page once before attempting the problem if you wish, nonetheless we will be providing all the information needed here itself.
Laddu Accrual System is our new goodie distribution program. In this program, we will be distributing Laddus in place of goodies for your winnings and various other activities (described below), that you perform on our system. Once you collect enough number of Laddus, you can then redeem them to get yourself anything from a wide range of CodeChef goodies.
Let us know about various activities and amount of laddus you get corresponding to them.
- Contest Win (CodeChef’s Long, Cook-Off, LTIME, or any contest hosted with us) : 300 + Bonus (Bonus = 20 - contest rank). Note that if your rank is > 20, then you won't get any bonus.
- Top Contributor on Discuss : 300
- Bug Finder : 50 - 1000 (depending on the bug severity). It may also fetch you a CodeChef internship!
- Contest Hosting : 50
You can do a checkout for redeeming laddus once a month. The minimum laddus redeemable at Check Out are 200 for Indians and 400 for the rest of the world.
You are given history of various activities of a user. The user has not redeemed any of the its laddus accrued.. Now the user just wants to redeem as less amount of laddus he/she can, so that the laddus can last for as long as possible. Find out for how many maximum number of months he can redeem the laddus.
-----Input-----
- The first line of input contains a single integer T denoting number of test cases
- For each test case:
- First line contains an integer followed by a string denoting activities, origin respectively, where activities denotes number of activities of the user, origin denotes whether the user is Indian or the rest of the world. origin can be "INDIAN" or "NON_INDIAN".
- For each of the next activities lines, each line contains an activity.
An activity can be of four types as defined above.
- Contest Win : Input will be of form of CONTEST_WON rank, where rank denotes the rank of the user.
- Top Contributor : Input will be of form of TOP_CONTRIBUTOR.
- Bug Finder : Input will be of form of BUG_FOUND severity, where severity denotes the severity of the bug.
- Contest Hosting : Input will be of form of CONTEST_HOSTED.
-----Output-----
- For each test case, find out the maximum number of months for which the user can redeem the laddus accrued.
-----Constraints-----
- 1 ≤ T, activities ≤ 100
- 1 ≤ rank ≤ 5000
- 50 ≤ severity ≤ 1000
-----Subtasks-----
There is only a single subtask with 100 points.
-----Example-----
Input:
2
4 INDIAN
CONTEST_WON 1
TOP_CONTRIBUTOR
BUG_FOUND 100
CONTEST_HOSTED
4 NON_INDIAN
CONTEST_WON 1
TOP_CONTRIBUTOR
BUG_FOUND 100
CONTEST_HOSTED
Output:
3
1
-----Explanation-----
In the first example,
- For winning contest with rank 1, user gets 300 + 20 - 1 = 319 laddus.
- For top contributor, user gets 300 laddus.
- For finding a bug with severity of 100, user gets 100 laddus.
- For hosting a contest, user gets 50 laddus.
So, overall user gets 319 + 300 + 100 + 50 = 769 laddus.
Now, the user is an Indian user, he can redeem only 200 laddus per month. So, for first three months, he will redeem 200 * 3 = 600 laddus. The remaining 169 laddus, he can not redeem as he requires at least 200 laddues in a month to redeem.
So, answer is 3.
In the second example, user is a non-Indian user, he can redeem 400 laddues per month. So, in the first month, he will redeem 400 laddus. The remaining 369 laddus, he can not redeem as he requires at least 400 laddues in a month to redeem.
So, answer is 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.
|
Solve the programming task below in a Python markdown code block.
The only difference between easy and hard versions are constraints on $n$ and $k$.
You are messaging in one of the popular social networks via your smartphone. Your smartphone can show at most $k$ most recent conversations with your friends. Initially, the screen is empty (i.e. the number of displayed conversations equals $0$).
Each conversation is between you and some of your friends. There is at most one conversation with any of your friends. So each conversation is uniquely defined by your friend.
You (suddenly!) have the ability to see the future. You know that during the day you will receive $n$ messages, the $i$-th message will be received from the friend with ID $id_i$ ($1 \le id_i \le 10^9$).
If you receive a message from $id_i$ in the conversation which is currently displayed on the smartphone then nothing happens: the conversations of the screen do not change and do not change their order, you read the message and continue waiting for new messages.
Otherwise (i.e. if there is no conversation with $id_i$ on the screen): Firstly, if the number of conversations displayed on the screen is $k$, the last conversation (which has the position $k$) is removed from the screen. Now the number of conversations on the screen is guaranteed to be less than $k$ and the conversation with the friend $id_i$ is not displayed on the screen. The conversation with the friend $id_i$ appears on the first (the topmost) position on the screen and all the other displayed conversations are shifted one position down.
Your task is to find the list of conversations (in the order they are displayed on the screen) after processing all $n$ messages.
-----Input-----
The first line of the input contains two integers $n$ and $k$ ($1 \le n, k \le 200)$ — the number of messages and the number of conversations your smartphone can show.
The second line of the input contains $n$ integers $id_1, id_2, \dots, id_n$ ($1 \le id_i \le 10^9$), where $id_i$ is the ID of the friend which sends you the $i$-th message.
-----Output-----
In the first line of the output print one integer $m$ ($1 \le m \le min(n, k)$) — the number of conversations shown after receiving all $n$ messages.
In the second line print $m$ integers $ids_1, ids_2, \dots, ids_m$, where $ids_i$ should be equal to the ID of the friend corresponding to the conversation displayed on the position $i$ after receiving all $n$ messages.
-----Examples-----
Input
7 2
1 2 3 2 1 3 2
Output
2
2 1
Input
10 4
2 3 3 1 1 2 1 2 3 3
Output
3
1 3 2
-----Note-----
In the first example the list of conversations will change in the following way (in order from the first to last message): $[]$; $[1]$; $[2, 1]$; $[3, 2]$; $[3, 2]$; $[1, 3]$; $[1, 3]$; $[2, 1]$.
In the second example the list of conversations will change in the following way: $[]$; $[2]$; $[3, 2]$; $[3, 2]$; $[1, 3, 2]$; and then the list will not change till the end.
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.
|
Solve the programming task below in a Python markdown code block.
According to Berland laws it is only allowed to sell alcohol to people not younger than 18 years. Vasya's job is to monitor the law's enforcement. Tonight he entered a bar and saw n people sitting there. For every one of them Vasya happened to determine either the age or the drink the person is having. Vasya can check any person, i.e. learn his age and the drink he is having at the same time. What minimal number of people should Vasya check additionally to make sure that there are no clients under 18 having alcohol drinks?
The list of all alcohol drinks in Berland is: ABSINTH, BEER, BRANDY, CHAMPAGNE, GIN, RUM, SAKE, TEQUILA, VODKA, WHISKEY, WINE
Input
The first line contains an integer n (1 ≤ n ≤ 100) which is the number of the bar's clients. Then follow n lines, each describing one visitor. A line either contains his age (an integer from 0 to 1000) or his drink (a string of capital Latin letters from 1 to 100 in length). It is guaranteed that the input data does not contain spaces and other unnecessary separators.
Only the drinks from the list given above should be considered alcohol.
Output
Print a single number which is the number of people Vasya should check to guarantee the law enforcement.
Examples
Input
5
18
VODKA
COKE
19
17
Output
2
Note
In the sample test the second and fifth clients should be checked.
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.
|
Solve the programming task below in a Python markdown code block.
You are given a sequence $a_1, a_2, \dots, a_n$ consisting of $n$ integers.
You may perform the following operation on this sequence: choose any element and either increase or decrease it by one.
Calculate the minimum possible difference between the maximum element and the minimum element in the sequence, if you can perform the aforementioned operation no more than $k$ times.
-----Input-----
The first line contains two integers $n$ and $k$ $(2 \le n \le 10^{5}, 1 \le k \le 10^{14})$ — the number of elements in the sequence and the maximum number of times you can perform the operation, respectively.
The second line contains a sequence of integers $a_1, a_2, \dots, a_n$ $(1 \le a_i \le 10^{9})$.
-----Output-----
Print the minimum possible difference between the maximum element and the minimum element in the sequence, if you can perform the aforementioned operation no more than $k$ times.
-----Examples-----
Input
4 5
3 1 7 5
Output
2
Input
3 10
100 100 100
Output
0
Input
10 9
4 5 5 7 5 4 5 2 4 3
Output
1
-----Note-----
In the first example you can increase the first element twice and decrease the third element twice, so the sequence becomes $[3, 3, 5, 5]$, and the difference between maximum and minimum is $2$. You still can perform one operation after that, but it's useless since you can't make the answer less than $2$.
In the second example all elements are already equal, so you may get $0$ as the answer even without applying any operations.
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.
|
Solve the programming task below in a Python markdown code block.
In this problem is used an extremely simplified version of HTML table markup. Please use the statement as a formal document and read it carefully.
A string is a bHTML table, if it satisfies the grammar:
TABLE ::= <table>ROWS</table>
ROWS ::= ROW | ROW ROWS
ROW ::= <tr>CELLS</tr>
CELLS ::= CELL | CELL CELLS
CELL ::= <td></td> | <td>TABLE</td>
Blanks in the grammar are only for purposes of illustration, in the given data there will be no spaces. The bHTML table is very similar to a simple regular HTML table in which meet only the following tags : "table", "tr", "td", all the tags are paired and the table contains at least one row and at least one cell in each row. Have a look at the sample tests as examples of tables.
As can be seen, the tables may be nested. You are given a table (which may contain other(s)). You need to write a program that analyzes all the tables and finds the number of cells in each of them. The tables are not required to be rectangular.
Input
For convenience, input data can be separated into non-empty lines in an arbitrary manner. The input data consist of no more than 10 lines. Combine (concatenate) all the input lines into one, to get a text representation s of the specified table. String s corresponds to the given grammar (the root element of grammar is TABLE), its length does not exceed 5000. Only lower case letters are used to write tags. There are no spaces in the given string s.
Output
Print the sizes of all the tables in the non-decreasing order.
Examples
Input
<table><tr><td></td></tr></table>
Output
1
Input
<table>
<tr>
<td>
<table><tr><td></td></tr><tr><td></
td
></tr><tr
><td></td></tr><tr><td></td></tr></table>
</td>
</tr>
</table>
Output
1 4
Input
<table><tr><td>
<table><tr><td>
<table><tr><td>
<table><tr><td></td><td></td>
</tr><tr><td></td></tr></table>
</td></tr></table>
</td></tr></table>
</td></tr></table>
Output
1 1 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.
|
Solve the programming task below in a Python markdown code block.
Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:
* He never visits a point with coordinate less than 0, or a point with coordinate greater than L.
* He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.
* He only changes direction at a point with integer coordinate.
Each time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.
After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:
* Put a stone in one of Snuke's ears.
* Remove a stone from one of Snuke's ears.
Find the minimum number of operations required when Ringo can freely decide how Snuke walks.
Constraints
* 1 \leq L \leq 2\times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq L)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
L
A_1
:
A_L
Output
Print the minimum number of operations required when Ringo can freely decide how Snuke walks.
Examples
Input
4
1
0
2
3
Output
1
Input
8
2
0
0
2
1
3
4
1
Output
3
Input
7
314159265
358979323
846264338
327950288
419716939
937510582
0
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.
|
Solve the programming task below in a Python markdown code block.
In one of the games Arkady is fond of the game process happens on a rectangular field. In the game process Arkady can buy extensions for his field, each extension enlarges one of the field sizes in a particular number of times. Formally, there are n extensions, the i-th of them multiplies the width or the length (by Arkady's choice) by a_{i}. Each extension can't be used more than once, the extensions can be used in any order.
Now Arkady's field has size h × w. He wants to enlarge it so that it is possible to place a rectangle of size a × b on it (along the width or along the length, with sides parallel to the field sides). Find the minimum number of extensions needed to reach Arkady's goal.
-----Input-----
The first line contains five integers a, b, h, w and n (1 ≤ a, b, h, w, n ≤ 100 000) — the sizes of the rectangle needed to be placed, the initial sizes of the field and the number of available extensions.
The second line contains n integers a_1, a_2, ..., a_{n} (2 ≤ a_{i} ≤ 100 000), where a_{i} equals the integer a side multiplies by when the i-th extension is applied.
-----Output-----
Print the minimum number of extensions needed to reach Arkady's goal. If it is not possible to place the rectangle on the field with all extensions, print -1. If the rectangle can be placed on the initial field, print 0.
-----Examples-----
Input
3 3 2 4 4
2 5 4 10
Output
1
Input
3 3 3 3 5
2 3 5 4 2
Output
0
Input
5 5 1 2 3
2 2 3
Output
-1
Input
3 4 1 1 3
2 3 2
Output
3
-----Note-----
In the first example it is enough to use any of the extensions available. For example, we can enlarge h in 5 times using the second extension. Then h becomes equal 10 and it is now possible to place the rectangle on the field.
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.
|
Solve the programming task below in a Python markdown code block.
One day shooshuns found a sequence of n integers, written on a blackboard. The shooshuns can perform one operation with it, the operation consists of two steps:
1. Find the number that goes k-th in the current sequence and add the same number to the end of the sequence;
2. Delete the first number of the current sequence.
The shooshuns wonder after how many operations all numbers on the board will be the same and whether all numbers will ever be the same.
Input
The first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 105).
The second line contains n space-separated integers: a1, a2, ..., an (1 ≤ ai ≤ 105) — the sequence that the shooshuns found.
Output
Print the minimum number of operations, required for all numbers on the blackboard to become the same. If it is impossible to achieve, print -1.
Examples
Input
3 2
3 1 1
Output
1
Input
3 1
3 1 1
Output
-1
Note
In the first test case after the first operation the blackboard will have sequence [1, 1, 1]. So, one operation is enough to make all numbers the same. Thus, the answer equals one.
In the second test case the sequence will never consist of the same numbers. It will always contain at least two distinct numbers 3 and 1. Thus, the answer equals -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.
|
Solve the programming task below in a Python markdown code block.
Mr. A, who will graduate next spring, decided to move when he got a job. The company that finds a job has offices in several towns, and the offices that go to work differ depending on the day. So Mr. A decided to live in a town where he had a short time to go to any office.
So you decided to find the most convenient town to live in to help Mr. A.
<image>
Towns are numbered starting with 0 and there is a road between towns. Commuting time is fixed for each road. If Mr. A lives in a town, the commuting time to the office in his town is 0. At this time, consider the total commuting time to all towns. For example, if the layout of towns and roads is as shown in the figure above and Mr. A lives in town 1, the commuting time to each town will be
Town 0 to 80
0 to town 1
Up to town 2 20
Up to town 3 70
Town 4 to 90
And the sum is 260.
Enter the number of roads and information on all roads, calculate the total commuting time when living in each town, and output the number of the town that minimizes it and the total commuting time at that time. Create a program. However, if there are multiple towns with the smallest total commuting time, please output the number of the smallest town and the total commuting time at that time. The total number of towns is 10 or less, the total number of roads is 45 or less, all roads can move in both directions, and commuting time does not change depending on the direction. We also assume that there are routes from any town to all other towns.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
a1 b1 c1
a2 b2 c2
::
an bn cn
The number of roads n (1 ≤ n ≤ 45) is given on the first line. The following n lines give information on the i-th way. ai, bi (0 ≤ ai, bi ≤ 9) is the number of the town to which the i-th road connects, and ci (0 ≤ ci ≤ 100) is the commute time for that road.
Output
For each data set, the town number that minimizes the total commuting time and the total commuting time at that time are output on one line separated by blanks.
Example
Input
6
0 1 80
1 2 20
0 2 60
2 3 50
3 4 60
1 4 90
2
0 1 1
1 2 1
0
Output
2 240
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.
|
Solve the programming task below in a Python markdown code block.
Let's define a forest as a non-directed acyclic graph (also without loops and parallel edges). One day Misha played with the forest consisting of n vertices. For each vertex v from 0 to n - 1 he wrote down two integers, degreev and sv, were the first integer is the number of vertices adjacent to vertex v, and the second integer is the XOR sum of the numbers of vertices adjacent to v (if there were no adjacent vertices, he wrote down 0).
Next day Misha couldn't remember what graph he initially had. Misha has values degreev and sv left, though. Help him find the number of edges and the edges of the initial graph. It is guaranteed that there exists a forest that corresponds to the numbers written by Misha.
Input
The first line contains integer n (1 ≤ n ≤ 216), the number of vertices in the graph.
The i-th of the next lines contains numbers degreei and si (0 ≤ degreei ≤ n - 1, 0 ≤ si < 216), separated by a space.
Output
In the first line print number m, the number of edges of the graph.
Next print m lines, each containing two distinct numbers, a and b (0 ≤ a ≤ n - 1, 0 ≤ b ≤ n - 1), corresponding to edge (a, b).
Edges can be printed in any order; vertices of the edge can also be printed in any order.
Examples
Input
3
2 3
1 0
1 0
Output
2
1 0
2 0
Input
2
1 1
1 0
Output
1
0 1
Note
The XOR sum of numbers is the result of bitwise adding numbers modulo 2. This operation exists in many modern programming languages. For example, in languages C++, Java and Python it is represented as "^", and in Pascal — as "xor".
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.
|
Solve the programming task below in a Python markdown code block.
B: Dansunau www --Dance Now!-
story
Last lab life! Daigakuin! !! Dosanko Snow has won 9th place in the event "Master Idol World", which can be said to be the outpost of the biggest competition "Lab Life" where master idols compete. The sharp dance is ridiculed as "9th place dance", and the whole body's deciding pose is also ridiculed as "9th place stance", which causes deep emotional wounds. In the upcoming Lab Life Preliminary Qualifying, we can never take 9th place ... Dosanko Snow, who renewed his determination, refined his special skill "self-control" and headed for the battlefield. ..
problem
A tournament "Lab Life" will be held in which N groups of units compete. In this tournament, the three divisions of Smile Pure Cool will be played separately, and the overall ranking will be decided in descending order of the total points scored in each game. The ranking of the smile category is determined in descending order of the smile value of each unit. Similarly, in the pure / cool category, the ranking is determined in descending order of pure / cool value. The score setting according to the ranking is common to all divisions, and the unit ranked i in a division gets r_i points in that division.
Here, if there are a plurality of units having the same value as the unit with the rank i, they are regarded as the same rate i rank, and the points r_i are equally obtained. More specifically, when k units are in the same ratio i position, k units get equal points r_i, and no unit gets points from r_ {i + 1} to r_ {i + k-1}. Also, the next largest unit (s) gets the score r_ {i + k}. As a specific example, consider a case where there are five units with smile values of 1, 3, 2, 3, and 2, and 10, 8, 6, 4, and 2 points are obtained in descending order of rank. At this time, the 2nd and 4th units will get 10 points, the 3rd and 5th units will get 6 points, and the 1st unit will get 2 points.
Unit Dosanko Snow, who participates in the Lab Life Preliminary Qualifying, thinks that "Lab Life is not a play", so he entered the tournament first and became the first unit. However, when we obtained information on the smile value, pure value, and cool value (hereinafter referred to as 3 values) of all N groups participating in the tournament, we found that their overall ranking was (equal rate) 9th. Dosanko Snow can raise any one of the three values by the special skill "Self Control", but if you raise it too much, you will get tired and it will affect the main battle, so you want to make the rise value as small as possible. Dosanko Snow wants to get out of 9th place anyway, so when you raise any one of the 3 values by self-control so that it will be 8th or higher at the same rate, find the minimum value that needs to be raised.
Input format
The input is given in the following format.
N
r_1 ... r_N
s_1 p_1 c_1
...
s_N p_N c_N
The first line is given the integer N, which represents the number of units, in one line. The second line that follows is given N integers separated by blanks. The i (1 \ leq i \ leq N) th integer represents the score r_i that can be obtained when the ranking is i in each division. Of the following Nth line, the jth line is given three integers s_j, p_j, c_j. These represent the smile value s_j, pure value p_j, and cool value c_j of the jth unit, respectively. Dosanko Snow is the first unit.
Constraint
* 9 \ leq N \ leq 100
* 100 \ geq r_1> ...> r_N \ geq 1
* 1 \ leq s_j, p_j, c_j \ leq 100 (1 \ leq j \ leq N)
* Before self-control, Dosanko Snow was 9th (sometimes 9th, but never more than 8th)
Output format
By increasing any of the three values by x by self-control, output the minimum x that makes Dosanko Snow 8th or higher at the same rate on one line. However, if self-control does not raise the ranking no matter how much you raise it, output "Saiko".
Input example 1
9
9 8 7 6 5 4 3 2 1
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
Output example 1
2
For example, if you raise the smile value by 2 by self-control, the rankings in each division of Dosanko Snow will be 7th, 9th, and 9th, respectively, and you will get 3 + 1 + 1 = 5 points. On the other hand, the ranking of the second unit in each division is 9th, 8th, and 8th, respectively, and 1 + 2 + 2 = 5 points are obtained. Since the other units get 6 points or more, these two units will be ranked 8th at the same rate, satisfying the conditions.
Input example 2
9
9 8 7 6 5 4 3 2 1
1 1 1
2 6 9
6 9 2
9 2 6
3 5 8
5 8 3
8 3 5
4 7 4
7 4 7
Output example 2
Saiko
No matter how much you raise the value, Dosanko Snow can only get up to 11 points, but other units can always get 14 points or more, so Dosanko Snow is immovable in 9th place.
Example
Input
9
9 8 7 6 5 4 3 2 1
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
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.
|
Solve the programming task below in a Python markdown code block.
Write a function that takes a positive integer and returns the next smaller positive integer containing the same digits.
For example:
```python
next_smaller(21) == 12
next_smaller(531) == 513
next_smaller(2071) == 2017
```
Return -1 (for `Haskell`: return `Nothing`, for `Rust`: return `None`), when there is no smaller number that contains the same digits. Also return -1 when the next smaller number with the same digits would require the leading digit to be zero.
```python
next_smaller(9) == -1
next_smaller(135) == -1
next_smaller(1027) == -1 # 0721 is out since we don't write numbers with leading zeros
```
```ruby
next_smaller(9) == -1
next_smaller(135) == -1
next_smaller(1027) == -1 # 0721 is out since we don't write numbers with leading zeros
```
* some tests will include very large numbers.
* test data only employs positive integers.
*The function you write for this challenge is the inverse of this kata: "[Next bigger number with the same digits](http://www.codewars.com/kata/next-bigger-number-with-the-same-digits)."*
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.
|
Solve the programming task below in a Python markdown code block.
problem
Five students, Taro, Jiro, Saburo, Shiro, and Hanako, participated in the JOI High School class.
In this class, a final exam was conducted. All five people took the final exam. For students with a final exam score of 40 or higher, the final exam score was used as is. All students with a final exam score of less than 40 received supplementary lessons and scored 40 points.
Create a program that calculates the average score of the five students' grades given the final exam scores of the five students.
Example
Input
10
65
100
30
95
Output
68
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.
|
Solve the programming task below in a Python markdown code block.
Write a program which computes the greatest common divisor (GCD) and the least common multiple (LCM) of given a and b.
Constraints
* 0 < a, b ≤ 2,000,000,000
* LCM(a, b) ≤ 2,000,000,000
* The number of data sets ≤ 50
Input
Input consists of several data sets. Each data set contains a and b separated by a single space in a line. The input terminates with EOF.
Output
For each data set, print GCD and LCM separated by a single space in a line.
Example
Input
8 6
50000000 30000000
Output
2 24
10000000 150000000
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.
|
Solve the programming task below in a Python markdown code block.
You have a string s = s_1s_2...s_{|}s|, where |s| is the length of string s, and s_{i} its i-th character.
Let's introduce several definitions: A substring s[i..j] (1 ≤ i ≤ j ≤ |s|) of string s is string s_{i}s_{i} + 1...s_{j}. The prefix of string s of length l (1 ≤ l ≤ |s|) is string s[1..l]. The suffix of string s of length l (1 ≤ l ≤ |s|) is string s[|s| - l + 1..|s|].
Your task is, for any prefix of string s which matches a suffix of string s, print the number of times it occurs in string s as a substring.
-----Input-----
The single line contains a sequence of characters s_1s_2...s_{|}s| (1 ≤ |s| ≤ 10^5) — string s. The string only consists of uppercase English letters.
-----Output-----
In the first line, print integer k (0 ≤ k ≤ |s|) — the number of prefixes that match a suffix of string s. Next print k lines, in each line print two integers l_{i} c_{i}. Numbers l_{i} c_{i} mean that the prefix of the length l_{i} matches the suffix of length l_{i} and occurs in string s as a substring c_{i} times. Print pairs l_{i} c_{i} in the order of increasing l_{i}.
-----Examples-----
Input
ABACABA
Output
3
1 4
3 2
7 1
Input
AAA
Output
3
1 3
2 2
3 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.
|
Solve the programming task below in a Python markdown code block.
You manage 4 buildings, each of which has 3 floors, each of which consists of 10 rooms. Write a program which reads a sequence of tenant/leaver notices, and reports the number of tenants for each room.
For each notice, you are given four integers b, f, r and v which represent that v persons entered to room r of fth floor at building b. If v is negative, it means that −v persons left.
Assume that initially no person lives in the building.
Constraints
* No incorrect building, floor and room numbers are given.
* 0 ≤ the number of tenants during the management ≤ 9
Input
In the first line, the number of notices n is given. In the following n lines, a set of four integers b, f, r and v which represents ith notice is given in a line.
Output
For each building, print the information of 1st, 2nd and 3rd floor in this order. For each floor information, print the number of tenants of 1st, 2nd, .. and 10th room in this order. Print a single space character before the number of tenants. Print "####################" (20 '#') between buildings.
Example
Input
3
1 1 3 8
3 2 2 7
4 3 8 1
Output
0 0 8 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
####################
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
####################
0 0 0 0 0 0 0 0 0 0
0 7 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
####################
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 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.
|
Solve the programming task below in a Python markdown code block.
Takahashi has a lot of peculiar devices. These cylindrical devices receive balls from left and right. Each device is in one of the two states A and B, and for each state, the device operates as follows:
* When a device in state A receives a ball from either side (left or right), the device throws out the ball from the same side, then immediately goes into state B.
* When a device in state B receives a ball from either side, the device throws out the ball from the other side, then immediately goes into state A.
The transition of the state of a device happens momentarily and always completes before it receives another ball.
Takahashi built a contraption by concatenating N of these devices. In this contraption,
* A ball that was thrown out from the right side of the i-th device from the left (1 \leq i \leq N-1) immediately enters the (i+1)-th device from the left side.
* A ball that was thrown out from the left side of the i-th device from the left (2 \leq i \leq N) immediately enters the (i-1)-th device from the right side.
The initial state of the i-th device from the left is represented by the i-th character in a string S. From this situation, Takahashi performed the following K times: put a ball into the leftmost device from the left side, then wait until the ball comes out of the contraption from either end. Here, it can be proved that the ball always comes out of the contraption after a finite time. Find the state of each device after K balls are processed.
Constraints
* 1 \leq N \leq 200,000
* 1 \leq K \leq 10^9
* |S|=N
* Each character in S is either `A` or `B`.
Input
The input is given from Standard Input in the following format:
N K
S
Output
Print a string that represents the state of each device after K balls are processed. The string must be N characters long, and the i-th character must correspond to the state of the i-th device from the left.
Examples
Input
5 1
ABAAA
Output
BBAAA
Input
5 2
ABAAA
Output
ABBBA
Input
4 123456789
AABB
Output
BABA
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.
|
Solve the programming task below in a Python markdown code block.
See the following triangle:
```
____________________________________
1
2 4 2
3 6 9 6 3
4 8 12 16 12 8 4
5 10 15 20 25 20 15 10 5
___________________________________
```
The total sum of the numbers in the triangle, up to the 5th line included, is ```225```, part of it, ```144```, corresponds to the total sum of the even terms and ```81``` to the total sum of the odd terms.
Create a function that may output an array with three results for each value of n.
```python
triang_mult(n) ----> [total_sum, total_even_sum, total_odd_sum]
```
Our example will be:
```python
triang_mult(5) ----> [225, 144, 81]
```
Features of the random tests:
```
number of tests = 100
49 < n < 5000
```
Enjoy it!
This kata will be translated in another languages soon
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.
|
Solve the programming task below in a Python markdown code block.
Step through my `green glass door`.
You can take the `moon`, but not the `sun`.
You can take your `slippers`, but not your `sandals`.
You can go through `yelling`, but not `shouting`.
You can't run through `fast`, but you can run with `speed`.
You can take a `sheet`, but not your `blanket`.
You can wear your `glasses`, but not your `contacts`.
Have you figured it out? Good! Then write a program that can figure it out as well.
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.
|
Solve the programming task below in a Python markdown code block.
You are given a string S of length 2N, containing N occurrences of `a` and N occurrences of `b`.
You will choose some of the characters in S. Here, for each i = 1,2,...,N, it is not allowed to choose exactly one of the following two: the i-th occurrence of `a` and the i-th occurrence of `b`. (That is, you can only choose both or neither.) Then, you will concatenate the chosen characters (without changing the order).
Find the lexicographically largest string that can be obtained in this way.
Constraints
* 1 \leq N \leq 3000
* S is a string of length 2N containing N occurrences of `a` and N occurrences of `b`.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the lexicographically largest string that satisfies the condition.
Examples
Input
3
aababb
Output
abab
Input
3
bbabaa
Output
bbabaa
Input
6
bbbaabbabaaa
Output
bbbabaaa
Input
9
abbbaababaababbaba
Output
bbaababababa
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.
|
Solve the programming task below in a Python markdown code block.
10^{10^{10}} participants, including Takahashi, competed in two programming contests.
In each contest, all participants had distinct ranks from first through 10^{10^{10}}-th.
The score of a participant is the product of his/her ranks in the two contests.
Process the following Q queries:
- In the i-th query, you are given two positive integers A_i and B_i. Assuming that Takahashi was ranked A_i-th in the first contest and B_i-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's.
-----Constraints-----
- 1 \leq Q \leq 100
- 1\leq A_i,B_i\leq 10^9(1\leq i\leq Q)
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
Q
A_1 B_1
:
A_Q B_Q
-----Output-----
For each query, print the maximum possible number of participants whose scores are smaller than Takahashi's.
-----Sample Input-----
8
1 4
10 5
3 3
4 11
8 9
22 40
8 36
314159265 358979323
-----Sample Output-----
1
12
4
11
14
57
31
671644785
Let us denote a participant who was ranked x-th in the first contest and y-th in the second contest as (x,y).
In the first query, (2,1) is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print 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.
|
Solve the programming task below in a Python markdown code block.
After you had helped Fedor to find friends in the «Call of Soldiers 3» game, he stopped studying completely. Today, the English teacher told him to prepare an essay. Fedor didn't want to prepare the essay, so he asked Alex for help. Alex came to help and wrote the essay for Fedor. But Fedor didn't like the essay at all. Now Fedor is going to change the essay using the synonym dictionary of the English language.
Fedor does not want to change the meaning of the essay. So the only change he would do: change a word from essay to one of its synonyms, basing on a replacement rule from the dictionary. Fedor may perform this operation any number of times.
As a result, Fedor wants to get an essay which contains as little letters «R» (the case doesn't matter) as possible. If there are multiple essays with minimum number of «R»s he wants to get the one with minimum length (length of essay is the sum of the lengths of all the words in it). Help Fedor get the required essay.
Please note that in this problem the case of letters doesn't matter. For example, if the synonym dictionary says that word cat can be replaced with word DOG, then it is allowed to replace the word Cat with the word doG.
-----Input-----
The first line contains a single integer m (1 ≤ m ≤ 10^5) — the number of words in the initial essay. The second line contains words of the essay. The words are separated by a single space. It is guaranteed that the total length of the words won't exceed 10^5 characters.
The next line contains a single integer n (0 ≤ n ≤ 10^5) — the number of pairs of words in synonym dictionary. The i-th of the next n lines contains two space-separated non-empty words x_{i} and y_{i}. They mean that word x_{i} can be replaced with word y_{i} (but not vise versa). It is guaranteed that the total length of all pairs of synonyms doesn't exceed 5·10^5 characters.
All the words at input can only consist of uppercase and lowercase letters of the English alphabet.
-----Output-----
Print two integers — the minimum number of letters «R» in an optimal essay and the minimum length of an optimal essay.
-----Examples-----
Input
3
AbRb r Zz
4
xR abRb
aA xr
zz Z
xr y
Output
2 6
Input
2
RuruRu fedya
1
ruruRU fedor
Output
1 10
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.
|
Solve the programming task below in a Python markdown code block.
Gerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.
One day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?
The formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of n marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least n marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want.
Input
The single line contains a single integer n (1 ≤ n ≤ 1017).
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.
Output
In a single line print an integer: the maximum number of coins the unlucky buyer could have paid with.
Examples
Input
1
Output
1
Input
4
Output
2
Note
In the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.
In the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives.
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.
|
Solve the programming task below in a Python markdown code block.
N of us are going on a trip, by train or taxi.
The train will cost each of us A yen (the currency of Japan).
The taxi will cost us a total of B yen.
How much is our minimum total travel expense?
-----Constraints-----
- All values in input are integers.
- 1 \leq N \leq 20
- 1 \leq A \leq 50
- 1 \leq B \leq 50
-----Input-----
Input is given from Standard Input in the following format:
N A B
-----Output-----
Print an integer representing the minimum total travel expense.
-----Sample Input-----
4 2 9
-----Sample Output-----
8
The train will cost us 4 \times 2 = 8 yen, and the taxi will cost us 9 yen, so the minimum total travel expense is 8 yen.
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.
|
Solve the programming task below in a Python markdown code block.
Pari wants to buy an expensive chocolate from Arya. She has n coins, the value of the i-th coin is c_{i}. The price of the chocolate is k, so Pari will take a subset of her coins with sum equal to k and give it to Arya.
Looking at her coins, a question came to her mind: after giving the coins to Arya, what values does Arya can make with them? She is jealous and she doesn't want Arya to make a lot of values. So she wants to know all the values x, such that Arya will be able to make x using some subset of coins with the sum k.
Formally, Pari wants to know the values x such that there exists a subset of coins with the sum k such that some subset of this subset has the sum x, i.e. there is exists some way to pay for the chocolate, such that Arya will be able to make the sum x using these coins.
-----Input-----
The first line contains two integers n and k (1 ≤ n, k ≤ 500) — the number of coins and the price of the chocolate, respectively.
Next line will contain n integers c_1, c_2, ..., c_{n} (1 ≤ c_{i} ≤ 500) — the values of Pari's coins.
It's guaranteed that one can make value k using these coins.
-----Output-----
First line of the output must contain a single integer q— the number of suitable values x. Then print q integers in ascending order — the values that Arya can make for some subset of coins of Pari that pays for the chocolate.
-----Examples-----
Input
6 18
5 6 1 10 12 2
Output
16
0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18
Input
3 50
25 25 50
Output
3
0 25 50
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.
|
Solve the programming task below in a Python markdown code block.
Write a program which reads three integers a, b and c, and prints "Yes" if a < b < c, otherwise "No".
Constraints
* 0 ≤ a, b, c ≤ 100
Input
Three integers a, b and c separated by a single space are given in a line.
Output
Print "Yes" or "No" in a line.
Examples
Input
1 3 8
Output
Yes
Input
3 8 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.
|
Solve the programming task below in a Python markdown code block.
A population of bears consists of black bears, brown bears, and white bears.
The input is an array of two elements.
Determine whether the offspring of the two bears will return `'black'`, `'brown'`, `'white'`, `'dark brown'`, `'grey'`, `'light brown'`, or `'unknown'`.
Elements in the the array will always be a string.
## Examples:
bear_fur(['black', 'black']) returns 'black'
bear_fur(['brown', 'brown']) returns 'brown'
bear_fur(['white', 'white']) returns 'white'
bear_fur(['black', 'brown']) returns 'dark brown'
bear_fur(['black', 'white']) returns 'grey'
bear_fur(['brown', 'white']) returns 'light brown'
bear_fur(['yellow', 'magenta']) returns 'unknown'
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.
|
Solve the programming task below in a Python markdown code block.
You're given an array $a$. You should repeat the following operation $k$ times: find the minimum non-zero element in the array, print it, and then subtract it from all the non-zero elements of the array. If all the elements are 0s, just print 0.
-----Input-----
The first line contains integers $n$ and $k$ $(1 \le n,k \le 10^5)$, the length of the array and the number of operations you should perform.
The second line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ $(1 \le a_i \le 10^9)$, the elements of the array.
-----Output-----
Print the minimum non-zero element before each operation in a new line.
-----Examples-----
Input
3 5
1 2 3
Output
1
1
1
0
0
Input
4 2
10 3 5 3
Output
3
2
-----Note-----
In the first sample:
In the first step: the array is $[1,2,3]$, so the minimum non-zero element is 1.
In the second step: the array is $[0,1,2]$, so the minimum non-zero element is 1.
In the third step: the array is $[0,0,1]$, so the minimum non-zero element is 1.
In the fourth and fifth step: the array is $[0,0,0]$, so we printed 0.
In the second sample:
In the first step: the array is $[10,3,5,3]$, so the minimum non-zero element is 3.
In the second step: the array is $[7,0,2,0]$, so the minimum non-zero element is 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.
|
Solve the programming task below in a Python markdown code block.
Recently Vladik discovered a new entertainment — coding bots for social networks. He would like to use machine learning in his bots so now he want to prepare some learning data for them.
At first, he need to download t chats. Vladik coded a script which should have downloaded the chats, however, something went wrong. In particular, some of the messages have no information of their sender. It is known that if a person sends several messages in a row, they all are merged into a single message. It means that there could not be two or more messages in a row with the same sender. Moreover, a sender never mention himself in his messages.
Vladik wants to recover senders of all the messages so that each two neighboring messages will have different senders and no sender will mention himself in his messages.
He has no idea of how to do this, and asks you for help. Help Vladik to recover senders in each of the chats!
-----Input-----
The first line contains single integer t (1 ≤ t ≤ 10) — the number of chats. The t chats follow. Each chat is given in the following format.
The first line of each chat description contains single integer n (1 ≤ n ≤ 100) — the number of users in the chat.
The next line contains n space-separated distinct usernames. Each username consists of lowercase and uppercase English letters and digits. The usernames can't start with a digit. Two usernames are different even if they differ only with letters' case. The length of username is positive and doesn't exceed 10 characters.
The next line contains single integer m (1 ≤ m ≤ 100) — the number of messages in the chat. The next m line contain the messages in the following formats, one per line: <username>:<text> — the format of a message with known sender. The username should appear in the list of usernames of the chat. <?>:<text> — the format of a message with unknown sender.
The text of a message can consist of lowercase and uppercase English letter, digits, characters '.' (dot), ',' (comma), '!' (exclamation mark), '?' (question mark) and ' ' (space). The text doesn't contain trailing spaces. The length of the text is positive and doesn't exceed 100 characters.
We say that a text mention a user if his username appears in the text as a word. In other words, the username appears in a such a position that the two characters before and after its appearance either do not exist or are not English letters or digits. For example, the text "Vasya, masha13 and Kate!" can mention users "Vasya", "masha13", "and" and "Kate", but not "masha".
It is guaranteed that in each chat no known sender mention himself in his messages and there are no two neighboring messages with the same known sender.
-----Output-----
Print the information about the t chats in the following format:
If it is not possible to recover senders, print single line "Impossible" for this chat. Otherwise print m messages in the following format:
<username>:<text>
If there are multiple answers, print any of them.
-----Examples-----
Input
1
2
Vladik netman
2
?: Hello, Vladik!
?: Hi
Output
netman: Hello, Vladik!
Vladik: Hi
Input
1
2
netman vladik
3
netman:how are you?
?:wrong message
vladik:im fine
Output
Impossible
Input
2
3
netman vladik Fedosik
2
?: users are netman, vladik, Fedosik
vladik: something wrong with this chat
4
netman tigerrrrr banany2001 klinchuh
4
?: tigerrrrr, banany2001, klinchuh, my favourite team ever, are you ready?
klinchuh: yes, coach!
?: yes, netman
banany2001: yes of course.
Output
Impossible
netman: tigerrrrr, banany2001, klinchuh, my favourite team ever, are you ready?
klinchuh: yes, coach!
tigerrrrr: yes, netman
banany2001: yes of course.
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.
|
Solve the programming task below in a Python markdown code block.
Arithmetic Progressions
An arithmetic progression is a sequence of numbers $a_1, a_2, ..., a_k$ where the difference of consecutive members $a_{i+1} - a_i$ is a constant ($1 \leq i \leq k-1$). For example, the sequence 5, 8, 11, 14, 17 is an arithmetic progression of length 5 with the common difference 3.
In this problem, you are requested to find the longest arithmetic progression which can be formed selecting some numbers from a given set of numbers. For example, if the given set of numbers is {0, 1, 3, 5, 6, 9}, you can form arithmetic progressions such as 0, 3, 6, 9 with the common difference 3, or 9, 5, 1 with the common difference -4. In this case, the progressions 0, 3, 6, 9 and 9, 6, 3, 0 are the longest.
Input
The input consists of a single test case of the following format.
$n$
$v_1$ $v_2$ ... $v_n$
$n$ is the number of elements of the set, which is an integer satisfying $2 \leq n \leq 5000$. Each $v_i$ ($1 \leq i \leq n$) is an element of the set, which is an integer satisfying $0 \leq v_i \leq 10^9$. $v_i$'s are all different, i.e., $v_i \ne v_j$ if $i \ne j$.
Output
Output the length of the longest arithmetic progressions which can be formed selecting some numbers from the given set of numbers.
Sample Input 1
6
0 1 3 5 6 9
Sample Output 1
4
Sample Input 2
7
1 4 7 3 2 6 5
Sample Output 2
7
Sample Input 3
5
1 2 4 8 16
Sample Output 3
2
Example
Input
6
0 1 3 5 6 9
Output
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.
|
Solve the programming task below in a Python markdown code block.
A triple of numbers is said to be poor when two of those numbers are equal but the other number is different from those two numbers.
You will be given three integers A, B, and C. If this triple is poor, print Yes; otherwise, print No.
-----Constraints-----
- A, B, and C are all integers between 1 and 9 (inclusive).
-----Input-----
Input is given from Standard Input in the following format:
A B C
-----Output-----
If the given triple is poor, print Yes; otherwise, print No.
-----Sample Input-----
5 7 5
-----Sample Output-----
Yes
A and C are equal, but B is different from those two numbers, so this triple is poor.
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.
|
Solve the programming task below in a Python markdown code block.
Takahashi and Aoki are going to together construct a sequence of integers.
First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:
- The length of a is N.
- Each element in a is an integer between 1 and K, inclusive.
- a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.
Then, Aoki will perform the following operation an arbitrary number of times:
- Move the first element in a to the end of a.
How many sequences a can be obtained after this procedure, modulo 10^9+7?
-----Constraints-----
- 1≤N≤10^9
- 1≤K≤10^9
-----Input-----
The input is given from Standard Input in the following format:
N K
-----Output-----
Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.
-----Sample Input-----
4 2
-----Sample Output-----
6
The following six sequences can be obtained:
- (1, 1, 1, 1)
- (1, 1, 2, 2)
- (1, 2, 2, 1)
- (2, 2, 1, 1)
- (2, 1, 1, 2)
- (2, 2, 2, 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.
|
Solve the programming task below in a Python markdown code block.
We have N+1 integers: 10^{100}, 10^{100}+1, ..., 10^{100}+N.
We will choose K or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo (10^9+7).
-----Constraints-----
- 1 \leq N \leq 2\times 10^5
- 1 \leq K \leq N+1
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N K
-----Output-----
Print the number of possible values of the sum, modulo (10^9+7).
-----Sample Input-----
3 2
-----Sample Output-----
10
The sum can take 10 values, as follows:
- (10^{100})+(10^{100}+1)=2\times 10^{100}+1
- (10^{100})+(10^{100}+2)=2\times 10^{100}+2
- (10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\times 10^{100}+3
- (10^{100}+1)+(10^{100}+3)=2\times 10^{100}+4
- (10^{100}+2)+(10^{100}+3)=2\times 10^{100}+5
- (10^{100})+(10^{100}+1)+(10^{100}+2)=3\times 10^{100}+3
- (10^{100})+(10^{100}+1)+(10^{100}+3)=3\times 10^{100}+4
- (10^{100})+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+5
- (10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+6
- (10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\times 10^{100}+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.
|
Solve the programming task below in a Python markdown code block.
Ivan unexpectedly saw a present from one of his previous birthdays. It is array of $n$ numbers from $1$ to $200$. Array is old and some numbers are hard to read. Ivan remembers that for all elements at least one of its neighbours ls not less than it, more formally:
$a_{1} \le a_{2}$,
$a_{n} \le a_{n-1}$ and
$a_{i} \le max(a_{i-1}, \,\, a_{i+1})$ for all $i$ from $2$ to $n-1$.
Ivan does not remember the array and asks to find the number of ways to restore it. Restored elements also should be integers from $1$ to $200$. Since the number of ways can be big, print it modulo $998244353$.
-----Input-----
First line of input contains one integer $n$ ($2 \le n \le 10^{5}$) — size of the array.
Second line of input contains $n$ integers $a_{i}$ — elements of array. Either $a_{i} = -1$ or $1 \le a_{i} \le 200$. $a_{i} = -1$ means that $i$-th element can't be read.
-----Output-----
Print number of ways to restore the array modulo $998244353$.
-----Examples-----
Input
3
1 -1 2
Output
1
Input
2
-1 -1
Output
200
-----Note-----
In the first example, only possible value of $a_{2}$ is $2$.
In the second example, $a_{1} = a_{2}$ so there are $200$ different values because all restored elements should be integers between $1$ and $200$.
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.
|
Solve the programming task below in a Python markdown code block.
General primality test are often computationally expensive, so in the biggest prime number race the idea is to study special sub-families of prime number and develop more effective tests for them.
[Mersenne Primes](https://en.wikipedia.org/wiki/Mersenne_prime) are prime numbers of the form: Mn = 2^(n) - 1. So far, 49 of them was found between M2 (3) and M74,207,281 which contains 22,338,618 digits and is (by September 2015) the biggest known prime. It has been found by GIMPS (Great Internet Mersenne Prime Search), wich use the test srudied here. (plus heuristics mentionned below)
Lucas and Lehmer have developed a [simple test](https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test) for Mersenne primes:
> for `p` (an odd prime), the Mersenne number Mp is prime if and only if `S(p − 1) = 0 mod Mp`,
>where `S(n + 1) = S(n) * S(n) − 2` and `S(1) = 4`
The goal of this kata is to implement this test. Given an integer `>=2`, the program should calculate the sequence `S(n)` up to `p-1` and calculate the remainder modulo `Mp`, then return `True` or `False` as a result of the test. The case `n = 2` should return `True`.
You should take advantage of the fact that:
```k = (k mod 2^n + floor(k/2^n)) mod Mn```
Or in other words, if we take the least significant `n` bits of `k`, and add the remaining bits of `k`, and then do this repeatedly until at most `n` bits remain, we can compute the remainder after dividing `k` by the Mersenne number `2^n−1` without using division.
This test can be improved using the fact that if `n` is not prime, `2^n-1` will not be prime. So in theory you can test for the primality of `n` beforehand. But in practice the test for the primality of `n` will rapidly outgrow in difficulty the Lucas-Lehmer test. So we can only use heuristics to rule out `n` with small factors but not complete factorization algorithm. You don't need to implement such heuristics here.
The rapid growth of `s^2` makes javascript reach its integer limit quickly (coherent result for `n = 13`, but not `17`). Whereas python seems to be only limited by the execution time limit and let us see that M11,213 is prime (contains 3376 digits).
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.
|
Solve the programming task below in a Python markdown code block.
Karafs is some kind of vegetable in shape of an 1 × h rectangle. Tavaspolis people love Karafs and they use Karafs in almost any kind of food. Tavas, himself, is crazy about Karafs. [Image]
Each Karafs has a positive integer height. Tavas has an infinite 1-based sequence of Karafses. The height of the i-th Karafs is s_{i} = A + (i - 1) × B.
For a given m, let's define an m-bite operation as decreasing the height of at most m distinct not eaten Karafses by 1. Karafs is considered as eaten when its height becomes zero.
Now SaDDas asks you n queries. In each query he gives you numbers l, t and m and you should find the largest number r such that l ≤ r and sequence s_{l}, s_{l} + 1, ..., s_{r} can be eaten by performing m-bite no more than t times or print -1 if there is no such number r.
-----Input-----
The first line of input contains three integers A, B and n (1 ≤ A, B ≤ 10^6, 1 ≤ n ≤ 10^5).
Next n lines contain information about queries. i-th line contains integers l, t, m (1 ≤ l, t, m ≤ 10^6) for i-th query.
-----Output-----
For each query, print its answer in a single line.
-----Examples-----
Input
2 1 4
1 5 3
3 3 10
7 10 2
6 4 8
Output
4
-1
8
-1
Input
1 5 2
1 5 10
2 7 4
Output
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.
|
Solve the programming task below in a Python markdown code block.
Your task is to determine the top 3 place finishes in a pole vault competition involving several different competitors. This is isn't always so simple, and it is often a source of confusion for people who don't know the actual rules.
Here's what you need to know:
As input, you will receive an array of objects. Each object contains the respective competitor's name (as a string) and his/her results at the various bar heights (as an array of strings):
[{name: "Sergey", results: ["", "O", "XO", "O", "XXO", "XXX", "", ""]}{name: "Jan", results: ["", "", "", "O", "O", "XO", "XXO", "XXX"]}{name: "Bruce", results: ["", "XO", "XXO", "XXX", "", "", "", ""]}{name: "HerrWert", results: ["XXX", "", "", "", "", "", "", ""]}]
In the array of strings described above, each string represents the vaulter's performance at a given height. The possible values are based on commonly used written notations on a pole vault scoresheet:
An empty string indicates that the vaulter did not jump at this height for a variety of possible reasons ("passed" at this height, was temporarily called away to a different track and field event, was already eliminated from competition, or withdrew due to injury, for example).An upper-case X in the string represents an unsuccessful attempt at the height. (As you may know, the vaulter is eliminated from the competition after three consecutive failed attempts.)An upper-case O represents a successful attempt. If present at all, this will be the final character in the string, because it indicates that the vaulter has now successfully completed this height and is ready to move on.
All vaulters will have a result string (though possibly empty) for every height involved in the competition, making it possible to match up the results of different vaulters with less confusion.
Obviously, your first task is to determine who cleared the greatest height successfully. In other words, who has a "O" mark at a higher array element than any other competitor? You might want to work through the arrays from right to left to determine this. In the most straightforward case, you would first determine the winner, then second place, and finally third place by this simple logic.
But what if there's a tie for one of these finishing places? Proceed as follows (according to American high school rules, at least):
First trace backwards to find the greatest height that both vaulters cleared successfully. Then determine who had the fewest unsuccessful attempts at this height (i.e., the fewest X's in the string for this height). This person wins the tie-break.But what if they're still tied with one another? Do NOT continue to trace backwards through the heights! Instead, compare their total numbers of unsuccessful attempts at all heights in the competition. The vaulter with the fewest total misses wins the tie-break.But what if they're still tied? It depends on the finishing place:If it's for second or third place, the tie stands (i.e., is not broken).But if it's for first place, there must be a jump-off (like overtime or penalty kicks in other sports) to break the tie and determine the winner. (This jump-off occurs - hypothetically - after your code runs and is thus not a part of this kata.)
Return a single object as your result. Each place-finish that is included in the results (including at least first place as property "1st" and possibly second and third places as properties "2nd" and "3rd") should have as its value the respective vaulter's name. In the event of a tie, the value of the property is the names of all tied vaulters, in alphabetical order, separated by commas, and followed by the notation "(jump-off)" if the tie is for first place or "(tie)" if it's for second or third place.
Here are some possible outcomes to show you what I mean:
{1st: "Jan", 2nd: "Sergey"; 3rd: "Bruce"} (These results correspond to the sample input data given above.){1st: "Julia", 2nd: "Madi, Emily (tie)}"{1st: "Caleb, Dustin (jump-off)", 3rd: "Sam"}{1st: "Meredith", 2nd: "Maddy", 3rd: "Cierra, Sara (tie)"}{1st: "Alex, Basti, Max (jump-off)"}
If you are familiar with the awarding of place finishes in sporting events or team standings in a league, then you know that there won't necessarily be a 2nd or 3rd place, because ties in higher places "bump" all lower places downward accordingly.
One more thing: You really shouldn't change the array of objects that you receive as input. This represents the physical scoresheet. We need this "original document" to be intact, so that we can refer back to it to resolve a disputed result!
Have fun with this!
- - - - -
Notes for the Python version:
The rules for the Python version are the same as the original JavaScript version.
The input and output will look the same as the JavaScript version. But, the JavaScript objects will be replaced by Python dictionaries. The JavaScript arrays will be replaced by Python lists. The Python function name was changed to include underscores as is customary with Python names. The example below should help clarify all of this.
The input for the Python version will be a list containing dictionaries with the competitors' names and results. The names in the dictionaries are strings. The results are lists with a list of strings. And example follows.
score_pole_vault([
{"name": "Linda", "results": ["XXO", "O","XXO", "O"]},
{"name": "Vickie", "results": ["O","X", "", ""]},
{"name": "Debbie", "results": ["XXO", "O","XO", "XXX"]},
{"name": "Michelle", "results": ["XO","XO","XXX",""]},
{"name": "Carol", "results": ["XXX", "","",""]}
])
The returned results should be in a dictionary with one to three elements.
Examples of possible returned results:
{'1st': 'Linda', '2nd': 'Debbie', '3rd': 'Michelle'}
{'1st': 'Green, Hayes (jump-off)', '3rd': 'Garcia'}
Note: Since first place was tied in this case, there is no 2nd place awarded.
{'1st': 'Wilson', '2nd': 'Laurie', '3rd': 'Joyce, Moore (tie)'}
I have tried to create test cases that have every concievable tie situation.
Have fun with this version, as well!
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.
|
Solve the programming task below in a Python markdown code block.
One day, Niwango-kun, an employee of Dwango Co., Ltd., found an integer sequence (a_1, ..., a_N) of length N. He is interested in properties of the sequence a.
For a nonempty contiguous subsequence a_l, ..., a_r (1 \leq l \leq r \leq N) of the sequence a, its beauty is defined as a_l + ... + a_r. Niwango-kun wants to know the maximum possible value of the bitwise AND of the beauties of K nonempty contiguous subsequences among all N(N+1)/2 nonempty contiguous subsequences. (Subsequences may share elements.)
Find the maximum possible value for him.
Constraints
* 2 \leq N \leq 1000
* 1 \leq a_i \leq 10^9
* 1 \leq K \leq N(N+1)/2
* All numbers given in input are integers
Input
Input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the answer.
Examples
Input
4 2
2 5 2 5
Output
12
Input
8 4
9 1 8 2 7 5 6 4
Output
32
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.
|
Solve the programming task below in a Python markdown code block.
Zonk is addictive dice game. In each round player rolls 6 dice. Then (s)he composes combinations from them. Each combination gives certain points.
Then player can take one or more dice combinations to his hand and re-roll remaining dice or save his score. Dice in player's hand won't be taken into account in subsequent rolls.
If no combinations can be composed - situation is called "zonk". Player thrown zonk loses all points in this round and next player moves. So it's player decision when to reroll and when to stop and save his score.
Your task is simple - just evaluate current roll and return maximum number of points can be scored from it. If no combinations can be made - function must return string ``"Zonk"`` (without quotes).
There are different variations of Zonk. In this kata, we will use most common table of combinations:
CombinationExample rollPoints
Straight (1,2,3,4,5 and 6)6 3 1 2 5 41000 points
Three pairs of any dice2 2 4 4 1 1750 points
Three of 11 4 1 11000 points
Three of 22 3 4 2 2200 points
Three of 33 4 3 6 3 2300 points
Three of 44 4 4400 points
Three of 52 5 5 5 4500 points
Three of 66 6 2 6600 points
Four of a kind1 1 1 1 4 62 × Three-of-a-kind score (in example, 2000 pts)
Five of a kind5 5 5 4 5 53 × Three-of-a-kind score (in example, 1500 pts)
Six of a kind4 4 4 4 4 44 × Three-of-a-kind score (in example, 1600 pts)
Every 14 3 1 2 2100 points
Every 55 2 650 points
Each die cannot be used in multiple combinations the same time, so three pairs of 2, 3 and 5 will worth you only ``750`` points (for three pairs), not 850 (for three pairs and two fives). But you can select multiple combinations, ``2 2 2 1 6`` will worth you ``300`` points (200 for three-of-kind '2' plus 100 for single '1' die)
Examples:
```python
get_score([1,2,3]) # returns 100 = points from one 1
get_score([3,4,1,1,5]) # returns 250 = points from two 1 and one 5
get_score([2,3,2,3,3,2]) # returns 500 = three of 2 + three of 3
get_score([1,1,1,1,1,5]) # returns 3050 = five 1 + one 5
get_score([2,3,4,3,6,6]) # returns "Zonk" = no combinations here
get_score([2,2,6,6,2,2]) # returns 400 = four 2, this cannot be scored as three pairs
get_score([1,3,4,3,4,1]) # returns 750 = three pairs
get_score([3,3,3,3]) # returns 600 = four of 3
get_score([1,2,3,4,5]) # returns 150 = it's not straight
```
Of course, in real Zonk game it's sometimes not worth to collect all combination from roll. Taking less dice and rerolling more remaining may be better, but task is just to calculate maximum possible score from current single roll.
P.S. Inspired by this kata: http://www.codewars.com/kata/5270d0d18625160ada0000e4
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.
|
Solve the programming task below in a Python markdown code block.
King of Berland Berl IV has recently died. Hail Berl V! As a sign of the highest achievements of the deceased king the new king decided to build a mausoleum with Berl IV's body on the main square of the capital.
The mausoleum will be constructed from 2n blocks, each of them has the shape of a cuboid. Each block has the bottom base of a 1 × 1 meter square. Among the blocks, exactly two of them have the height of one meter, exactly two have the height of two meters, ..., exactly two have the height of n meters.
The blocks are arranged in a row without spacing one after the other. Of course, not every arrangement of blocks has the form of a mausoleum. In order to make the given arrangement in the form of the mausoleum, it is necessary that when you pass along the mausoleum, from one end to the other, the heights of the blocks first were non-decreasing (i.e., increasing or remained the same), and then — non-increasing (decrease or remained unchanged). It is possible that any of these two areas will be omitted. For example, the following sequences of block height meet this requirement:
[1, 2, 2, 3, 4, 4, 3, 1]; [1, 1]; [2, 2, 1, 1]; [1, 2, 3, 3, 2, 1].
Suddenly, k more requirements appeared. Each of the requirements has the form: "h[x_{i}] sign_{i} h[y_{i}]", where h[t] is the height of the t-th block, and a sign_{i} is one of the five possible signs: '=' (equals), '<' (less than), '>' (more than), '<=' (less than or equals), '>=' (more than or equals). Thus, each of the k additional requirements is given by a pair of indexes x_{i}, y_{i} (1 ≤ x_{i}, y_{i} ≤ 2n) and sign sign_{i}.
Find the number of possible ways to rearrange the blocks so that both the requirement about the shape of the mausoleum (see paragraph 3) and the k additional requirements were met.
-----Input-----
The first line of the input contains integers n and k (1 ≤ n ≤ 35, 0 ≤ k ≤ 100) — the number of pairs of blocks and the number of additional requirements.
Next k lines contain listed additional requirements, one per line in the format "x_{i} sign_{i} y_{i}" (1 ≤ x_{i}, y_{i} ≤ 2n), and the sign is on of the list of the five possible signs.
-----Output-----
Print the sought number of ways.
-----Examples-----
Input
3 0
Output
9
Input
3 1
2 > 3
Output
1
Input
4 1
3 = 6
Output
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.
|
Solve the programming task below in a Python markdown code block.
Professor Matsuzaki is a scientist studying the truth of the universe. Life, the universe, all the answers are said to be 42, but Professor Matsuzaki thinks that this alone is not enough to elucidate the truth of the universe. Professor Matsuzaki believes that the truth of the universe is represented by a function consisting of two parameters, and 42 is just one of them.
The function M (N, P) defined by Professor Matsuzaki selects two prime numbers larger than N (the same number can be two) and sums them, in order from the smallest number. Represents the number that appears in the Pth position when arranged. Here, there are numbers that can be represented by two or more sums, but such numbers are arranged in the same number as the number of combinations of sums.
As an example, consider the case of N = 0. In this case, two are selected from all the prime numbers and summed. Considering the smallest number among such sums, it is permissible to select the same number twice, which shows that 2 + 2 = 4. That is, M (0, 1) = 4. The next smallest number is 2 + 3 = 5, so M (0, 2) = 5. Considering in the same way, it can be seen that the sums are arranged as 4, 5, 6, 7, 8, 9, 10, 10, 12, 13, 14, 14, 16, .... That is, for example, M (0, 9) = 12.
Considering the case of N = 10 in the same way, in this case, two prime numbers greater than 10 {11, 13, 17, 19, ...} are selected, and the sums obtained are arranged in ascending order. And 22, 24, 26, 28, 30, 30, 32, ...
Your job is to write a program that calculates M (N, P) given N and P.
Input
The input consists of multiple datasets. The dataset is one line, given two integers N (0 ≤ N ≤ 100,000) and P (1 ≤ P ≤ 100) separated by a single space.
The end of the input is indicated by a single line containing two blank-separated -1s.
Output
For each dataset, output the value of M (N, P) on one line. The output must not contain extra blanks or line breaks.
Sample Input
0 55
0 1
0 2
0 3
10 1
10 2
10 3
10 4
10 5
10 6
11 1
11 2
11 3
100000 100
-1 -1
Output for the Sample Input
42
Four
Five
6
twenty two
twenty four
26
28
30
30
26
30
32
200274
Example
Input
0 55
0 1
0 2
0 3
10 1
10 2
10 3
10 4
10 5
10 6
11 1
11 2
11 3
100000 100
-1 -1
Output
42
4
5
6
22
24
26
28
30
30
26
30
32
200274
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.
|
Solve the programming task below in a Python markdown code block.
A robot is put at the origin in a two-dimensional plane.
Initially, the robot is facing in the positive x-axis direction.
This robot will be given an instruction sequence s.
s consists of the following two kinds of letters, and will be executed in order from front to back.
- F : Move in the current direction by distance 1.
- T : Turn 90 degrees, either clockwise or counterclockwise.
The objective of the robot is to be at coordinates (x, y) after all the instructions are executed.
Determine whether this objective is achievable.
-----Constraints-----
- s consists of F and T.
- 1 \leq |s| \leq 8 000
- x and y are integers.
- |x|, |y| \leq |s|
-----Input-----
Input is given from Standard Input in the following format:
s
x y
-----Output-----
If the objective is achievable, print Yes; if it is not, print No.
-----Sample Input-----
FTFFTFFF
4 2
-----Sample Output-----
Yes
The objective can be achieved by, for example, turning counterclockwise in the first T and turning clockwise in the second T.
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.
|
Solve the programming task below in a Python markdown code block.
You are given a string $s$ of length $n$ consisting only of lowercase Latin letters.
A substring of a string is a contiguous subsequence of that string. So, string "forces" is substring of string "codeforces", but string "coder" is not.
Your task is to calculate the number of ways to remove exactly one substring from this string in such a way that all remaining characters are equal (the number of distinct characters either zero or one).
It is guaranteed that there is at least two different characters in $s$.
Note that you can remove the whole string and it is correct. Also note that you should remove at least one character.
Since the answer can be rather large (not very large though) print it modulo $998244353$.
If you are Python programmer, consider using PyPy instead of Python when you submit your code.
-----Input-----
The first line of the input contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the length of the string $s$.
The second line of the input contains the string $s$ of length $n$ consisting only of lowercase Latin letters.
It is guaranteed that there is at least two different characters in $s$.
-----Output-----
Print one integer — the number of ways modulo $998244353$ to remove exactly one substring from $s$ in such way that all remaining characters are equal.
-----Examples-----
Input
4
abaa
Output
6
Input
7
aacdeee
Output
6
Input
2
az
Output
3
-----Note-----
Let $s[l; r]$ be the substring of $s$ from the position $l$ to the position $r$ inclusive.
Then in the first example you can remove the following substrings: $s[1; 2]$; $s[1; 3]$; $s[1; 4]$; $s[2; 2]$; $s[2; 3]$; $s[2; 4]$.
In the second example you can remove the following substrings: $s[1; 4]$; $s[1; 5]$; $s[1; 6]$; $s[1; 7]$; $s[2; 7]$; $s[3; 7]$.
In the third example you can remove the following substrings: $s[1; 1]$; $s[1; 2]$; $s[2; 2]$.
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.
|
Solve the programming task below in a Python markdown code block.
In the Bus of Characters there are $n$ rows of seat, each having $2$ seats. The width of both seats in the $i$-th row is $w_i$ centimeters. All integers $w_i$ are distinct.
Initially the bus is empty. On each of $2n$ stops one passenger enters the bus. There are two types of passengers: an introvert always chooses a row where both seats are empty. Among these rows he chooses the one with the smallest seats width and takes one of the seats in it; an extrovert always chooses a row where exactly one seat is occupied (by an introvert). Among these rows he chooses the one with the largest seats width and takes the vacant place in it.
You are given the seats width in each row and the order the passengers enter the bus. Determine which row each passenger will take.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 200\,000$) — the number of rows in the bus.
The second line contains the sequence of integers $w_1, w_2, \dots, w_n$ ($1 \le w_i \le 10^{9}$), where $w_i$ is the width of each of the seats in the $i$-th row. It is guaranteed that all $w_i$ are distinct.
The third line contains a string of length $2n$, consisting of digits '0' and '1' — the description of the order the passengers enter the bus. If the $j$-th character is '0', then the passenger that enters the bus on the $j$-th stop is an introvert. If the $j$-th character is '1', the the passenger that enters the bus on the $j$-th stop is an extrovert. It is guaranteed that the number of extroverts equals the number of introverts (i. e. both numbers equal $n$), and for each extrovert there always is a suitable row.
-----Output-----
Print $2n$ integers — the rows the passengers will take. The order of passengers should be the same as in input.
-----Examples-----
Input
2
3 1
0011
Output
2 1 1 2
Input
6
10 8 9 11 13 5
010010011101
Output
6 6 2 3 3 1 4 4 1 2 5 5
-----Note-----
In the first example the first passenger (introvert) chooses the row $2$, because it has the seats with smallest width. The second passenger (introvert) chooses the row $1$, because it is the only empty row now. The third passenger (extrovert) chooses the row $1$, because it has exactly one occupied seat and the seat width is the largest among such rows. The fourth passenger (extrovert) chooses the row $2$, because it is the only row with an empty place.
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.
|
Solve the programming task below in a Python markdown code block.
We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.
Vertex i has an integer a_i written on it.
For every integer k from 1 through N, solve the following problem:
- We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.
Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.
-----Constraints-----
- 2 \leq N \leq 2 \times 10^5
- 1 \leq a_i \leq 10^9
- 1 \leq u_i , v_i \leq N
- u_i \neq v_i
- The given graph is a tree.
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}
-----Output-----
Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.
-----Sample Input-----
10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10
-----Sample Output-----
1
2
3
3
4
4
5
2
2
3
For example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 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.
|
Solve the programming task below in a Python markdown code block.
We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7.
The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string.
Input
The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106.
Output
Print the minimum number of steps modulo 109 + 7.
Examples
Input
ab
Output
1
Input
aab
Output
3
Note
The first example: "ab" → "bba".
The second example: "aab" → "abba" → "bbaba" → "bbbbaa".
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.
|
Solve the programming task below in a Python markdown code block.
Iroha has a sequence of N strings S_1, S_2, ..., S_N. The length of each string is L.
She will concatenate all of the strings in some order, to produce a long string.
Among all strings that she can produce in this way, find the lexicographically smallest one.
Here, a string s=s_1s_2s_3...s_n is lexicographically smaller than another string t=t_1t_2t_3...t_m if and only if one of the following holds:
- There exists an index i(1≦i≦min(n,m)), such that s_j = t_j for all indices j(1≦j<i), and s_i<t_i.
- s_i = t_i for all integers i(1≦i≦min(n,m)), and n<m.
-----Constraints-----
- 1 ≦ N, L ≦ 100
- For each i, the length of S_i equals L.
- For each i, S_i consists of lowercase letters.
-----Input-----
The input is given from Standard Input in the following format:
N L
S_1
S_2
:
S_N
-----Output-----
Print the lexicographically smallest string that Iroha can produce.
-----Sample Input-----
3 3
dxx
axx
cxx
-----Sample Output-----
axxcxxdxx
The following order should be used: axx, cxx, dxx.
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.
|
Solve the programming task below in a Python markdown code block.
Suppose there is a $h \times w$ grid consisting of empty or full cells. Let's make some definitions:
$r_{i}$ is the number of consecutive full cells connected to the left side in the $i$-th row ($1 \le i \le h$). In particular, $r_i=0$ if the leftmost cell of the $i$-th row is empty. $c_{j}$ is the number of consecutive full cells connected to the top end in the $j$-th column ($1 \le j \le w$). In particular, $c_j=0$ if the topmost cell of the $j$-th column is empty.
In other words, the $i$-th row starts exactly with $r_i$ full cells. Similarly, the $j$-th column starts exactly with $c_j$ full cells.
[Image] These are the $r$ and $c$ values of some $3 \times 4$ grid. Black cells are full and white cells are empty.
You have values of $r$ and $c$. Initially, all cells are empty. Find the number of ways to fill grid cells to satisfy values of $r$ and $c$. Since the answer can be very large, find the answer modulo $1000000007\,(10^{9} + 7)$. In other words, find the remainder after division of the answer by $1000000007\,(10^{9} + 7)$.
-----Input-----
The first line contains two integers $h$ and $w$ ($1 \le h, w \le 10^{3}$) — the height and width of the grid.
The second line contains $h$ integers $r_{1}, r_{2}, \ldots, r_{h}$ ($0 \le r_{i} \le w$) — the values of $r$.
The third line contains $w$ integers $c_{1}, c_{2}, \ldots, c_{w}$ ($0 \le c_{j} \le h$) — the values of $c$.
-----Output-----
Print the answer modulo $1000000007\,(10^{9} + 7)$.
-----Examples-----
Input
3 4
0 3 1
0 2 3 0
Output
2
Input
1 1
0
1
Output
0
Input
19 16
16 16 16 16 15 15 0 5 0 4 9 9 1 4 4 0 8 16 12
6 12 19 15 8 6 19 19 14 6 9 16 10 11 15 4
Output
797922655
-----Note-----
In the first example, this is the other possible case.
[Image]
In the second example, it's impossible to make a grid to satisfy such $r$, $c$ values.
In the third example, make sure to print answer modulo $(10^9 + 7)$.
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.
|
Solve the programming task below in a Python markdown code block.
In the online judge system, a judge file may include multiple datasets to check whether the submitted program outputs a correct answer for each test case. This task is to practice solving a problem with multiple datasets.
Write a program which reads an integer x and print it as is. Note that multiple datasets are given for this problem.
Constraints
* 1 ≤ x ≤ 10000
* The number of datasets ≤ 10000
Input
The input consists of multiple datasets. Each dataset consists of an integer x in a line.
The input ends with an integer 0. You program should not process (print) for this terminal symbol.
Output
For each dataset, print x in the following format:
Case i: x
where i is the case number which starts with 1. Put a single space between "Case" and i. Also, put a single space between ':' and x.
Example
Input
3
5
11
7
8
19
0
Output
Case 1: 3
Case 2: 5
Case 3: 11
Case 4: 7
Case 5: 8
Case 6: 19
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.
|
Solve the programming task below in a Python markdown code block.
You have a statistic of price changes for one product represented as an array of $n$ positive integers $p_0, p_1, \dots, p_{n - 1}$, where $p_0$ is the initial price of the product and $p_i$ is how the price was increased during the $i$-th month.
Using these price changes you are asked to calculate the inflation coefficients for each month as the ratio of current price increase $p_i$ to the price at the start of this month $(p_0 + p_1 + \dots + p_{i - 1})$.
Your boss said you clearly that the inflation coefficients must not exceed $k$ %, so you decided to increase some values $p_i$ in such a way, that all $p_i$ remain integers and the inflation coefficients for each month don't exceed $k$ %.
You know, that the bigger changes — the more obvious cheating. That's why you need to minimize the total sum of changes.
What's the minimum total sum of changes you need to make all inflation coefficients not more than $k$ %?
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains two integers $n$ and $k$ ($2 \le n \le 100$; $1 \le k \le 100$) — the length of array $p$ and coefficient $k$.
The second line of each test case contains $n$ integers $p_0, p_1, \dots, p_{n - 1}$ ($1 \le p_i \le 10^9$) — the array $p$.
-----Output-----
For each test case, print the minimum total sum of changes you need to make all inflation coefficients not more than $k$ %.
-----Examples-----
Input
2
4 1
20100 1 202 202
3 100
1 1 1
Output
99
0
-----Note-----
In the first test case, you can, for example, increase $p_0$ by $50$ and $p_1$ by $49$ and get array $[20150, 50, 202, 202]$. Then you get the next inflation coefficients:
$\frac{50}{20150} \le \frac{1}{100}$;
$\frac{202}{20150 + 50} \le \frac{1}{100}$;
$\frac{202}{20200 + 202} \le \frac{1}{100}$;
In the second test case, you don't need to modify array $p$, since the inflation coefficients are already good:
$\frac{1}{1} \le \frac{100}{100}$;
$\frac{1}{1 + 1} \le \frac{100}{100}$;
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.
|
Solve the programming task below in a Python markdown code block.
All of the animals are having a feast! Each animal is bringing one dish. There is just one rule: the dish must start and end with the same letters as the animal's name. For example, the great blue heron is bringing garlic naan and the chickadee is bringing chocolate cake.
Write a function `feast` that takes the animal's name and dish as arguments and returns true or false to indicate whether the beast is allowed to bring the dish to the feast.
Assume that `beast` and `dish` are always lowercase strings, and that each has at least two letters. `beast` and `dish` may contain hyphens and spaces, but these will not appear at the beginning or end of the string. They will not contain numerals.
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.
|
Solve the programming task below in a Python markdown code block.
<image> <image>
*The two images are equivalent, feel free to use either one.
Input
The input contains a single integer a (-100 ≤ a ≤ 100).
Output
Output the result – an integer number.
Example
Input
1
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.
|
Solve the programming task below in a Python markdown code block.
There are S sheep and W wolves.
If the number of wolves is greater than or equal to that of sheep, the wolves will attack the sheep.
If the wolves will attack the sheep, print unsafe; otherwise, print safe.
-----Constraints-----
- 1 \leq S \leq 100
- 1 \leq W \leq 100
-----Input-----
Input is given from Standard Input in the following format:
S W
-----Output-----
If the wolves will attack the sheep, print unsafe; otherwise, print safe.
-----Sample Input-----
4 5
-----Sample Output-----
unsafe
There are four sheep and five wolves. The number of wolves is not less than that of sheep, so they will attack them.
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.
|
Solve the programming task below in a Python markdown code block.
In a very ancient country the following game was popular. Two people play the game. Initially first player writes a string s1, consisting of exactly nine digits and representing a number that does not exceed a. After that second player looks at s1 and writes a string s2, consisting of exactly nine digits and representing a number that does not exceed b. Here a and b are some given constants, s1 and s2 are chosen by the players. The strings are allowed to contain leading zeroes.
If a number obtained by the concatenation (joining together) of strings s1 and s2 is divisible by mod, then the second player wins. Otherwise the first player wins. You are given numbers a, b, mod. Your task is to determine who wins if both players play in the optimal manner. If the first player wins, you are also required to find the lexicographically minimum winning move.
Input
The first line contains three integers a, b, mod (0 ≤ a, b ≤ 109, 1 ≤ mod ≤ 107).
Output
If the first player wins, print "1" and the lexicographically minimum string s1 he has to write to win. If the second player wins, print the single number "2".
Examples
Input
1 10 7
Output
2
Input
4 0 9
Output
1 000000001
Note
The lexical comparison of strings is performed by the < operator in modern programming languages. String x is lexicographically less than string y if exists such i (1 ≤ i ≤ 9), that xi < yi, and for any j (1 ≤ j < i) xj = yj. These strings always have length 9.
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.
|
Solve the programming task below in a Python markdown code block.
The pair of integer numbers `(m, n)`, such that `10 > m > n > 0`, (below 10), that its sum, `(m + n)`, and rest, `(m - n)`, are perfect squares, is (5, 4).
Let's see what we have explained with numbers.
```
5 + 4 = 9 = 3²
5 - 4 = 1 = 1²
(10 > 5 > 4 > 0)
```
The pair of numbers `(m, n)`, closest to and below 50, having the property described above is `(45, 36)`.
```
45 + 36 = 81 = 9²
45 - 36 = 9 = 3²
(50 > 45 > 36 > 0)
```
With the function `closest_pair_tonum()`, that receives a number `upper_limit`, as an upper limit, we should be able to obtain the closest pair to `upper_limit`, that fulfills the property described above.
The function should return the largest pair of numbers `(m, n)`, satisfying `upper_limit > m > n > 0`. Note that we say pair A `(a0, a1)` is larger than pair B `(b0, b1)` when `a0 > b0` or `a0 == b0 and
a1 > b1`.
Let's see some cases:
```python
closest_pair_tonum(10) == (5, 4) # (m = 5, n = 4)
closest_pair_tonum(30) == (29, 20)
closest_pair_tonum(50) == (45, 36)
```
Happy coding and enjoy it!!
(We will be having a second part of a similar exercise (in some days) that will need a faster algorithm for values of `upper_limit` < 1000)
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.
|
Solve the programming task below in a Python markdown code block.
# Task
Alireza and Ali have a `3×3 table` and playing on that. they have 4 table(2×2) A,B,C and D in this table.
At beginning all of 9 numbers in 3×3 table is zero.
Alireza in each move choose a 2×2 table from A, B, C and D and increase all of 4 numbers in that by one.
He asks Ali, how much he increase table A, B, C and D. (if he cheats you should return `[-1]`)
Your task is to help Ali.
# Example
For
```
table=
[[1,2,1],
[2,4,2],
[1,2,1]]```
The result should be `[1,1,1,1]`
For:
```
Table=
[[3,7,4],
[5,16,11],
[2,9,7]]```
The result should be `[3,4,2,7]`
# Input/Output
- `[input]` 2D integer array `table`
`3×3` table.
- `[output]` an integer array
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.
|
Solve the programming task below in a Python markdown code block.
Takahashi had a pair of two positive integers not exceeding N, (a,b), which he has forgotten. He remembers that the remainder of a divided by b was greater than or equal to K. Find the number of possible pairs that he may have had.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N-1
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
Output
Print the number of possible pairs that he may have had.
Examples
Input
5 2
Output
7
Input
10 0
Output
100
Input
31415 9265
Output
287927211
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.
|
Solve the programming task below in a Python markdown code block.
Food contains three nutrients called "protein", "fat" and "carbohydrate", which are called three major nutrients. It is calculated that protein and carbohydrate are 4 kcal (kilocalories) and fat is 9 kcal per 1 g (gram). For example, according to the table below, the number 1 cake contains 7 g of protein, 14 g of fat and 47 g of carbohydrates. If you calculate the calories contained based on this, it will be 4 x 7 + 9 x 14 + 4 x 47 = 342 kcal. Others are calculated in the same way.
Number | Name | Protein (g) | Lipids (g) | Carbohydrates (g) | Calories (kcal)
--- | --- | --- | --- | --- | ---
1 | Cake | 7 | 14 | 47 | 342
2 | Potato Chips | 5 | 35 | 55 | 555
3 | Dorayaki | 6 | 3 | 59 | 287
4 | Pudding | 6 | 5 | 15 | 129
Input the number of sweets to be classified n, the information of each sweet, and the limit information, and output a list of sweets that do not exceed the limit (may be eaten) if only one sweet is used. Create a program.
The candy information consists of the candy number s, the weight p of the protein contained in the candy, the weight q of the lipid, and the weight r of the carbohydrate. The limit information consists of the maximum protein weight P that can be included, the fat weight Q, the carbohydrate weight R, and the maximum calorie C that can be consumed, of protein, fat, carbohydrate, and calories. If any one of them is exceeded, the restriction will be violated and it will be judged as "sweets that should not be eaten".
For a list of sweets that you can eat, output the numbers of sweets that you can eat in the order in which you entered them. If there are no sweets you can eat, please output "NA". For the four sweets in the table above, if the limit is P = 10, Q = 15, R = 50, C = 400, cake and pudding may be eaten as their respective nutrients and calories are below the limit. Although it is classified as sweets, potato chips are classified as sweets that should not be eaten because the amount of carbohydrates exceeds the limit value.
input
Given a sequence of multiple datasets. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
s1 p1 q1 r1
s2 p2 q2 r2
::
sn pn qn rn
P Q R C
The first line gives the number of sweets n (1 ≤ n ≤ 1000). The next n lines are given the number si (1 ≤ si ≤ 1000) of the i-th candy and the integers pi, qi, ri (0 ≤ pi, qi, ri ≤ 100) representing the weight of each nutrient.
The following lines are given the integers P, Q, R (0 ≤ P, Q, R ≤ 100), C (0 ≤ C ≤ 1700) representing the limits for each nutrient and calorie.
The number of datasets does not exceed 100.
output
For each dataset, it outputs the number of sweets you can eat or "NA".
Example
Input
4
1 7 14 47
2 5 35 55
3 6 3 59
4 6 5 15
10 15 50 400
2
1 8 10 78
2 4 18 33
10 10 50 300
0
Output
1
4
NA
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.
|
Solve the programming task below in a Python markdown code block.
Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.
Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.
Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.
-----Input-----
The first line contains two integers, n and k (1 ≤ n ≤ 10^5; 1 ≤ k ≤ 10^9).
Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 10^5. Each string of the group consists only of lowercase English letters.
-----Output-----
If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
-----Examples-----
Input
2 3
a
b
Output
First
Input
3 1
a
b
c
Output
First
Input
1 2
ab
Output
Second
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.
|
Solve the programming task below in a Python markdown code block.
I'm traveling to a country with a rabbit. There are n cities in this country numbered from 1 to n, and the rabbit is now in city 1. City i is a point on the coordinate plane (xi, yi) ).
Rabbits travel to meet the following conditions.
* The travel path is a polygonal line, each part of which must be a line segment connecting two different cities.
* The total length of the travel route must be r or less. The overlapping part of the route is also counted for the number of times it has passed.
* When the direction of movement changes, the bending angle must be less than or equal to θ. There is no limit to the initial direction of movement.
If you move from one city to another, you will get one carrot in the destination city. You can visit the same city multiple times, and you will get a carrot each time you visit. Find the maximum number of carrots you can put in.
Input
One integer n is given on the first line of the input, and two real numbers r and θ are given on the second line, separated by a space.
1 ≤ n ≤ 20
0 <r <104
0 ° <θ <180 °
The following n lines are given the integers xi and yi separated by spaces.
-10 000 ≤ xi, yi ≤ 10 000
The answer does not change even if r and θ are changed within ± 10-3.
The locations of both cities are different.
Output
Output the maximum number of carrots that the rabbit can get on this trip in one line.
Example
Input
5
100.1 90.1
0 0
0 10
5 5
10 0
10 10
Output
10
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.
|
Solve the programming task below in a Python markdown code block.
Numbers of black and white points are placed on a plane. Let's imagine that a straight line of infinite length is drawn on the plane. When the line does not meet any of the points, the line divides these points into two groups. If the division by such a line results in one group consisting only of black points and the other consisting only of white points, we say that the line "separates black and white points".
Let's see examples in Figure 3. In the leftmost example, you can easily find that the black and white points can be perfectly separated by the dashed line according to their colors. In the remaining three examples, there exists no such straight line that gives such a separation.
<image>
Figure 3: Example planes
In this problem, given a set of points with their colors and positions, you are requested to decide whether there exists a straight line that separates black and white points.
Input
The input is a sequence of datasets, each of which is formatted as follows.
n m
x1 y1
.
.
.
xn yn
xn+1 yn+1
.
.
.
xn+m yn+m
The first line contains two positive integers separated by a single space; n is the number of black points, and m is the number of white points. They are less than or equal to 100. Then n + m lines representing the coordinates of points follow. Each line contains two integers xi and yi separated by a space, where (xi , yi ) represents the x-coordinate and the y-coordinate of the i-th point. The color of the i-th point is black for 1 ≤ i ≤ n, and is white for n + 1 ≤ i ≤ n + m.
All the points have integral x- and y-coordinate values between 0 and 10000 inclusive. You can also assume that no two points have the same position.
The end of the input is indicated by a line containing two zeros separated by a space.
Output
For each dataset, output "YES" if there exists a line satisfying the condition. If not, output "NO". In either case, print it in one line for each input dataset.
Example
Input
3 3
100 700
200 200
600 600
500 100
500 300
800 500
3 3
100 300
400 600
400 100
600 400
500 900
300 300
3 4
300 300
500 300
400 600
100 100
200 900
500 900
800 100
1 2
300 300
100 100
500 500
1 1
100 100
200 100
2 2
0 0
500 700
1000 1400
1500 2100
2 2
0 0
1000 1000
1000 0
0 1000
3 3
0 100
4999 102
10000 103
5001 102
10000 102
0 101
3 3
100 100
200 100
100 200
0 0
400 0
0 400
3 3
2813 1640
2583 2892
2967 1916
541 3562
9298 3686
7443 7921
0 0
Output
YES
NO
NO
NO
YES
YES
NO
NO
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.
|
Solve the programming task below in a Python markdown code block.
Consider a tic-tac-toe on a 3x3 board. Tic-tac-toe is a two-player battle game. Decide the first attack and the second attack, one hits Kuroishi and one hits Shiraishi. The winner is the person who puts stones one by one on the board alternately and arranges three of his own stones first in either the vertical, horizontal, or diagonal direction.
Create a program that inputs the information on the board, judges the victory or defeat, outputs "b" if black wins, "w" if white wins, and "NA" if neither is available. please. The board information consists of 3 rows and 3 columns of character strings. "B" is Kuroishi, "w" is Shiraishi, and "+" (half-width plus) is nothing. However, three blacks and three whites cannot be lined up at the same time.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
board1
board2
board3
The i-line is given the string boardi that represents the information on the i-th line of the board.
The number of datasets does not exceed 50.
Output
Outputs "b", "w", or "NA" on one line for each data set.
Example
Input
bbw
wbw
+b+
bwb
wbw
wbw
0
Output
b
NA
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.
|
Solve the programming task below in a Python markdown code block.
Petya has come to the math exam and wants to solve as many problems as possible. He prepared and carefully studied the rules by which the exam passes.
The exam consists of $n$ problems that can be solved in $T$ minutes. Thus, the exam begins at time $0$ and ends at time $T$. Petya can leave the exam at any integer time from $0$ to $T$, inclusive.
All problems are divided into two types: easy problems — Petya takes exactly $a$ minutes to solve any easy problem; hard problems — Petya takes exactly $b$ minutes ($b > a$) to solve any hard problem.
Thus, if Petya starts solving an easy problem at time $x$, then it will be solved at time $x+a$. Similarly, if at a time $x$ Petya starts to solve a hard problem, then it will be solved at time $x+b$.
For every problem, Petya knows if it is easy or hard. Also, for each problem is determined time $t_i$ ($0 \le t_i \le T$) at which it will become mandatory (required). If Petya leaves the exam at time $s$ and there is such a problem $i$ that $t_i \le s$ and he didn't solve it, then he will receive $0$ points for the whole exam. Otherwise (i.e if he has solved all such problems for which $t_i \le s$) he will receive a number of points equal to the number of solved problems. Note that leaving at time $s$ Petya can have both "mandatory" and "non-mandatory" problems solved.
For example, if $n=2$, $T=5$, $a=2$, $b=3$, the first problem is hard and $t_1=3$ and the second problem is easy and $t_2=2$. Then: if he leaves at time $s=0$, then he will receive $0$ points since he will not have time to solve any problems; if he leaves at time $s=1$, he will receive $0$ points since he will not have time to solve any problems; if he leaves at time $s=2$, then he can get a $1$ point by solving the problem with the number $2$ (it must be solved in the range from $0$ to $2$); if he leaves at time $s=3$, then he will receive $0$ points since at this moment both problems will be mandatory, but he will not be able to solve both of them; if he leaves at time $s=4$, then he will receive $0$ points since at this moment both problems will be mandatory, but he will not be able to solve both of them; if he leaves at time $s=5$, then he can get $2$ points by solving all problems.
Thus, the answer to this test is $2$.
Help Petya to determine the maximal number of points that he can receive, before leaving the exam.
-----Input-----
The first line contains the integer $m$ ($1 \le m \le 10^4$) — the number of test cases in the test.
The next lines contain a description of $m$ test cases.
The first line of each test case contains four integers $n, T, a, b$ ($2 \le n \le 2\cdot10^5$, $1 \le T \le 10^9$, $1 \le a < b \le 10^9$) — the number of problems, minutes given for the exam and the time to solve an easy and hard problem, respectively.
The second line of each test case contains $n$ numbers $0$ or $1$, separated by single space: the $i$-th number means the type of the $i$-th problem. A value of $0$ means that the problem is easy, and a value of $1$ that the problem is hard.
The third line of each test case contains $n$ integers $t_i$ ($0 \le t_i \le T$), where the $i$-th number means the time at which the $i$-th problem will become mandatory.
It is guaranteed that the sum of $n$ for all test cases does not exceed $2\cdot10^5$.
-----Output-----
Print the answers to $m$ test cases. For each set, print a single integer — maximal number of points that he can receive, before leaving the exam.
-----Example-----
Input
10
3 5 1 3
0 0 1
2 1 4
2 5 2 3
1 0
3 2
1 20 2 4
0
16
6 20 2 5
1 1 0 1 0 0
0 8 2 9 11 6
4 16 3 6
1 0 1 1
8 3 5 6
6 20 3 6
0 1 0 0 1 0
20 11 3 20 16 17
7 17 1 6
1 1 0 1 0 0 0
1 7 0 11 10 15 10
6 17 2 6
0 0 1 0 0 1
7 6 3 7 10 12
5 17 2 5
1 1 1 1 0
17 11 10 6 4
1 1 1 2
0
1
Output
3
2
1
0
1
4
0
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.
|
Solve the programming task below in a Python markdown code block.
"Hey, it's homework time" — thought Polycarpus and of course he started with his favourite subject, IT. Polycarpus managed to solve all tasks but for the last one in 20 minutes. However, as he failed to solve the last task after some considerable time, the boy asked you to help him.
The sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.
You are given an arbitrary sequence a1, a2, ..., an containing n integers. Each integer is not less than 1 and not greater than 5000. Determine what minimum number of elements Polycarpus needs to change to get a permutation (he should not delete or add numbers). In a single change he can modify any single sequence element (i. e. replace it with another integer).
Input
The first line of the input data contains an integer n (1 ≤ n ≤ 5000) which represents how many numbers are in the sequence. The second line contains a sequence of integers ai (1 ≤ ai ≤ 5000, 1 ≤ i ≤ n).
Output
Print the only number — the minimum number of changes needed to get the permutation.
Examples
Input
3
3 1 2
Output
0
Input
2
2 2
Output
1
Input
5
5 3 3 3 1
Output
2
Note
The first sample contains the permutation, which is why no replacements are required.
In the second sample it is enough to replace the first element with the number 1 and that will make the sequence the needed permutation.
In the third sample we can replace the second element with number 4 and the fourth element with number 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.
|
Solve the programming task below in a Python markdown code block.
Vasya is reading a e-book. The file of the book consists of $n$ pages, numbered from $1$ to $n$. The screen is currently displaying the contents of page $x$, and Vasya wants to read the page $y$. There are two buttons on the book which allow Vasya to scroll $d$ pages forwards or backwards (but he cannot scroll outside the book). For example, if the book consists of $10$ pages, and $d = 3$, then from the first page Vasya can scroll to the first or to the fourth page by pressing one of the buttons; from the second page — to the first or to the fifth; from the sixth page — to the third or to the ninth; from the eighth — to the fifth or to the tenth.
Help Vasya to calculate the minimum number of times he needs to press a button to move to page $y$.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 10^3$) — the number of testcases.
Each testcase is denoted by a line containing four integers $n$, $x$, $y$, $d$ ($1\le n, d \le 10^9$, $1 \le x, y \le n$) — the number of pages, the starting page, the desired page, and the number of pages scrolled by pressing one button, respectively.
-----Output-----
Print one line for each test.
If Vasya can move from page $x$ to page $y$, print the minimum number of times he needs to press a button to do it. Otherwise print $-1$.
-----Example-----
Input
3
10 4 5 2
5 1 3 4
20 4 19 3
Output
4
-1
5
-----Note-----
In the first test case the optimal sequence is: $4 \rightarrow 2 \rightarrow 1 \rightarrow 3 \rightarrow 5$.
In the second test case it is possible to get to pages $1$ and $5$.
In the third test case the optimal sequence is: $4 \rightarrow 7 \rightarrow 10 \rightarrow 13 \rightarrow 16 \rightarrow 19$.
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.
|
Solve the programming task below in a Python markdown code block.
Read problems statements in Mandarin Chinese and Russian.
Chef loves to prepare delicious dishes. This time, Chef has decided to prepare a special dish for you, and needs to gather several apples to do so.
Chef has N apple trees in his home garden. Each tree has a certain (non-zero) number of apples on it. In order to create his dish, Chef wants to pluck every apple from every tree.
Chef has an unusual method of collecting apples. In a single minute, he can perform the following task:
Pick any subset of trees such that every tree in the subset has the same number of apples.
From each tree in the subset, pluck any number of apples, as long as the number of apples left on the tree equals the number of apples on a tree not in the subset.
If all trees have the same number of apples left, Chef can pluck all of the apples remaining in a single minute.
Chef does not want to keep you waiting, so wants to achieve this task in the minimum possible time. Can you tell him what the minimum time required is?
------ Input ------
The first line of the input contains a single integer T denoting the number of test cases. This will be followed by T test cases. The first line of each test case contains a single integer N denoting the number of apple trees in Chef's garden. The next line of each test case contains N space separated integers denoting the number of apples on each tree.
------ Output ------
For each of the T test cases, output a single line - the minimum time to pluck all apples from all trees.
------ Constraints ------
$1 ≤ T ≤ 10$
$1 ≤ N ≤ 10^{5}$
$1 ≤ Number of apples on a tree ≤ 10^{5}$
------ Scoring ------
$Subtask 1 : 1 ≤ T ≤ 10 , 1 ≤ N ≤ 10^{3}: (27 pts) $
$Subtask 2 : 1 ≤ T ≤ 10 , 1 ≤ N ≤ 10^{4}: (25 pts) $
$Subtask 3 : 1 ≤ T ≤ 10 , 1 ≤ N ≤ 10^{5}: (48 pts) $
----- Sample Input 1 ------
2
3
3 3 3
4
1 2 3 3
----- Sample Output 1 ------
1
3
----- explanation 1 ------
For test 1, Chef can select all the trees and can pluck all the apples in 1 minute.
For test 2, there are many ways Chef can pluck all of the apples in 3 minutes. Here is one example:
First minute: Select the third and fourth trees. Pluck 1 apple from the third tree, and 2 apples from the fourth tree.
Second minute: Select the second and third tree. Pluck 1 apple from each tree.
Third minute: Select all of the trees and pluck the last apple from each tree.
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.
|
Solve the programming task below in a Python markdown code block.
Write a function
```python
alternate_sort(l)
```
that combines the elements of an array by sorting the elements ascending by their **absolute value** and outputs negative and non-negative integers alternatingly (starting with the negative value, if any).
E.g.
```python
alternate_sort([5, -42, 2, -3, -4, 8, -9,]) == [-3, 2, -4, 5, -9, 8, -42]
alternate_sort([5, -42, 2, -3, -4, 8, 9]) == [-3, 2, -4, 5, -42, 8, 9]
alternate_sort([5, 2, -3, -4, 8, -9]) == [-3, 2, -4, 5, -9, 8]
alternate_sort([5, 2, 9, 3, 8, 4]) == [2, 3, 4, 5, 8, 9]
```
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.
|
Solve the programming task below in a Python markdown code block.
Leha plays a computer game, where is on each level is given a connected graph with n vertices and m edges. Graph can contain multiple edges, but can not contain self loops. Each vertex has an integer d_{i}, which can be equal to 0, 1 or - 1. To pass the level, he needs to find a «good» subset of edges of the graph or say, that it doesn't exist. Subset is called «good», if by by leaving only edges from this subset in the original graph, we obtain the following: for every vertex i, d_{i} = - 1 or it's degree modulo 2 is equal to d_{i}. Leha wants to pass the game as soon as possible and ask you to help him. In case of multiple correct answers, print any of them.
-----Input-----
The first line contains two integers n, m (1 ≤ n ≤ 3·10^5, n - 1 ≤ m ≤ 3·10^5) — number of vertices and edges.
The second line contains n integers d_1, d_2, ..., d_{n} ( - 1 ≤ d_{i} ≤ 1) — numbers on the vertices.
Each of the next m lines contains two integers u and v (1 ≤ u, v ≤ n) — edges. It's guaranteed, that graph in the input is connected.
-----Output-----
Print - 1 in a single line, if solution doesn't exist. Otherwise in the first line k — number of edges in a subset. In the next k lines indexes of edges. Edges are numerated in order as they are given in the input, starting from 1.
-----Examples-----
Input
1 0
1
Output
-1
Input
4 5
0 0 0 -1
1 2
2 3
3 4
1 4
2 4
Output
0
Input
2 1
1 1
1 2
Output
1
1
Input
3 3
0 -1 1
1 2
2 3
1 3
Output
1
2
-----Note-----
In the first sample we have single vertex without edges. It's degree is 0 and we can not get 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.
|
Solve the programming task below in a Python markdown code block.
We define $x \bmod y$ as the remainder of division of $x$ by $y$ ($\%$ operator in C++ or Java, mod operator in Pascal).
Let's call an array of positive integers $[a_1, a_2, \dots, a_k]$ stable if for every permutation $p$ of integers from $1$ to $k$, and for every non-negative integer $x$, the following condition is met:
$ (((x \bmod a_1) \bmod a_2) \dots \bmod a_{k - 1}) \bmod a_k = (((x \bmod a_{p_1}) \bmod a_{p_2}) \dots \bmod a_{p_{k - 1}}) \bmod a_{p_k} $
That is, for each non-negative integer $x$, the value of $(((x \bmod a_1) \bmod a_2) \dots \bmod a_{k - 1}) \bmod a_k$ does not change if we reorder the elements of the array $a$.
For two given integers $n$ and $k$, calculate the number of stable arrays $[a_1, a_2, \dots, a_k]$ such that $1 \le a_1 < a_2 < \dots < a_k \le n$.
-----Input-----
The only line contains two integers $n$ and $k$ ($1 \le n, k \le 5 \cdot 10^5$).
-----Output-----
Print one integer — the number of stable arrays $[a_1, a_2, \dots, a_k]$ such that $1 \le a_1 < a_2 < \dots < a_k \le n$. Since the answer may be large, print it modulo $998244353$.
-----Examples-----
Input
7 3
Output
16
Input
3 7
Output
0
Input
1337 42
Output
95147305
Input
1 1
Output
1
Input
500000 1
Output
500000
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.
|
Solve the programming task below in a Python markdown code block.
Some programming contest problems are really tricky: not only do they
require a different output format from what you might have expected, but
also the sample output does not show the difference. For an example,
let us look at permutations.
A permutation of the integers 1 to n is an
ordering of
these integers. So the natural way to represent a permutation is
to list the integers in this order. With n = 5, a
permutation might look like 2, 3, 4, 5, 1.
However, there is another possibility of representing a permutation:
You create a list of numbers where the i-th number is the
position of the integer i in the permutation.
Let us call this second
possibility an inverse permutation. The inverse permutation
for the sequence above is 5, 1, 2, 3, 4.
An ambiguous permutation is a permutation which cannot be
distinguished from its inverse permutation. The permutation 1, 4, 3, 2
for example is ambiguous, because its inverse permutation is the same.
To get rid of such annoying sample test cases, you have to write a
program which detects if a given permutation is ambiguous or not.
-----Input Specification-----
The input contains several test cases.
The first line of each test case contains an integer n
(1 ≤ n ≤ 100000).
Then a permutation of the integers 1 to n follows
in the next line. There is exactly one space character
between consecutive integers.
You can assume that every integer between 1 and n
appears exactly once in the permutation.
The last test case is followed by a zero.
-----Output Specification-----
For each test case output whether the permutation is ambiguous or not.
Adhere to the format shown in the sample output.
-----Sample Input-----
4
1 4 3 2
5
2 3 4 5 1
1
1
0
-----Sample Output-----
ambiguous
not ambiguous
ambiguous
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.
|
Solve the programming task below in a Python markdown code block.
Lexicographic permutations are ordered combinations of a set of items ordered in a specific way.
For instance, the first 8 permutations of the digits 0123, in lexicographic order, are:
```
1st 0123
2nd 0132
3rd 0213
4th 0231
5th 0312
6th 0321
7th 1023
8th 1032
```
Your task is to write a function ```L( n, d )``` that will return a `string` representing the `nth` permutation of the `d` digit, starting with 0 (i.e. d=10 means all digits 0123456789).
So for `d = 4`, `L(7,4)` should return `'1023'`, and `L(4,4)` should return `'0231'`
.
Some things to bear in mind:
• The function should return a `string`, otherwise permutations beginning with a 0 will have it removed.
• Test cases will not exceed the highest possible valid values for `n`
• The function should work for any `d` between `1` and `10`.
• A value of 1 for `n` means the 1st permutation, so `n = 0` is not a valid input.
• Oh, and no itertools ;)
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.
|
Solve the programming task below in a Python markdown code block.
There are n boys and m girls attending a theatre club. To set a play "The Big Bang Theory", they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.
Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.
Input
The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).
Output
Find the required number of ways.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.
Examples
Input
5 2 5
Output
10
Input
4 3 5
Output
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.
|
Solve the programming task below in a Python markdown code block.
There is a special offer in Vasya's favourite supermarket: if the customer buys $a$ chocolate bars, he or she may take $b$ additional bars for free. This special offer can be used any number of times.
Vasya currently has $s$ roubles, and he wants to get as many chocolate bars for free. Each chocolate bar costs $c$ roubles. Help Vasya to calculate the maximum possible number of chocolate bars he can get!
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of testcases.
Each of the next $t$ lines contains four integers $s, a, b, c~(1 \le s, a, b, c \le 10^9)$ — the number of roubles Vasya has, the number of chocolate bars you have to buy to use the special offer, the number of bars you get for free, and the cost of one bar, respectively.
-----Output-----
Print $t$ lines. $i$-th line should contain the maximum possible number of chocolate bars Vasya can get in $i$-th test.
-----Example-----
Input
2
10 3 1 1
1000000000 1 1000000000 1
Output
13
1000000001000000000
-----Note-----
In the first test of the example Vasya can buy $9$ bars, get $3$ for free, buy another bar, and so he will get $13$ bars.
In the second test Vasya buys $1000000000$ bars and gets $1000000000000000000$ for free. So he has $1000000001000000000$ bars.
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.
|
Solve the programming task below in a Python markdown code block.
There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.
Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.
-----Constraints-----
- 2 ≤ H, W ≤ 10^5
-----Input-----
Input is given from Standard Input in the following format:
H W
-----Output-----
Print the minimum possible value of S_{max} - S_{min}.
-----Sample Input-----
3 5
-----Sample Output-----
0
In the division below, S_{max} - S_{min} = 5 - 5 = 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.
|
Solve the programming task below in a Python markdown code block.
Tattah is asleep if and only if Tattah is attending a lecture. This is a well-known formula among Tattah's colleagues.
On a Wednesday afternoon, Tattah was attending Professor HH's lecture. At 12:21, right before falling asleep, he was staring at the digital watch around Saher's wrist. He noticed that the digits on the clock were the same when read from both directions i.e. a palindrome.
In his sleep, he started dreaming about such rare moments of the day when the time displayed on a digital clock is a palindrome. As soon as he woke up, he felt destined to write a program that finds the next such moment.
However, he still hasn't mastered the skill of programming while sleeping, so your task is to help him.
Input
The first and only line of the input starts with a string with the format "HH:MM" where "HH" is from "00" to "23" and "MM" is from "00" to "59". Both "HH" and "MM" have exactly two digits.
Output
Print the palindromic time of day that comes soonest after the time given in the input. If the input time is palindromic, output the soonest palindromic time after the input time.
Examples
Input
12:21
Output
13:31
Input
23:59
Output
00:00
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.
|
Solve the programming task below in a Python markdown code block.
J: City
Santa decides to deliver a present to a city.
The city has a rectangular shape divided into north-south $ H $ parcels x east-west $ W $ parcels, with one house delivering gifts to each parcel.
The $ X $ th section from the north and the $ Y $ th section from the west are represented by $ (X, Y) $.
Santa moves under the following conditions.
* First, get off at block $ (S, T) $ and start from this place.
* You can move to the adjacent sections in the north, south, east, and west with one move, and you cannot move outside the city.
* You will never enter the area you visited once.
Determine if Santa can visit all the houses in the city.
input
$ H, W, S, T $ are given separated by blanks.
output
Output "Yes" if Santa can visit all the homes in the city, otherwise output "No".
Constraint
* $ H, W $ are integers greater than or equal to $ 2 $ and less than or equal to $ 1 \ 000 \ 000 \ 000 $
* $ S $ is an integer greater than or equal to $ 1 $ and less than or equal to $ H $
* $ T $ is an integer greater than or equal to $ 1 $ and less than or equal to $ W $
Input example 1
4 5 2 3
Output example 1
Yes
For example, you can go to the figure.
<image>
Input example 2
3 3 1 2
Output example 2
No
Example
Input
4 5 2 3
Output
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.
|
Solve the programming task below in a Python markdown code block.
Vasya plays the LionAge II. He was bored of playing with a stupid computer, so he installed this popular MMORPG, to fight with his friends. Vasya came up with the name of his character — non-empty string s, consisting of a lowercase Latin letters. However, in order not to put up a front of friends, Vasya has decided to change no more than k letters of the character name so that the new name sounded as good as possible. Euphony of the line is defined as follows: for each pair of adjacent letters x and y (x immediately precedes y) the bonus c(x, y) is added to the result. Your task is to determine what the greatest Euphony can be obtained by changing at most k letters in the name of the Vasya's character.
Input
The first line contains character's name s and an integer number k (0 ≤ k ≤ 100). The length of the nonempty string s does not exceed 100. The second line contains an integer number n (0 ≤ n ≤ 676) — amount of pairs of letters, giving bonus to the euphony. The next n lines contain description of these pairs «x y c», which means that sequence xy gives bonus c (x, y — lowercase Latin letters, - 1000 ≤ c ≤ 1000). It is guaranteed that no pair x y mentioned twice in the input data.
Output
Output the only number — maximum possible euphony оf the new character's name.
Examples
Input
winner 4
4
s e 7
o s 8
l o 13
o o 8
Output
36
Input
abcdef 1
5
a b -10
b c 5
c d 5
d e 5
e f 5
Output
20
Note
In the first example the most euphony name will be looser. It is easy to calculate that its euphony is 36.
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.
|
Solve the programming task below in a Python markdown code block.
Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.
-----Constraints-----
- 2 \leq K \leq 10^5
- K is an integer.
-----Input-----
Input is given from Standard Input in the following format:
K
-----Output-----
Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.
-----Sample Input-----
6
-----Sample Output-----
3
12=6×2 yields the smallest sum.
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.
|
Solve the programming task below in a Python markdown code block.
Problem Statement
The Animal School is a primary school for animal children. You are a fox attending this school.
One day, you are given a problem called "Arithmetical Restorations" from the rabbit teacher, Hanako. Arithmetical Restorations are the problems like the following:
* You are given three positive integers, $A$, $B$ and $C$.
* Several digits in these numbers have been erased.
* You should assign a digit in each blank position so that the numbers satisfy the formula $A+B=C$.
* The first digit of each number must not be zero. It is also the same for single-digit numbers.
You are clever in mathematics, so you immediately solved this problem. Furthermore, you decided to think of a more difficult problem, to calculate the number of possible assignments to the given Arithmetical Restorations problem. If you can solve this difficult problem, you will get a good grade.
Shortly after beginning the new task, you noticed that there may be too many possible assignments to enumerate by hand. So, being the best programmer in the school as well, you are now trying to write a program to count the number of possible assignments to Arithmetical Restoration problems.
Input
The input is a sequence of datasets. The number of datasets is less than 100. Each dataset is formatted as follows.
> $A$
> $B$
> $C$
Each dataset consists of three strings, $A$, $B$ and $C$. They indicate that the sum of $A$ and $B$ should be $C$. Each string consists of digits (`0`-`9`) and/or question mark (`?`). A question mark (`?`) indicates an erased digit. You may assume that the first character of each string is not `0` and each dataset has at least one `?`.
It is guaranteed that each string contains between 1 and 50 characters, inclusive. You can also assume that the lengths of three strings are equal.
The end of input is indicated by a line with a single zero.
Output
For each dataset, output the number of possible assignments to the given problem modulo 1,000,000,007. Note that there may be no way to solve the given problems because Ms. Hanako is a careless rabbit.
Sample Input
3?4
12?
5?6
?2?4
5?7?
?9?2
?????
?????
?????
0
Output for the Sample Input
2
40
200039979
Note
The answer of the first dataset is 2. They are shown below.
* 384 + 122 = 506
* 394 + 122 = 516
Example
Input
3?4
12?
5?6
?2?4
5?7?
?9?2
?????
?????
?????
0
Output
2
40
200039979
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.
|
Solve the programming task below in a Python markdown code block.
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
- Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
-----Constraints-----
- 1 \leq N \leq 200
- 1 \leq A_i \leq 10^9
-----Input-----
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
-----Output-----
Print the maximum possible number of operations that Snuke can perform.
-----Sample Input-----
3
8 12 40
-----Sample Output-----
2
Initially, [8, 12, 40] are written on the blackboard.
Since all those integers are even, Snuke can perform the operation.
After the operation is performed once, [4, 6, 20] are written on the blackboard.
Since all those integers are again even, he can perform the operation.
After the operation is performed twice, [2, 3, 10] are written on the blackboard.
Now, there is an odd number 3 on the blackboard, so he cannot perform the operation any more.
Thus, Snuke can perform the operation at most twice.
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.
|
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