Chef recently started working at ABC corporation. Let's number weekdays (Monday through Friday) by integers $1$ through $5$. For each valid $i$, the number of hours Chef spent working at the office on weekday $i$ was $A_i$.
Unfortunately, due to the COVID-19 pandemic, Chef started working from home and his productivity decreased by a considerable amount. As per Chef's analysis, $1$ hour of work done at the office is equivalent to $P$ hours of work done at home.
Now, in order to complete his work properly, Chef has to spend more hours working from home, possibly at the cost of other things like sleep. However, he does not have to do the same work on each day as he would have in the office ― for each weekday, he can start the work for this day on an earlier day and/or complete it on a later day. The only requirement is that his work does not pile up indefinitely, i.e. he can complete his work for each week during the same week. One day has $24$ hours.
If Chef is unable to complete his work for a week during those five weekdays, then he has to work during the weekend too. Chef wishes to know whether he has to work on weekends or if he can complete his work by working only on weekdays. Help him answer that question. (It is possible that Chef would be unable to finish his work even if he worked all the time, but he does not want to know about that.)

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains six space-separated integers $A_1$, $A_2$, $A_3$, $A_4$, $A_5$ and $P$.

-----Output-----
For each test case, print a single line containing the string "Yes" if Chef has to work on weekends or "No" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 1,000$
- $0 \le A_i \le 24$ for each valid $i$
- $1 \le P \le 24$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
2
14 10 12 6 18 2
10 10 10 10 10 3

-----Example Output-----
No
Yes

-----Explanation-----
Example case 1: Here, $P=2$, so the number of hours Chef has to work from home to handle his workload for days $1$ through $5$ is $[28,20,24,12,36]$. If he works for full $24$ hours on each of the five weekdays, he finishes all the work, so he does not have to work on weekends.
Example case 2: No matter what Chef does, he will have to work on weekends.


There are $N$ cities on a circle, numbered $1$ through $N$. For each $i$ ($1 \le i \le N-1$), cities $i$ and $i+1$ are directly connected by a bidirectional road with length $A_i$, and cities $N$ and $1$ are also directly connected by a bidirectional road with length $A_N$. However, we do not know the lengths of some roads.
For each city $i$, we do know that it has an opposite city — formally, there is a city $j \neq i$ such that the clockwise distance between cities $i$ and $j$ is equal to the counterclockwise distance between these cities.
Please find the lengths of all roads in such a way that the above condition is satisfied and the sum of lengths of all roads is minimised.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$. For each valid $i$, $A_i = -1$ denotes that the length of road $i$ is unknown.

-----Output-----
For each test case, print a line containing the string "NO" if there is no solution or "YES" otherwise. If a solution exists, print a second line containing $N$ space-separated positive integers — the lengths of all roads in your solution. Each of these integers should be $\le 10^9$. If there are multiple solutions, you may print any one.

-----Constraints-----
- $1 \le T \le 100$
- $3 \le N \le 10^5$
- $1 \le A_i \le 10^9$ or $A_i = -1$ for each valid $i$
- the sum of $N$ for all test cases does not exceed $3\cdot 10^5$

-----Subtasks-----
Subtask #1 (10 points): $N \le 4$
Subtask #2 (20 points): $A_i = \pm 1$ for each valid $i$
Subtask #3 (70 points): original constraints

-----Example Input-----
4
4
1 1 1 1
4
1 1 1 2
4
1 -1 -1 4
4
1 -1 2 -1

-----Example Output-----
YES
1 1 1 1
NO
YES
1 4 1 4
NO

question_and_tests_only_no_solution_or_reasoning; test_cases are the VERIFIER not an answer


Chef has some numbers. His girlfriend Chefina feels good when chef gives her a particular pattern number also called as Armstrong number.
Armstrong number is a number whose sum of its all individual digit raise to the power of the number of digit in that number is equal to that number itself
eg.. 153 = 1^3 + 5^3 + 3^3 (153 is an Armstrong number)
1634 = 1^4 + 6^4 + 3^4 + 4^4 (1634 is an Armstrong number)
As a love guru of chef you have to help chef to find Armstrong numbers Among the numbers which chef has initially so that Chefina feels good

-----Input:-----
First line will contain a positive Integer $T$ which is the number of testcases
Next $T$ lines follows an Integer $N$.

-----Output:-----
For Every n You have to print "FEELS GOOD" without qoutes if it is an armstrong number otherwise Print "FEELS BAD" without quotes

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq N \leq 10^6$

-----Sample Input:-----
3
153
11
1634

-----Sample Output:-----
FEELS GOOD
FEELS BAD
FEELS GOOD

-----EXPLANATION:-----
For test case 1 --> 153 = 1^3 + 5^3 + 3^3 (153 is an armstrong number)


Ada is playing pawn chess with Suzumo.
Pawn chess is played on a long board with N$N$ squares in one row. Initially, some of the squares contain pawns.
Note that the colours of the squares and pawns do not matter in this game, but otherwise, the standard chess rules apply:
- no two pawns can occupy the same square at the same time
- a pawn cannot jump over another pawn (they are no knights!), i.e. if there is a pawn at square i$i$, then it can only be moved to square i−2$i-2$ if squares i−1$i-1$ and i−2$i-2$ are empty
- pawns cannot move outside of the board (outs are forbidden)
The players alternate turns; as usual, Ada plays first. In each turn, the current player must choose a pawn and move it either one or two squares to the left of its current position. The player that cannot make a move loses.
Can Ada always beat Suzumo? Remember that Ada is a chess grandmaster, so she always plays optimally.

-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first and only line of each test case contains a single string S$S$ with length N$N$ describing the initial board from left to right. An empty square and a square containing a pawn are denoted by the characters '.' and 'P' respectively.

-----Output-----
For each test case, print a single line containing the string "Yes" if Ada wins the game or "No" otherwise (without quotes).

-----Constraints-----
- 1≤T≤500$1 \le T \le 500$
- 2≤N≤128$2 \le N \le 128$
- S$S$ contains only characters '.' and 'P'

-----Example Input-----
1
..P.P

-----Example Output-----
Yes

-----Explanation-----
Example case 1: Ada can move the first pawn two squares to the left; the board after this move looks like
P...P

and now, Suzumo can only move the second pawn. If he moves it one square to the left, Ada will move it two squares to the left on her next move, and if he moves it two squares to the left, Ada will move it one square to the left, so the board after Ada's next move will look like
PP...

and Suzumo cannot make any move here.


Chef wants to gift pairs to his friends this new year. But his friends like good pairs
only.
A pair (a , b) is called a good pair if 1 <= a < b <= N such that GCD(a*b , P) = 1.
Since Chef is busy in preparation for the party, he wants your help to find all the
good pairs.
—————————————————————————————————————
INPUT
• The first line of the input contains a single integer T.
• The first and only line of each test case contain two integer N,P.
————————————————————————————————————————
OUTPUT
For each test case, print a single line containing one integer — the total number of good
pairs
————————————————————————————————————————
CONSTRAINTS
• 1 ≤ T≤ 50
• 2 ≤ N,P ≤10^5
—————————————————————————————————————
Example Input
2
2 3
3 3
————————————————————————————————————————
Example Output
1
1


You are given positive integers $N$ and $D$. You may perform operations of the following two types:
- add $D$ to $N$, i.e. change $N$ to $N+D$
- change $N$ to $\mathop{\mathrm{digitsum}}(N)$
Here, $\mathop{\mathrm{digitsum}}(x)$ is the sum of decimal digits of $x$. For example, $\mathop{\mathrm{digitsum}}(123)=1+2+3=6$, $\mathop{\mathrm{digitsum}}(100)=1+0+0=1$, $\mathop{\mathrm{digitsum}}(365)=3+6+5=14$.
You may perform any number of operations (including zero) in any order. Please find the minimum obtainable value of $N$ and the minimum number of operations required to obtain this value.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $N$ and $D$.

-----Output-----
For each test case, print a single line containing two space-separated integers — the minimum value of $N$ and the minimum required number of operations.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N, D \le 10^{10}$

-----Subtasks-----
Subtask #1 (30 points): $1 \le N, D \le 100$
Subtask #2 (70 points): original constraints

-----Example Input-----
3
2 1
9 3
11 13

-----Example Output-----
1 9
3 2
1 4

-----Explanation-----
Example case 1: The value $N=1$ can be achieved by 8 successive "add" operations (changing $N$ to $10$) and one "digit-sum" operation.
Example case 2: You can prove that you cannot obtain $N=1$ and $N=2$, and you can obtain $N=3$.
The value $N=3$ can be achieved by one "add" and one "digitsum" operation, changing $9$ to $12$ and $12$ to $3$.
Example case 3: $N=1$ can be achieved by operations "add", "add", "digitsum", "digitsum": $11 \rightarrow 24 \rightarrow 37 \rightarrow 10 \rightarrow 1$.


There is a popular apps named “Exbook” like “Facebook”. To sign up in this app , You have to make a strong password with more than 3 digits and less than 10 digits . But I am a pro hacker and so I make a Exbook hacking site . You need to login in this site to hack exbook account and then you will get a portal. You can give any user exbook login link using this site and when anyone login into exbook using your link ,you can see his/her password .
But I made a mistake and so you cannot find original password in your portal . The portal showing you by adding two in every digit . So , now you have to find out the original password of an user if I give you the password which is showing in your portal .

-----Input:-----
The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains a single integer n which is showing in your portal . Mind it , every digit of n is greater than one .

-----Output:-----
Print , original password of user .

-----Sample Input:-----
2
3527
47269

-----Sample Output:-----
1305
25047


Write a program to find the remainder when an integer A is divided by an integer B.

-----Input-----

The first line contains an integer T, the total number of test cases. Then T lines follow, each line contains two Integers A and B.

-----Output-----
For each test case, find the remainder when A is divided by  B, and display it in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ A,B ≤ 10000

-----Example-----
Input
3
1 2
100 200
40 15

Output
1
100
10


Shivam is the youngest programmer in the world, he is just 12 years old. Shivam is learning programming and today he is writing his first program.

Program is very simple, Given two integers A and B, write a program to add these two numbers.

-----Input-----

The first line contains an integer T, the total number of test cases. Then follow T lines, each line contains two Integers A and B.

-----Output-----
For each test case, add A and B and display it in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 0 ≤ A,B ≤ 10000

-----Example-----
Input
3
1 2
100 200
10 40

Output
3
300
50


Chef is making Window frames for his new office, for this he has  n wooden Logs whose lengths are l1, l2, … ln respectively. Chef Doesn’t want to break any logs or Stick 2 or more logs together.
To make a  h × w Window Frame, he needs two Logs with lengths equal h and two with length .
The Chef wants as much sunlight in as possible and for it he has decided to make from the available logs as many frames as possible. Help him in finding the number of window Frames that he can make.
Note : Chef do not need to use all the logs
Input:
The first line of the input contains a single integer T denoting the number of test cases. The description of each test case follows :.
The first line of each test case contains a single integer n the number of wooden logs.
The second line contains  n space-separated integers l1,l2,l3….ln The length of each wooden log
Output:
The only line in Output Contains single Integer denoting the maximum possible number of Wooden Frames.
Constraints:
1 ≤ T ≤ 10
1 ≤ n ≤ 100
1 ≤ li ≤ 10000
Example Input:
2
4
1 2 1 2
8
1 2 1 3 4 1 5 6
Example Output:
1
0
Explanation :
First Case :  We can build a frame of dimension 1x2 as two logs of each dimension are available.
Second Case :  We can’t build any Frame as no logs of length except 1 have more than one piece.


A spy needs your help to encrypt a 5 letter message.
To encrypt the message the following steps are need to be done:
1)Each letter of the message will be converted to it's equivalent number (i.e A=0, B=1,..Z=25)
2)98, 57, 31, 45, 46 are the 5 numbers in the key.
3)Add the equivalent number of the first letter of the message to the first number of the key, then the equivalent number of the second letter of the message to the second number of the key and so on.
4)Take modulo 26 of the sum of each expression.
5)Convert the newly obtained numbers into it's equivalent letters (i.e 0=A, 1=B,…25=Z)
Print the final encrypted string.
Note: It is guaranteed that the given string only contains Only Upper-case Latin Letters.

-----Input:-----
- The first line of the input contains a single Integer $T$. $T$ denoting the number of testcases, description of each testcases contains.
- The first line of the each testcase contains a single string $S$. $S$ denoting the string which you need to encrypt

-----Output:-----
- For each test case, print encypted string i.e result of above operation.
Note: Each testcase output must be printed on new line

-----Constraints:-----
- $1 \leq T \leq 100$
- $1 \leq S \leq 5$

-----Sample Input:-----
2
HELLO
HELL

-----Sample Output:-----
BJQEI
BJQE

-----Explanation:-----
- For 1st Testcase : The conversion of "HELLO" to its equivalent number will be 7, 4, 11, 11, 14 respectively.
Then we add each equivalent number of the message with corresponding number in the key:
7 + 98 = 105
4 + 57 = 61
11 + 31 = 42
11 + 45 = 56
14 + 46 = 60
Further we take the sum:
105 modulo 26 = 1
61 modulo 26 = 9
42 modulo 26 = 16
56 modulo 26 = 4
60 modulo 26 = 8
Finally, convert the newly obtained numbers into it's equivalent letters:
B
J
Q
E
I
Print the final string:
BJQEI


The garden has a tree with too many leaves on it and gardner wants to cut the unwanted leaves. This is a rooted tree, where a node $v$ is called parent of another node $u$, if there exists a directed edge from $v$ to $u$. Leaf node is a node with no outgoing edges.
Gardner cuts the tree in a peculiar way:
- For each parent node(which has a valid leaf node attached to it), he cuts $x$ leaf nodes, such that $x$ is a multiple of 3.
Example : If a parent node has 7 leaf nodes, 6 leaf nodes will be cut and 1 will be left.
- If a parent has all its leaf nodes cut, only then the parent node itself becomes a new leaf node. If new leaf nodes are created, Gardner repeats step 1 until he can cut no more leaf nodes.
After completing all operations, gardner wants to know the minimum number of nodes left on the tree.

It is guaranteed that the given input is a rooted tree.
The root of the tree is vertex 1.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- First line of each testcase contains an integer $n$, the number of vertices in the tree.
- Second line of each testcase contains array $A$ of size $n-1$, where $A_{i}(1≤i≤n-1)$, is the index of the parent of the $(i+1)^{th}$ vertex.

-----Output:-----
For each testcase, output single integer, the number of nodes finally left on the tree.

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq n \leq 10^5$
- $1 \leq A_i \leq i$

-----Sample Input:-----
1

13

1 1 1 1 1 4 3 4 4 3 4 3

-----Sample Output:-----
4

-----EXPLANATION:-----


Zonal Computing Olympiad 2012, 26 Nov 2011

The year is 2102 and today is the day of ZCO. This year there are N contests and the starting and ending times of each contest is known to you. You have to participate in exactly one of these contests. Different contests may overlap. The duration of different contests might be different.

There is only one examination centre. There is a wormhole V that transports you from your house to the examination centre and another wormhole W that transports you from the examination centre back to your house. Obviously, transportation through a wormhole does not take any time; it is instantaneous. But the wormholes can be used at only certain fixed times, and these are known to you.

So, you use a V wormhole to reach the exam centre, possibly wait for some time before the next contest begins, take part in the contest, possibly wait for some more time and then use a W wormhole to return back home. If you leave through a V wormhole at time t1 and come back through a W wormhole at time t2, then the total time you have spent is (t2 - t1 + 1). Your aim is to spend as little time as possible overall while ensuring
that you take part in one of the contests.

You can reach the centre exactly at the starting time of the contest, if possible. And you can leave the examination centre the very second the contest ends, if possible. You can assume that you will always be able to attend at least one contest–that is, there will always be a contest such that there is a V wormhole before it and a W wormhole after it.

For instance, suppose there are 3 contests with (start,end) times (15,21), (5,10), and (7,25), respectively.  Suppose the V wormhole is available at times 4, 14, 25, 2 and the W wormhole is available at times 13 and 21.  In this case, you can leave by the V wormhole at time 14, take part in the contest from time 15 to 21, and then use the W wormhole at time 21 to get back home.  Therefore the time you have spent is (21 - 14 + 1) = 8. You can check that you cannot do better than this.

-----Input format-----
The first line contains 3 space separated integers N, X, and Y, where N is the number of contests, X is the number of time instances when wormhole V can be used and Y is the number of time instances when wormhole W can be used.  The next N lines describe each contest.  Each of these N lines contains two space separated integers S and E, where S is the starting time of the particular contest and E is the ending time of that contest, with S < E.  The next line contains X space separated integers which are the time instances when the wormhole V can be used.  The next line contains Y space separated integers which are the time instances when the wormhole W can be used.

-----Output format-----
Print a single line that contains a single integer, the minimum time needed to be spent to take part in a contest.

-----Testdata-----
All the starting and ending times of contests are distinct and no contest starts at the same time as another contest ends. The time instances when wormholes are available are all distinct, but may coincide with starting and ending times of contests. All the time instances (the contest timings and the wormhole timings) will be integers between 1 and 1000000 (inclusive).

- Subtask 1 (30 marks)
- Subtask 2 (70 marks)

You may assume that
1 ≤ N ≤ 105,
1 ≤ X ≤ 105, and
1 ≤ Y ≤ 105.

In 30% of the cases,
1 ≤ N ≤ 103,
1 ≤ X ≤ 103, and
1 ≤ Y ≤ 103.

-----Sample Input-----
3 4 2
15 21
5 10
7 25
4 14 25 2
13 21

-----Sample Output-----
8


On Miu's smart phone, there is a search feature which lets her search for a contact name by typing digits on the keypad where each digit may correspond to any of the characters given below it. For example, to search for TOM, she can type 866 and for MAX she can type 629.
+------+-----+------+
|   1  |  2  |   3  |
|      | ABC |  DEF |
+------+-----+------+
|   4  |  5  |   6  |
|  GHI | JKL |  MNO |
+------+-----+------+
|   7  |  8  |   9  |
| PQRS | TUV | WXYZ |
+------+-----+------+
|      |  0  |      |
+------+-----+------+

Miu typed a random string of digits $S$ on the keypad while playing around, where each digit is between 2 and 9 inclusive. Now she wants to know the number of possible strings which would map to $S$.
Since this number can be very large, output it modulo 10^9 + 7 (1000000007)

-----Input:-----
-
The first line of the input consists of a single integer $T$ denoting the number of test cases.
-
Each test case consists of a string $S$.

-----Output:-----
- For each test case, print a single line containing one integer - the count of all possible strings mod 1,000,000,007

-----Constraints-----
-
1 <= $T$ <= 10
-
1 <= $|S|$ <= 105

-----Subtasks-----
Subtask #1 (10 points):
- 1 <= $|S|$ <= 10
Subtask #2 (90 points):
- Original Constraints

-----Sample Input:-----
2

5

72

-----Sample Output:-----
3

12

-----EXPLANATION:-----
-
Example Case 1:

On the key 5, we have the character set JKL.

Hence the possible strings are J,K,L.

Hence the answer is 3 % (1000000007) = 3.
-
Example Case 2:
On key 7, we have the character set PQRS.

On key 2, we have the character set ABC.

Hence the possible strings are PA,PB,PC,QA,QB,QC,RA,RB,RC,SA,SB,SC.

Hence the answer is 12 % (1000000007) = 12.


Sumit and Dhiraj are roommates in a hostel of NIT Jamshedpur,One day after completing there boring assignments of Artificial Intelligence, they decided to play a game as it was dhiraj,s idea to play a game so he started explaining the rules of the game to sumit.
So the game was as follows-They randomly took a number N after that they find all its divisors.Suppose first sumit took a divisor then dhiraj and so on.The player who will be having the last divisor with him will win the game.Rohit their mutual friend,was observing them play. Can you help Rohit predict the outcome of game? If Sumit wins print "YES" without quotes and "NO" without quotes, if Dhiraj wins
the game.

-----Input-----
Input starts with an integer T denoting the number of test cases Each test case starts with a line containing an integer N the number.

-----Output-----
Outcome of each game in a separate line

-----Constraints-----
- 1 ≤ T ≤ 10^3
- 1 ≤ N ≤ 10^18

-----Sub tasks-----
- Subtask #1:(10 points)

- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 103
- Subtask #2:(25 points)

- 1 ≤ T ≤ 50
- 1 ≤ N ≤ 1016
- Subtask #3:(65 points)

- 1 ≤ T ≤ 103
- 1 ≤ N ≤ 1018

-----Example-----
Input:
2
4
5

Output:
YES
NO


-----Problem Statement-----
We have an integer sequence $A$, whose length is $N$.
Find the number of the non-empty contiguous subsequences of $A$ whose sum is $0$. Note that we are counting the ways to take out subsequences. That is, even if the contents of some two subsequences are the same, they are counted individually if they are taken from different positions.

-----Input-----
Input is given in the following format:
$N$
$A_1$ $A_2$  . . .  $A_N$

-----Output-----
Find the number of the non-empty contiguous subsequences of $A$ whose sum is $0$.

-----Constraints-----
- $1 \leq N \leq 2\times10^5$
- $-10^9 \leq A_i \leq 10^9$
- All values in input are integers.

-----Sample Input-----
6
1 3 -4 2 2 -2

-----Sample Output-----
3

-----EXPLANATION-----
There are three contiguous subsequences whose sums are $0$: $(1, 3, -4)$, $(-4, 2, 2)$ and $(2, -2)$


Ravi is very good student in mathematics and he also like Even numbers very much .

On the other hand his friend Jhon like Odd numbers . Both of them are preparing for IIT JEE Advance .One day they are solving a  question together the question was Find the sum of first $n$ terms of the given series  $1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+...........$
If the sum is odd then Jhon will be happy and will solve 2 more questions,and Ravi will not attempt more questions. If sum is even Ravi will  be happy and will solve 2 more questions and Jhon will not attempt more questions.
So Your task is to decide who will solve more questions.

-----Input:-----
- First line will contain $n$, number of terms  in the given series.

-----Output:-----
Output single line "Ravi" if he solve more questions or "Jhon" if he solve more questions.

-----Constraints-----
- $1 \leq n \leq 100$

-----Sample Input:-----
2

3

-----Sample Output:-----
Jhon
Ravi

-----EXPLANATION:-----
In the first test cases  sum of 2 terms is 9 (according to the given series) which is an odd number   so Jhon will solve 2 more questions and Ravi will not attempt more questions.
In second test case sum of 3 terms is 18 (according to the given series) which is an  even number according to the given series  so Ravi will solve 3 more questions and Jhon will not attempt more questions.


Nitika was once reading a history book and wanted to analyze it. So she asked her brother to create a list of names of the various famous personalities in the book. Her brother gave Nitika the list. Nitika was furious when she saw the list. The names of the people were not properly formatted. She doesn't like this and would like to properly format it.
A name can have at most three parts: first name, middle name and last name. It will have at least one part. The last name is always present. The rules of formatting a name are very simple:

- Only the first letter of each part of the name should be capital.
- All the parts of the name except the last part should be represented by only two characters. The first character should be the first letter of the part and should be capitalized. The second character should be ".".

Let us look at some examples of formatting according to these rules:
- gandhi -> Gandhi

- mahatma gandhI -> M. Gandhi
- Mohndas KaramChand ganDhi -> M. K. Gandhi

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
The only line of each test case contains the space separated parts of the name.

-----Output-----
For each case, output the properly formatted name.

-----Constraints-----
- 1 ≤ T ≤ 100
- 2 ≤ Length of each part of the name ≤ 10
- Each part of the name contains the letters from lower and upper case English alphabets (i.e. from 'a' to 'z', or 'A' to 'Z')

-----Subtasks-----
Subtask #1 (40 points)
- There is exactly one part in the name.

Subtask #2 (60 points)
- Original constraints.

-----Example-----
Input:
3
gandhi
mahatma gandhI
Mohndas KaramChand gandhi

Output:
Gandhi
M. Gandhi
M. K. Gandhi

-----Explanation-----
The examples are already explained in the problem statement.


Shaun was given $N$ pairs of parenthesis ( )  by his teacher who gave him a difficult task.The task consists of two steps. First,Shaun should colour all $N$ pairs of parenthesis each with different color but opening and closing bracket of a particular pair should be of same colour. Then,Shaun should report to his teacher the number of ways he can arrange all $2*N$ brackets such that sequence form is valid. Teacher defined valid sequence by these rules:
- Any left parenthesis '(' must have a corresponding right parenthesis ')'.
- Any right parenthesis ')' must have a corresponding left parenthesis '('.
- Left parenthesis '(' must go before the corresponding right parenthesis ')'.
Note: Shaun could match opening and closing brackets of different colours.
Since number of ways can be large, Shaun would report the answer as modulo 1000000007 ($10^9 + 7$).

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, one integer $N$.

-----Output:-----
For each testcase, output in a single line answer given by Shaun to his teacher modulo 1000000007.

-----Constraints-----
- $1 \leq T \leq 100000$
- $1 \leq N \leq 100000$

-----Sample Input:-----
3
1
2
3

-----Sample Output:-----
1
6
90

-----EXPLANATION:-----
Here numbers from $1$ to $N$ have been used to denote parenthesis.A unique number corresponds to a unique pair of parenthesis.
-In the first test case , you can use only one color to color the parenthesis  you could arrange it only in one way i.e, 1 1
-In the second test case  you can use two colors and the possible ways of arranging it are
1 1 2 2
1 2 2 1
1 2 1 2
2 2 1 1
2 1 1 2
2 1 2 1


The chef is very expert in coding, so to keep his password safe from the hackers. He always enters a decoded code of his password. You are a hacker and your work is to find the maximum number of possible ways to unlock his password in encoded form.

The encoded message containing only letters from A-Z is being encoded with numbers using the following mapping:

'A' -> 1

'B' -> 2 ...

'Z' -> 26

You have given a non-empty string containing only digits, determine the total number of ways to encode it.

If the total number of ways are even then you are able to unlock the password.

Input:
The first line has a single integer T, denoting the number of test cases. The first line of each test case contains string “S” decoded number.

Output:
For each test case, in a new line, print 'YES' if number of maximum ways are even, otherwise
'NO'. (without quotes)

Constraints:
1 ≤ T ≤ 50

1 ≤ S ≤ 30

Sample Input:
2

12

223

Sample Output:
YES

NO

Explanation:
For first test case, It could be encoded as "AB" (1 2) or "L" (12), hence the number of
maximum possible ways are 2 so output is “YES”.


In a bizarre game of chess ,knight was so drunk, that instead of his usual move he started walking straight. In every move Knight jumps on 2n steps forward (n is number of block that he had travelled so far from starting) but after that he has to take either 1 step forward or backward.
Now the Knight needs to get to position X so King (i.e. You) needs to decide the order of his backward or forward step in such a way that he can reach its destination in minimum number of steps. Remember he always travels in a straight line and the length of the board is infinite.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases, for each test case enter value X ( i.e. destination)
Note : initially knight is at n = 1.

-----Output-----
For each test case the output should be string of numbers 1 & 2 where 1 denotes backward step and 2 denote the forward step
Note : for no solution print 0.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ X ≤ 10^10

-----Example-----
Input:
2
17
10
Output:
2111
0

-----Explanation-----
Case 1 : starting from  n = 1 , knight moves to n = 3 ('2') , 5 ('1') , 9 ('1') , 17 ('1') i.e. string printed is 2 1 1 1
Case 2 : no solution is possible


Chef and his friends are playing the game AMONG US. They all have chosen their names as numbers. There are N people in Chef’s group including him, and each swears that he is not the imposter. However, it turns out there were N+1 people in the game. Now all that Chef needs to know is the name of the imposter, which is a number. Also remember that numbers can be duplicate. Can you help out Chef in finding the imposter?
Input :
First line contains the value of N. Second line contains the N numbers that Chef’s friends used as their names. Third line contains the N+1 numbers that people in the game have used as their names.
Output :
Print the extra number in new line.
Constraints :
1 ≤ Numbers used as names ≤ 1,000
1 ≤ N ≤ 1,000,000
Sample Input :
3
4 2 5
4 2 3 5
Sample Output :
3


Tom  has finally taken over the business empire and now looking for
a new Name of the business to make a new start.

Joe  (Tom's dear friend)  suggested a string $S$  consisting of
Uppercase and lowercase letters

Tom wants to make some changes as per the following criteria:

1) String should $not$ have any vowels .

2) Every other uppercase consonant(other characters except vowels) should
be in lowercase

For ex:

If the consonant character is Z then it should be z

3)  There should be  a character "." before each consonant.

Help Tom to make the required Changes.

-----Input:-----
- First line will contain string  $S$,This string only consists of uppercase and lowercase letters.

-----Output:-----
Print the resulting string. It is guaranteed that this string is not empty.

-----Constraints-----
- Length of string is in [1 .. 100]

-----Sample Input:-----
$CodeSprInT$

-----Sample Output:-----
.c.d.s.p.r.n.t

-----EXPLANATION:-----
C is a consonant and it is in uppercase so turn it in lower case and add a “.” before it
o is a vowel so it is deleted
d  is a consonant and in lowercase so just  add a “.” before it
e  is a vowel so it is deleted
S is a consonant and it is in uppercase so turn it in lower case and add a “.” before it
p is a consonant and in lowercase so just  add a “.” before it
r is a consonant and in lowercase so just  add a “.” before it
I is a vowel so it is deleted
n is a consonant and in lowercase so just  add a “.” before it
T is a consonant and it is in uppercase so turn it in lower case and add a “.” before it


Oliver and Nova are true lovers. Inspite of knowing that Nova will die Oliver married her at the lake where they met. But they had a conflict about even and odd numbers. Nova likes the odd numbers and Oliver prefers even. One day they went to a fair where Oliver bought some square shaped marshmallows and Nova bought some round shaped. Then they decided to play a game. They will pick a natural number N . Nova will sum up the odd numbers from 1 to N and and she will notedown LCM of R(R is defined in the picture) and the sum she calculated before. And Oliver will sum up the even numbers from 1 to N and and he will notedown LCM of S(S is defined in the picture) and the sum he calculated before. You must use the ceil value of R and S.

Now  whose LCM is strictly greater than the other will win.If both of their LCM is equal Nova will win because Oliver is afraid of Nova.
$N.B.$ define the value of pi with $acos(-1)$.
$N.B.$ Sum of all odd number and sum of all even number will not exceed 10^18.

-----Input:-----
The first line contains an integer $T$  — the number of test cases in the input. Next, T test cases are given, one per line.
Each test case is a positive integer $N$  .

-----Output:-----
Print T answers to the test cases.
In each test cases,
If Oliver wins the game, print "Nova's gonna kill me" (without quotes) .
If Nova wins the game, print "YESS(sunglass emo)" (without quotes) .

-----Constraints-----
- $1 \leq T \leq 2000$
- $1 \leq N \leq 1845271$

-----Sample Input:-----
1
111

-----Sample Output:-----
YESS(sunglass emo)


Chef has a natural number N. Cheffina challenges chef to check whether the given number is divisible by the sum of its digits or not. If the given number is divisible then print "Yes" else "No".

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, $N$.

-----Output:-----
For each test case, output in a single line answer.

-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$

-----Sample Input:-----
2
16
27

-----Sample Output:-----
No
Yes


Chef is a private detective. He was asked to investigate a case of murder in the city of Frangton.
Chef arrived in Frangton to find out that the mafia was involved in the case. Chef spent some time watching for people that belong to the clan and was able to build a map of relationships between them. He knows that a mafia's organizational structure consists of a single Don, heading a hierarchical criminal organization. Each member reports exactly to one other member of the clan. It's obvious that there are no cycles in the reporting system of the mafia.
There are N people in the clan, for simplicity indexed from 1 to N, and Chef knows who each of them report to. Member i reports to member Ri.
Now, Chef needs to identfy all potential killers to continue his investigation. Having considerable knowledge about the mafia's activities, Chef knows that the killer must be a minor criminal, that is, one of the members who nobody reports to. Please find the list of potential killers for Chef. Since Don reports to nobody, his Ri will be equal to 0.

-----Input-----
The first line of input contains one integer N.
Next line has N space-separated integers, the ith integer denotes Ri — the person whom the ith member reports to.

-----Output-----
Output a list of space-separated integers in ascending order — the indices of potential killers.

-----Constraints-----
- 1 ≤ N ≤ 105
- 1 ≤ Ri ≤ N except for Don, whose Ri equals to 0.
- It is guaranteed that there are no cycles in the reporting structure.

-----Subtasks-----
- Subtask #1 [50 points]: N ≤ 10000
- Subtask #2 [50 points]: No additional constraints

-----Example-----
Input:
6
0 1 1 2 2 3

Output:
4 5 6

-----Explanation-----
The reporting structure:


Chefland has all the cities on a straight line. There are $N$ cities in Chefland numbered $1$ to $N$. City $i$ is located at coordinate $x_i$ on the x-axis. Guru wants to travel from city $A$ to city $B$. He starts at time t=0. He has following choices to travel.
- He can walk $1$ metre in $P$ secs.
- There is a train that travels from city $C$ to city $D$ which travels $1$ metre in $Q$ secs which starts at time t=$Y$ secs. Guru can take the train only at city $C$ and leave the train only at city $D$.
Can you help Guru find the minimum time he will need to travel from city $A$ to $B$. Note that you cannot board the train after time t =$Y$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- First line of each testcase contains eight space separated integers $N, A, B, C, D, P, Q, Y $.
- Second line of each testcase contains $N$ space-separated integers with the $i$-th integer representing $x_i$.

-----Output:-----
For each testcase, output in a single line containing the minimum travel time.

-----Constraints-----
- $1 \leq T \leq 300$
- $2 \leq N \leq 300$
- $-1000 \leq x_i \leq 1000$
- $0 \leq Y \leq 100000$
- $1 \leq A,B,C,D \leq n $
- $A \neq B$
- $C \neq D$
- $1 \leq P, Q \leq 100$
- $x_i < x_j$  if $i < j$

-----Sample Input:-----
1
4 1 3 2 4 3 2 4
1 2 3 4

-----Sample Output:-----
6

-----EXPLANATION:-----
Guru can walk directly in 6 secs.
If Guru takes train, then he will need  atleast 11 secs.


Two sisters, A and B, play the piano every day. During the day, they can play in any order. That is, A might play first and then B, or it could be B first and then A. But each one of them plays the piano exactly once per day. They maintain a common log, in which they write their name whenever they play.
You are given the entries of the log, but you're not sure if it has been tampered with or not. Your task is to figure out whether these entries could be valid or not.

-----Input-----
- The first line of the input contains an integer $T$ denoting the number of test cases. The description of the test cases follows.
- The first line of each test case contains a string $s$ denoting the entries of the log.

-----Output-----
- For each test case, output yes or no according to the answer to the problem.

-----Constraints-----
- $1 \le T \le 500$
- $2 \le |s| \le 100$
- $|s|$ is even
- Each character of $s$ is either 'A' or 'B'

-----Example Input-----
4
AB
ABBA
ABAABB
AA

-----Example Output-----
yes
yes
no
no

-----Explanation-----
Testcase 1: There is only one day, and both A and B have played exactly once. So this is a valid log. Hence 'yes'.
Testcase 2: On the first day, A has played before B, and on the second day, B has played first. Hence, this is also a valid log.
Testcase 3: On the first day, A played before B, but on the second day, A seems to have played twice. This cannot happen, and hence this is 'no'.


Chef is solving mathematics problems. He is preparing for Engineering Entrance exam. He's stuck in a problem.
$f(n)=1^n*2^{n-1}*3^{n-2} * \ldots * n^{1} $
Help Chef to find the value of $f(n)$.Since this number could be very large, compute it modulo $1000000007$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input,  $N$.

-----Output:-----
For each testcase, output in a single line the value of $f(n)$ mod $1000000007$.

-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$

-----Subtasks-----
Subtask 1(24 points) :
- $1 \leq T \leq 5000$
- $1 \leq N \leq 5000$
Subtask 2(51 points) : original constraints

-----Sample Input:-----
1
3

-----Sample Output:-----
12


Chef and his competitor Kefa own two restaurants located at a straight road. The position of Chef's restaurant is $X_1$, the position of Kefa's restaurant is $X_2$.
Chef and Kefa found out at the same time that a bottle with a secret recipe is located on the road between their restaurants. The position of the bottle is $X_3$.
The cooks immediately started to run to the bottle. Chef runs with speed $V_1$, Kefa with speed $V_2$.
Your task is to figure out who reaches the bottle first and gets the secret recipe (of course, it is possible that both cooks reach the bottle at the same time).

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains five space-separated integers $X_1$, $X_2$, $X_3$, $V_1$ and $V_2$.

-----Output-----
For each test case, print a single line containing the string "Chef" if Chef reaches the bottle first, "Kefa" if Kefa reaches the bottle first or "Draw" if Chef and Kefa reach the bottle at the same time (without quotes).

-----Constraints-----
- $1 \le T \le 10^5$
- $|X_1|, |X_2|, |X_3| \le 10^5$
- $X_1 < X_3 < X_2$
- $1 \le V_1 \le 10^5$
- $1 \le V_2 \le 10^5$

-----Example Input-----
3
1 3 2 1 2
1 5 2 1 2
1 5 3 2 2

-----Example Output-----
Kefa
Chef
Draw

-----Explanation-----
Example case 1. Chef and Kefa are on the same distance from the bottle, but Kefa has speed $2$, while Chef has speed $1$.


Richik$Richik$ has just completed his engineering and has got a job in one of the firms at Sabrina$Sabrina$ which is ranked among the top seven islands in the world in terms of the pay scale.
Since Richik$Richik$ has to travel a lot to reach the firm, the owner assigns him a number X$X$, and asks him to come to work only on the day which is a multiple of X$X$. Richik joins the firm on 1-st day but starts working from X-th day. Richik$Richik$ is paid exactly the same amount in Dollars as the day number. For example, if Richik$Richik$ has been assigned X=3$X = 3$, then he will be paid 3$3$ dollars and 6$6$ dollars on the 3rd$3rd$ and 6th$6th$ day on which he comes for work.
On N−th$N-th$ day, the owner calls up Richik$Richik$ and asks him not to come to his firm anymore. Hence Richik$Richik$ demands his salary of all his working days together. Since it will take a lot of time to add, Richik$Richik$ asks help from people around him, let's see if you can help him out.

-----Input:-----
- First line will contain T$T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, two integers X,N$X, N$.

-----Output:-----
For each testcase, output in a single line which is the salary which Richik$Richik$ demands.

-----Constraints-----
- 1≤T≤1000$1 \leq T \leq 1000$
- 1≤X<=N≤107$1 \leq X<=N \leq 10^7$

-----Sample Input:-----
1
3 10

-----Sample Output:-----
18


It's the annual military parade, and all the soldier snakes have arrived at the parade arena, But they aren't standing properly. The entire parade must be visible from the main podium, and all the snakes must be in a line. But the soldiers are lazy, and hence you must tell the soldiers to move to their new positions in such a manner that the total movement is minimized.
Formally, the entire parade strip can be thought of as the integer line. There are N snakes, where each snake is a line segment of length L. The i-th snake is initially at the segment [Si, Si + L]. The initial positions of the snakes can overlap. The only segment of the strip visible from the podium is [A, B], and hence all the snakes should be moved so that all of them are visible from the podium. They should also all be in a line without gaps and every consecutive pair touching each other. In other words, they should occupy the segments [X, X + L], [X + L, X + 2*L], ... , [X + (N-1)*L, X + N*L], for some X, such that A ≤ X ≤ X + N*L ≤ B. You are guaranteed that the visible strip is long enough to fit all the snakes.

If a snake was initially at the position [X1, X1 + L] and finally is at the position [X2, X2 + L], then the snake is said to have moved a distance of |X2 - X1|. The total distance moved by the snakes is just the summation of this value over all the snakes. You need to move the snakes in such a manner that it satisfies all the conditions mentioned above, as well as minimize the total distance. You should output the minimum total distance achievable.

-----Input-----
- The first line contains a single integer, T, the number of testcases. The description of each testcase follows.
- The first line of each testcase contains four integers, N, L, A and B, where N denotes the number of snakes, L denotes the length of each snake, and [A, B] is the segment visible from the podium.
- The next line contains N integers, the i-th of which is Si. This denotes that the i-th snake is initially in the segment [Si, Si + L].

-----Output-----
- For each testcase, output a single integer in a new line: the minimum total distance achievable.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- 1 ≤ Si ≤ 109
- 1 ≤ L ≤ 109
- 1 ≤ A ≤ B ≤ 109
- N * L ≤ B - A

-----Example-----
Input:
2
3 4 11 23
10 11 30
3 4 11 40
10 11 30

Output:
16
16

-----Explanation-----
In the first testcase, the three snakes are initially at segments [10, 14], [11, 15], and [30, 34]. One optimal solution is to move the first snake which was at [10, 14] to [15, 19] and the third snake which was at [30, 34] to [19, 23]. After this, the snakes would form a valid parade because they will be from [11, 15], [15, 19] and [19, 23]. Hence they are all in a line without any gaps in between them, and they are all visible, because they all lie in the visible segment, which is [11, 23].
The distance traveled by the first snake is |15 - 10| = 5, by the second snake is |11 - 11| = 0 and by the third snake is |19 - 30| = 11. Hence the total distance traveled is 5 + 0 + 11 = 16. This is the best that you can do, and hence the answer is 16.
In the second testcase, only the visible segment has increased. But you can check that the same final configuration as in the first subtask is still optimal here. Hence the answer is 16.


AND gates and OR gates are basic components used in building digital circuits. Both gates have two input lines and one output line. The output of an AND gate is 1 if both inputs are 1, otherwise the output is 0. The output of an OR gate is 1 if at least one input is 1, otherwise the output is 0.

You are given a digital circuit composed of only AND and OR gates where one node (gate or input) is specially designated as the output. Furthermore, for any gate G and any input node I, at most one of the inputs to G depends on the value of node I.

Now consider the following random experiment. Fix some probability p in [0,1] and set each input bit to 1 independently at random with probability p (and to 0 with probability 1-p). The output is then 1 with some probability that depends on p. You wonder what value of p causes the circuit to output a 1 with probability 1/2.

-----Input-----

The first line indicates the number of test cases to follow (about 100).

Each test case begins with a single line containing a single integer n with 1 ≤ n ≤ 100 indicating the number of nodes (inputs and gates) in the circuit. Following this, n lines follow where the i'th line describes the i'th node. If the node is an input, the line simply consists of the integer 0. Otherwise, if the node is an OR gate then the line begins with a 1 and if the node is an AND gate then the line begins with a 2. In either case, two more integers a,b follow, both less than i, which indicate that the outputs from both a and b are used as the two input to gate i.

As stated before, the circuit will be such that no gate has both of its inputs depending on the value of a common input node.

Test cases are separated by a blank line including a blank line preceding the first test case.

-----Output-----

For each test case you are to output a single line containing the value p for which the output of node n is 1 with probability exactly 1/2 if the inputs are independently and randomly set to value 1 with probability p. The value p should be printed with exactly 5 digits after the decimal.

-----Example-----
Input:

4

1
0

3
0
0
1 1 2

3
0
0
2 1 2

5
0
0
0
2 1 2
1 3 4

Output:

0.50000
0.29289
0.70711
0.40303

-----Temporary Stuff-----

A horizontal rule follows.

***

Here's a definition list (with `definitionLists` option):

apples
: Good for making applesauce.
oranges
: Citrus!
tomatoes
: There's no "e" in tomatoe.

#PRACTICE
- This must be done
[http:codechef.com/users/dpraveen](http:codechef.com/users/dpraveen)

(0.8944272−0.44721360.4472136−0.8944272)(10005)(0.89442720.4472136−0.4472136−0.8944272)(10005)
\left(\begin{array}{cc}
0.8944272 & 0.4472136\\
-0.4472136 & -0.8944272
\end{array}\right)
\left(\begin{array}{cc}
10 & 0\\
0 & 5
\end{array}\right)


The chef is having one array of natural numbers. Cheffina challenges chef that find the sum of weights all the natural numbers present in the array, but the main problem is that all numbers have not original weights. After every 6 natural numbers weight is set to 1 as weight increases by 1 after that. (i.e. weight of 1 is 1, weight of 2 is 2 but the weight of 7 is 1 and weight of 8 is 2 and so on…). Help the chef to find the sum.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains two lines of input, one integer $N$.
- Next line has N space separate natural numbers.

-----Output:-----
For each testcase, output in a single line answer.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $1 \leq arr[i] \leq 10^6$

-----Sample Input:-----
1
6
6 7 9 11 4 16

-----Sample Output:-----
23

-----EXPLANATION:-----
Array after conversion = [6, 1, 3, 5, 4, 4]


Chef has recently learned about number bases and is becoming fascinated.
Chef learned that for bases greater than ten, new digit symbols need to be introduced, and that the convention is to use the first few letters of the English alphabet. For example, in base 16, the digits are 0123456789ABCDEF. Chef thought that this is unsustainable; the English alphabet only has 26 letters, so this scheme can only work up to base 36. But this is no problem for Chef, because Chef is very creative and can just invent new digit symbols when she needs them. (Chef is very creative.)
Chef also noticed that in base two, all positive integers start with the digit 1! However, this is the only base where this is true. So naturally, Chef wonders: Given some integer N, how many bases b are there such that the base-b representation of N starts with a 1?

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each test case consists of one line containing a single integer N (in base ten).

-----Output-----
For each test case, output a single line containing the number of bases b, or INFINITY if there are an infinite number of them.

-----Constraints-----

-----Subtasks-----Subtask #1 (16 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 103
Subtask #2 (24 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 106
Subtask #3 (28 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 1012
Subtask #4 (32 points):
- 1 ≤ T ≤ 105
- 0 ≤ N < 1012

-----Example-----
Input:4
6
9
11
24

Output:4
7
8
14

-----Explanation-----
In the first test case, 6 has a leading digit 1 in bases 2, 4, 5 and 6: 610 = 1102 = 124 = 115 = 106.


You are teaching students to generate strings consisting of unique lowercase latin characters (a-z). You give an example reference string $s$ to the students.
You notice that your students just copy paste the reference string instead of creating their own string. So, you tweak the requirements for strings submitted by the students.
Let us define a function F(s, t) where s and t are strings as the number of characters that are same in both the strings. Note that the position doesn't matter. Here are a few examples of F(s, t):
F("abc", "def") = 0
F("abc", "acb") = 3
F("back", "abcd") = 3
Now you ask your students to output a string t with lowercase unique characters of the same length as $s$, such that F(s, t) $\leq k$ where you are also given the value of $k$. If there are multiple such strings, you ask them to output the lexicographically smallest possible string. If no such string is possible, output the string "NOPE" without quotes.

-----Input:-----
- The first line will contain $T$, the number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, which contains a string $s$ and an integer $k$.

-----Output:-----
For each testcase, output in a single line the lexicographically smallest string t such that F(s, t) <= k or "NOPE" without quotes if no such string exists.

-----Constraints-----
- $1 \leq T \leq 10000$
- $1 \leq $length of string s $(|s|) \leq 26$
- $s$ only consists of characters $a$ to $z$
- There are no repeating characters in s
- $0 \leq k \leq |s|$

-----Sample Input:-----
4
helowrd 0
background 0
abcdefghijklmnopqrstuvwxyz 0
b 1

-----Sample Output:-----
abcfgij
efhijlmpqs
NOPE
a


An area named Renus, is divided into $(N \times M)$ cells. According to archaeological survey the area contains huge amount of treasure. Some cells out of $(N \times M)$ cells contain treasure. But problem is, you can't go to every cell as some of the cells are blocked.
For every $a_{ij}$ cell($1 \leq i \leq N$,$1 \leq j \leq M$), your task is to find the distance of the nearest cell having treasure.
Note:
- You can only traverse up, down, left and right from a given cell.
- Diagonal movements are not allowed.
- Cells having treasure can't be blocked, only empty cells ( cells without treasure) can be blocked.

-----Input Format:------
- First line contains $T$, the number of test cases.
- Second line contains two space-separated integers $N\ and\ M$.
- Third line contains a single integer $X$ denoting number of cells having treasures, followed by $X$ lines containing two space-separated integers $x_i$ and $y_i$ denoting  position of row and column of $i^{th}$ treasure, for every $1\leq i \leq X$
- The next line contains a single integer $Y$ denoting the number of cells that are blocked, and it is followed by subsequent $Y$ lines containing  two space-separated integers $u_i$ and $v_i$ denoting position of row and column of blocked cells , for every $1\leq i \leq Y$

-----Constraints:------
- $1\le T \le 100$
- $1 \le N, M \le 200$
- $1 \le X < N*M$
- $0 \le Y <(N*M) - X$
- $1 \le x_i,u_j \le N, for\ every\ 1 \le i \le X\ and\ 1 \le j \le Y$
- $1 \le y_i,v_j \le M, for\ every\ 1 \le i \le X\ and\ 1 \le j \le Y$

-----Output Format:------
For each test case print a $N \times M$ matrix where each cell consists of distance of nearest treasure. Cells that are blocked will show "$X$" (without quotes). Also cells that doesn't have access to any treasure will show "$-1$" (without quotes).
Note: Co-ordinate of top left cell is $(1,1)$.

-----Sample Input-----
1
3 3
2
1 1
1 3
2
2 1
2 2

-----Sample Output-----
0 1 0
X X 1
4 3 2

-----Explanation:-----
- Coordinates  (1,1) and (1,3)  shows "0" because they contain treasure and nearest distance is 0.
- Coordinates (2,1) and (2,2) shows "X" as they are blocked.
- Rest shows distance of nearest cell having treasure.


Once again, we have a lot of requests from coders for a challenging problem on geometry. Geometry expert Nitin is thinking about a problem with parabolas, icosahedrons, crescents and trapezoids, but for now, to encourage beginners, he chooses to work with circles and rectangles.
You are given two sequences $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_N$. You should choose a permutation $P_1, P_2, \ldots, P_N$ of the integers $1$ through $N$ and construct $N$ rectangles with dimensions $A_1 \times B_{P_1}, A_2 \times B_{P_2}, \ldots, A_N \times B_{P_N}$. Then, for each of these rectangles, you should construct an inscribed circle, i.e. a circle with the maximum possible area that is completely contained in that rectangle.
Let $S$ be the sum of diameters of these $N$ circles. Your task is to find the maximum value of $S$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains $N$ space-separated integers $B_1, B_2, \ldots, B_N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum value of $S$. It is guaranteed that this value is always an integer.

-----Constraints-----
- $1 \le T \le 50$
- $1 \le N \le 10^4$
- $1 \le A_i, B_i \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (20 points):
- $A_1 = A_2 = \ldots = A_N$
- $B_1 = B_2 = \ldots = B_N$
Subtask #2 (80 points): original constraints

-----Example Input-----
2
4
8 8 10 12
15 20 3 5
3
20 20 20
10 10 10

-----Example Output-----
30
30

-----Explanation-----
Example case 1: Four rectangles with dimensions $8 \times 3$, $8 \times 5$, $10 \times 20$ and $12 \times 15$ lead to an optimal answer.


Emily and Mia are friends. Emily got Mia’s essay paper, but since she is a prankster, she decided to meddle with the words present in the paper. She changes all the words in the paper into palindromes. To do this, she follows two rules:
- In one operation she can only reduce the value of an alphabet by 1, i.e.  she can change ‘d’ to ‘c’, but she cannot change ‘c’ to ‘d’ or ‘d’ to ‘b’.
- The alphabet ‘a’ will not be reduced any further.
Each reduction in the value of any alphabet is counted as a single operation. Find the minimum number of operations required to convert a given string into a palindrome.

-----Input:-----
- The first line contains an integer $T$, denoting the number of test cases.
- Each test case consists of a string $S$ containing only lowercase characters with no spaces.

-----Output:-----
For each test case on a new line, print the minimum number of operations for the corresponding test case.

-----Constraints-----
- $1<=T<=10$
- $1<=|S|<=10^7$, where $|S|$ denotes length of string S.

-----Sample Input:-----
4
abc
abcba
abcd
cba

-----Sample Output:-----
2
0
4
2

-----EXPLANATION:-----
For the first test case string = “abc”
c->b->a so the string become “aba” which is a palindrome. For this we perform 2 operations


Chef is learning linear algebra. Recently, he learnt that for a square matrix $M$, $\mathop{\rm trace}(M)$ is defined as the sum of all elements on the main diagonal of $M$ (an element lies on the main diagonal if its row index and column index are equal).
Now, Chef wants to solve some excercises related to this new quantity, so he wrote down a square matrix $A$ with size $N\times N$. A square submatrix of $A$ with size $l\times l$ is a contiguous block of $l\times l$ elements of $A$. Formally, if $B$ is a submatrix of $A$ with size $l\times l$, then there must be integers $r$ and $c$ ($1\le r, c \le N+1-l$) such that $B_{i,j} = A_{r+i-1, c+j-1}$ for each $1 \le i, j \le l$.
Help Chef find the maximum trace of a square submatrix of $A$.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$-th of these lines contains $N$ space-separated integers $A_{i,1}, A_{i,2}, \dots, A_{i, N}$ denoting the $i$-th row of the matrix $A$.

-----Output-----
For each test case, print a single line containing one integer — the maximum possible trace.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le N \le 100$
- $1 \le A_{i,j} \le 100$ for each valid $i, j$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
1
3
1 2 5
6 3 4
2 7 1

-----Example Output-----
13

-----Explanation-----
Example case 1: The submatrix with the largest trace is
6 3
2 7

which has trace equal to $6 + 7 = 13$. (This submatrix is obtained for $r=2, c=1, l=2$.)


You are given a grid of size N x M consisting of '.' (empty), 'W' (white) or 'B' (black) cells. We follow the convention that the top left corner is the position (1,1) and bottom right corner is (N,M).
From every '.' cell (i, j), a ray is shot towards the right. If the ray reaches a 'B' cell, it loses it's strength fully and stops there. When a ray
reaches a 'W' cell, it's strength drops drastically so that the  ray stops when it reaches a second 'W' cell. That is, if there is no 'B'
cell in between, a ray can cross at most one 'W' cell, and it will stop when it reaches the second 'W' cell. It passes unchanged through  any '.' cell. If it reaches a boundary cell (ie. (i,M), for some i), it stops there.
Let L(i, j) be length travelled by the ray starting from the cell (i, j). If (i,j) is 'W' or 'B', no ray starts from here, and hence L(i,j) is defined to be 0. If a ray starts from (i,j) and stops at (i,k), then the distance travelled by this ray is k-j+1. i.e, inclusive of both starting and ending cells.
For the given grid your task is to find the sum of L(i, j) over all 1 <= i <= N and 1 <= j <= M.
The description of the grid is given as follows: In addition to N and M, you are given the number of 'W' cells (w) and the number of 'B' cells (b)
and you are given the locations of these w + b cells.  (The other cells contain '.')

-----Constraints:-----
For all testcases,
- 1 <= N, M <= 10^6.
- 0 <= w,b <= 10^5
Subtask 1: 15%
It is guaranteed that 1 <= N,M <= 500
Subtask 2: 25%
It is guaranteed that 1 <= N,M <= 2000
Subtask 3: 60%
No additional guarantees.

-----Input format:-----
- There is only one line of input which contains 4 + 2w + 2b space separated integers. The first four integers are N, M, w and b.
- The next 2*w integers denote the cells which contains a 'W': x1 y1 x2 y2 .. xw yw. These denote that (xi,yi) contains 'W'.
- The next 2*b integers denote the cells which contains a 'B': x1 y1 x2 y2 .. xb yb. These denote that (xi,yi) contains 'B'.
- The cells which are not in the input have to be assumed to be '.'

-----Output format:-----
Output a single integer which is the sum of L(i,j) over all 1 <= i <= N and 1 <= j <= M.

-----Sample Input 1:-----
4 4 5 2 1 3 2 1 3 2 3 3 4 3 1 4 2 3

-----Sample Output 1:-----
22

-----Explanation:-----
The grid is:
. . W B
W . B .
. W W .
. . W .

L(i,j) for each cell is:
4 3 0 0
0 2 0 1
3 0 0 1
4 3 0 1

Therefore, the total is 22.

-----Note:-----
As the answer might be large, please use 64 bit integers (long long int in C/C++ and long in Java) instead of 32 bit int.


Chef has just started Programming, he is in first year of Engineering. Chef is reading about Relational Operators.

Relational Operators are operators which check relatioship between two values. Given two numerical values A and B you need to help chef in finding the relationship between them that is,

- First one is greater than second or,
- First one is less than second or,
- First and second one are equal.

-----Input-----
First line contains an integer T, which denotes the number of testcases. Each of the T lines contain two integers A and B.

-----Output-----
For each line of input produce one line of output. This line contains any one of the relational operators

'<' , '>' , '='.

-----Constraints-----

- 1 ≤ T ≤ 10000
- 1 ≤ A, B ≤ 1000000001

-----Example-----
Input:
3
10 20
20 10
10 10

Output:
<
>
=

-----Explanation-----
Example case 1. In this example 1 as 10 is lesser than 20.


The  Chef  has bought $N$ boxes of Tiles. The number of tiles present in  $i^{th}$ box is  $i$  ($i   $ varies from $1$ to $N$) . The Chef  has two houses  with  $N$  rooms  each, whose  floors  is a square with area $(i*i)$ ,i varies from $(1....N)$. He want to distribute equal number of tiles from $i^{th}$ box to any two rooms (each room must belong to one house ) such that all tiles  of $i^ { th}$  box is used and floor of  both rooms of different houses are tiled completely.
Since chef is busy doing some other works so he wants your help to count the total number of rooms of both houses that will be tiled completely.
Note $:$ size of  each tile present in boxes has length and breadth equal to $1$. It is not mandatory to use all the boxes.
A room should be tilled completely from a single box.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains one integer $N$.

-----Output:-----
For each testcase print  the total number of rooms of both houses that will be tiled completely.

-----Constraints-----
- $1 \leq T \leq 5000$
- $1 \leq N \leq 10^{12}$

-----Sample Input:-----
1
16

-----Sample Output:-----
4

-----EXPLANATION:-----
The room $1$ and $2$ of both the houses are completely tiled.


Raj is suffering from shot term memory loss so  he is unable to remember his laptop password  but he has a list of some string and the only thing that he remember about his password is alphanumeric and also that all the characters are unique.
Given a list of strings, your task is to find a valid password.

-----Input-----
Each String contains lower case alphabets and 0-9.

-----Output-----
print "Invalid"(without quotes) if password is not valid else print "Valid"(without quotes) and stop processing input after it.

-----Constraints-----
1<=length of string <=100

-----Example-----
Input:
absdbads
asdjenfef
tyerbet
abc564

Output:
Invalid
Invalid
Invalid
Valid


You are given an equilateral triangle ΔABC with the side BC being the base. Each side of the triangle is of length L. There are L-1 additional points on each of the sides dividing the sides into equal parts of unit lengths. Points on the sides of the triangle are called major points. Joining these points with lines parallel to the sides of ΔABC will produce some more equilateral triangles. The intersection points of these parallel lines are called minor points.

Look at the picture below. It contains

- Major points: A, B, C, P1, P2, Q1, Q3, R1, R4, S1, S2, S3 (note that we consider A, B, C as major points as well)
- Minor points: Q2, R2, R3
- Equilateral triangles ΔP1Q1Q2, ΔQ2S1S3, etc

We consider an equilateral triangle to be valid if

- Each of its vertices is either a major or a minor point, and
- The distance from its base (the base of a triangle is the side parallel to BC) to BC is less than the distance from the other vertex of the triangle (i.e. opposite vertex that doesn't lie on the base of triangle) to BC.

In the figure above, ΔQ2P1P2 is not a valid triangle but ΔQ2R2R3 is a valid triangle.

You will be given L, the length of the original triangle ΔABC. You need to find out the number of valid equilateral triangles with side length exactly K.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of each testcase follows.
- Each test case has one line containing two space-separated integers: L and K.

-----Output-----
For each testcase, print "Case i: ", and then the answer, where i is the testcase number, 1-indexed.

-----Constraints-----
- 1 ≤ T ≤ 500
-  1 ≤ L, K ≤ 5000

-----Example-----
Input:
2
4 3
4 4

Output:
Case 1: 3
Case 2: 1

-----Explanation-----

The figure presented in the problem description is a triangle with side length 4.
In testcase 1, the valid triangles are ΔAR1R4, ΔP1BS3, ΔP2S1C

In testcase 2, the only valid triangle is ΔABC


The government of Siruseri has just commissioned one of the longest and most modern railway routes in the world. This route runs the entire length of Siruseri and passes through many of the big cities and a large number of small towns and villages in Siruseri.
The railway stations along this route have all been constructed keeping in mind the comfort of the travellers. Every station has big parking lots, comfortable waiting rooms and plenty of space for eateries. The railway authorities would like to contract out the catering services of these eateries.
The Siruseri Economic Survey has done a through feasibility study of the different stations and documented the expected profits (or losses) for the eateries in all the railway stations on this route. The authorities would like to ensure that every station is catered to. To prevent caterers from bidding only for profitable stations, the authorities have decided to give out catering contracts for contiguous segments of stations.
The minister in charge realises that one of the bidders is his bitter adversary and he has decided to hand out as useless a segment as possible to him. On the other hand, he does not want to be seen to be blatantly unfair by handing out a large loss-making section to the adversary. Instead he wants to find the largest segment whose sum is closest to $0$, so that his adversary spends all his time running a large number of canteens and makes either a small loss or a small profit or, even better, nothing at all!
In other words, if the profits/losses at the stations are $p_1, p_2, ..., p_N$ the minister would like to handover a sequence $i, i+1, ..., j$ such that the absolute value of $p_i + p_{i+1} + ... + p_j$ is minimized. If there is more than one sequence with this minimum absolute value then he would like to hand over the longest one.
For example, suppose there are $8$ stations along the line and their profitability is as follows:
$ $
Station              1    2    3    4    5    6    7    8
Expected Profits   -20   90  -30  -20   80  -70  -60  125

$ $
If the adversary is awarded the section $1$ through $4$, he will make a net profit of $20$. On the other hand if he is given stations $6, 7$ and $8$, he will make loss of $5$ rupees. This is the best possible value.

-----Input:-----
The first line of the input contains a single integer $N$ indicating the number of stations. The next $N$ lines (lines $2, 3, ..., N+1$) describe the profitability of the $N$ stations. Line $i+1$ contains a single integer denoting the expected profit at station $i$.

-----Output:-----
The first line contains a single integer indicating the minimum possible profit/loss among all segments. The second line contains two integers indicating the starting and ending point of the longest sequence with this minimum profit/loss. If there is more than one answer, it suffices to print one.

-----Constraints:-----
- $1 \leq N \leq 100000$.
- $-10^9 \leq p_i \leq 10^9$

-----Subtasks-----
- Subtask 1 - 40% - $1 \leq N \leq 4000$
- Subtask 2 - 60% - Original constraints

-----Sample Input-----
8
-20
90
-30
-20
80
-70
-60
125

-----Sample Output-----
-5
6 8


Sometimes Sergey visits fast food restaurants. Today he is going to visit the one called PizzaKing.
Sergey wants to buy N meals, which he had enumerated by integers from 1 to N. He knows that the meal i costs Ci rubles. He also knows that there are M meal sets in the restaurant.
The meal set is basically a set of meals, where you pay Pj burles and get Qj meals - Aj, 1, Aj, 2, ..., Aj, Qj.
Sergey has noticed that sometimes he can save money by buying the meals in the meal sets instead of buying each one separately. And now he is curious about what is the smallest amount of rubles he needs to spend to have at least one portion of each of the meals.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a pair of integer numbers N and M denoting the number of meals and the number of the meal sets.
The second line contains N space-separated integers C1, C2, ..., CN denoting the costs of the meals, bought separately.
Each of the following M lines starts with a pair of integer numbers Pi and Qi, denoting the cost of the meal set and the number of meals in it, followed with the integer numbers Ai, 1 Ai, 2, ..., Ai, Qi denoting the meal numbers.

-----Output-----
For each test case, output a single line containing the minimal total amount of money Sergey needs to spend in order to have at least one portion of each meal.

-----Constraints-----
- 1 ≤ Pi, Ci ≤ 106
- 1 ≤ M ≤ min{2N, 2 × 100000}
- No meal appears in the set twice or more times.
- Subtask 1 (16 points): 1 ≤ T ≤ 103, 1 ≤ N ≤ 8
- Subtask 2 (23 points): For each test file, either 1 ≤ T ≤ 10, 1 ≤ N ≤ 12 or the constraints for Subtask 1 are held.
- Subtask 3 (61 points): For each test file, either T = 1, 1 ≤ N ≤ 18 or the constraints for Subtask 1 or 2 are held.

-----Example-----
Input:1
3 3
3 5 6
11 3 1 2 3
5 2 1 2
5 2 1 3

Output:10

-----Explanation-----
Example case 1. If Sergey buys all the meals separately, it would cost him 3 + 5 + 6 = 14 rubles. He can buy all of them at once by buying the first meal set, which costs for 11 rubles, but the optimal strategy would be either to buy the second and the third meal set, thus, paying 5 + 5 = 10 rubles, or to buy the third meal set and the second meal separately by paying the same amount of 10 rubles.


-----General Statement:-----
Read a number in scientific notation and output its equivalent decimal value.

-----Input:-----
All data is on a single line. The first integer indicates how many pairs of numbers follow. The first of each pair is A, the base number, and the second is E, the power of 10.

-----Output:-----
Round each answer to 2 decimal places. Trailing zeros to the right of the decimal point are required. A leading zero to the left of the decimal point is not required.
The output is to be formatted exactly like that for the sample output given below.

-----Assumptions:-----
E is in the range –10 .. 10. A is 1 or larger but less than 10.
Discussion:
If A = 3.926 and E = 4, the number represented is 3.926 X 104 or 39260, which is 39260.00 when rounded to 2 decimal places.

-----Sample Input:-----
4 4.296 3 3.8 -2 1.8 2 2.8678 1

-----Sample Output:-----
4296.00
0.04
180.00
28.68


Chef Watson uses a social network called ChefBook, which has a new feed consisting of posts by his friends. Each post can be characterized by f - the identifier of the friend who created the post, p - the popularity of the post(which is pre-calculated by ChefBook platform using some machine learning algorithm) and s - the contents of the post which is a string of lower and uppercase English alphabets.
Also, Chef has some friends, which he has marked as special.
The algorithm used by ChefBook for determining the order of posts in news feed is as follows:

- Posts of special friends should be shown first, irrespective of popularity. Among all such posts the popular ones should be shown earlier.
- Among all other posts, popular posts should be shown earlier.

Given, a list of identifiers of Chef's special friends and a list of posts, you have to implement this algorithm for engineers of ChefBook and output the correct ordering of posts in the new feed.

-----Input-----
First line contains N, number of special friends of Chef and M, the number of posts. Next line contains N integers A1, A2, ..., AN denoting the identifiers of special friends of Chef. Each of the next M lines contains a pair of integers and a string denoting f, p and s, identifier of the friend who created the post, the popularity of the post and the contents of the post, respectively. It is guaranteed that no two posts have same popularity, but the same friend might make multiple posts.

-----Output-----
Output correct ordering of posts in news feed in M lines. Output only the contents of a post.

-----Constraints-----
- 1 ≤ N, M ≤ 103
- 1 ≤ Ai, f, p ≤  105
- 1 ≤ length(s) ≤  100

-----Example-----
Input:
2 4
1 2
1 1 WhoDoesntLoveChefBook
2 2 WinterIsComing
3 10 TheseViolentDelightsHaveViolentEnds
4 3 ComeAtTheKingBestNotMiss

Output:
WinterIsComing
WhoDoesntLoveChefBook
TheseViolentDelightsHaveViolentEnds
ComeAtTheKingBestNotMiss

-----Explanation-----

First we should show posts created by friends with identifiers 1 and 2. Among the posts by these friends, the one with more popularity should be shown first.

Among remaining posts, we show those which are more popular first.

WinterIsComing
WhoDoesntLoveChefBook
TheseViolentDelightsHaveViolentEnds
ComeAtTheKingBestNotMiss


Chef owns an icecream shop in Chefland named scoORZ. There are only three types of coins in Chefland: Rs. 5, Rs. 10 and Rs. 15. An icecream costs Rs. 5.
There are $N$ people (numbered $1$ through $N$) standing in a queue to buy icecream from scoORZ. Each person wants to buy exactly one icecream. For each valid $i$, the $i$-th person has one coin with value $a_i$. It is only possible for someone to buy an icecream when Chef can give them back their change exactly ― for example, if someone pays with a Rs. 10 coin, Chef needs to have a Rs. 5 coin that he gives to this person as change.
Initially, Chef has no money. He wants to know if he can sell icecream to everyone in the queue, in the given order. Since he is busy eating his own icecream, can you tell him if he can serve all these people?

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $a_1, a_2, \ldots, a_N$.

-----Output-----
For each test case, print a single line containing the string "YES" if all people can be served or "NO" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 10^3$
- $a_i \in \{5, 10, 15\}$ for each valid $i$

-----Subtasks-----
Subtask #1 (40 points): $a_i \in \{5, 10\}$ for each valid $i$
Subtask #2 (60 points): original constraints

-----Example Input-----
3
2
5 10
2
10 5
2
5 15

-----Example Output-----
YES
NO
NO

-----Explanation-----
Example case 1: The first person pays with a Rs. 5 coin. The second person pays with a Rs. 10 coin and Chef gives them back the Rs. 5 coin (which he got from the first person) as change.
Example case 2: The first person already cannot buy an icecream because Chef cannot give them back Rs. 5.
Example case 3: The first person pays with a Rs. 5 coin. The second person cannot buy the icecream because Chef has only one Rs. 5 coin, but he needs to give a total of Rs. 10 back as change.


Master Shifu is training Po to become The Dragon Warrior and as a final assignment he must obtain maximum deliciousness from dumplings. There are  $N$ plates of dumplings in front of him with deliciousness $A_1, A_2, \ldots, A_N$, Po can choose any number of continuous plates of  dumplings. The total deliciousness is the sum of deliciousness of all the  chosen dumplings.
What is the minimum number of plates he must choose so that total deliciousness is maximum possible?
Note: Po must choose atleast one plate.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, print a single line containing one integer.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 2 \cdot 10^5$
- $0 \le A_i \le 10^9$

-----Sample Input:-----
2
4
1 2 3 4
5
3 2 0 3 0

-----Sample Output:-----
4
4


Chef made $N$ pieces of cakes, numbered them $1$ through $N$ and arranged them in a row in this order. There are $K$ possible types of flavours (numbered $1$ through $K$); for each valid $i$, the $i$-th piece of cake has a flavour $A_i$.
Chef wants to select a contiguous subsegment of the pieces of cake such that there is at least one flavour which does not occur in that subsegment. Find the maximum possible length of such a subsegment of cakes.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two integers $N$ and $K$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum length of a valid subsegment.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $2 \le K \le 10^5$
- $1 \le A_i \le K$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $N \le 10^3$
- $K = 2$
- the sum of $N$ over all test cases does not exceed $10^4$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
6 2
1 1 1 2 2 1
5 3
1 1 2 2 1

-----Example Output-----
3
5


The chef was searching for his pen in the garage but he found his old machine with a display and some numbers on it. If some numbers entered then some different output occurs on the display. Chef wants to crack the algorithm that the machine is following.
Example to identify the pattern :
Input                            Output
9                                   36
5                                   10
1                                    0
2                                    1

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, $N$.

-----Output:-----
For each test case, output in a single line answer as displayed on the screen.

-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$

-----Sample Input:-----
1
7

-----Sample Output:-----
21


In India, every individual is charged with income tax on the total income each year. This tax is applied to specific ranges of income, which are called income tax slabs. The slabs of income tax keep changing from year to year. This fiscal year (2020-21), the tax slabs and their respective tax rates are as follows:Total income (in rupees)Tax rateup to Rs. 250,0000%from Rs. 250,001 to Rs. 500,0005%from Rs. 500,001 to Rs. 750,00010%from Rs. 750,001 to Rs. 1,000,00015%from Rs. 1,000,001 to Rs. 1,250,00020%from Rs. 1,250,001 to Rs. 1,500,00025%above Rs. 1,500,00030%
See the sample explanation for details on how the income tax is calculated.
You are given Chef's total income: $N$ rupees (Rs.). Find his net income. The net income is calculated by subtracting the total tax (also called tax reduction) from the total income. Note that you do not need to worry about any other kind of tax reductions, only the one described above.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single integer $N$.

-----Output-----
For each test case, print a single line containing one integer — Chef's net income.

-----Constraints-----
- $1 \le T \le 10^3$
- $0 \le N \le 10^7$
- $N$ is a multiple of $100$

-----Example Input-----
2
600000
250000

-----Example Output-----
577500
250000

-----Explanation-----
Example case 1: We know that the total income is Rs. $6$ lakh ($1$ lakh rupees = $10^5$ rupees). The total tax for each slab is calculated as follows:
- Up to $2.5$ lakh, the tax is Rs. $0$, since the tax rate is $0$ percent.
- From above Rs. $2.5$ lakh to Rs. $5$ lakh, the tax rate is $5$ percent. Therefore, this tax is $0.05 \cdot (500,000-250,000)$, which is Rs. $12,500$.
- From above Rs. $5$ lakh to Rs. $6$ lakh, the tax rate is $10$ percent. Therefore, this tax is $0.10 \cdot (600,000-500,000)$, which is Rs. $10,000$.
- Summing them up, we get that the total tax on Chef's whole income is Rs. $22,500$. Since the net income is the total income minus the tax reduction, it is Rs. $600,000$ minus Rs. $22,500$, which is Rs. $577,500$.
Example case 2: For income up to Rs. $2.5$ lakh, we have no tax, so the net income is the same as the total income: Rs. $2.5$ lakh.


Chef's pizza is the tastiest pizza to exist, and the reason for that is his special, juicy homegrown tomatoes.
Tomatoes can be grown in rectangular patches of any side lengths. However, Chef only has a limited amount of land.
Consider the entire town of Chefville to be consisting of cells in a rectangular grid of positive coordinates.
Chef own all cells (x,y)$(x, y)$ that satisfy x∗y≤N$x*y \leq N$
As an example if N=4$N = 4$, Chef owns the following cells:
(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(3,1),(4,1)$(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (4, 1) $
Chef can only grow tomatoes in rectangular patches consisting only of cells which belong to him. Also, if he uses a cell, he must use it entirely. He cannot use only a portion of it.
Help Chef find the number of unique patches of rectangular land that he can grow tomatoes in! Since this number can be very large, output it modulo 1000000007$1000000007$.

-----Input:-----
- The first line of the input contains T$T$, the number of test cases.
- The next T$T$ lines of input contains one integer N$N$.

-----Output:-----
For each testcase, output the number of ways modulo 1000000007$1000000007$.

-----Constraints-----
- 1≤T≤5$1 \leq T \leq 5$
- 1≤N≤1010$1 \leq N \leq 10^{10}$

-----Sample Input:-----
2
4
10000000000

-----Sample Output:-----
23
227374950


Give me Chocolate

Anushka wants to buy chocolates.there are many chocolates in front of her, tagged with their prices.

Anushka has only a certain amount to spend, and she wants to maximize the number of chocolates she buys with this money.

Given a list of prices and an amount to spend, what is the maximum number of chocolates Anushka can buy?

For example,

if prices =[1,2,3,4]
and Anushka has k=7 to spend, she can buy items [1,2,3] for 6 , or [3,4] for 7 units of currency. she would choose the first group of 3 items.

Input Format

The first line contains two integers, n and k , the number of priced chocolates and the amount Anushka has to spend.

The next line contains n space-separated integers prices[i]

Constraints

1<= n <= 105

1<= k <= 109

1<= prices[i] <= 109

A chocolate can't be bought multiple times.

Output Format

An integer that denotes the maximum number of chocolates Anushka can buy for her.

Sample Input

7 50

1 12 5 111 200 1000 10

Sample Output

4

Explanation

she can buy only 4 chocolatess at most. These chocolates have the following prices: 1, 12, 5, 10.


Motu and Patlu are racing against each other on a circular track of radius $R$. Initially they are at the same point on the track and will run in same direction .The coach ordered them to run $X$ rounds of the circular field. Patlu wants to know how many times they will meet after the race starts and  before any of them finishes $X$ rounds. But he is busy in warm up so he wants you to calculate this. You are given speed of both Motu and Patlu ($A$ and $B$).

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, four integers $X, R, A, B$.

-----Output:-----
For each testcase, output in a single line answer the number of times whey will meet before any of them completes $X$ rounds.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq R \leq 10^9$
- $1 \leq X \leq 10^9$
- $1 \leq A \leq 10^9$
- $1 \leq B \leq 10^9$
- Speed of both are different

-----Sample Input:-----
2
3 10 2 5
2 20 5 10

-----Sample Output:-----
1
0


Mr. Wilson was planning to record his new Progressive Rock music album called "Digits. Cannot. Separate". Xenny and PowerShell, popular pseudo-number-theoreticists from the Land of Lazarus were called by him to devise a strategy to ensure the success of this new album. Xenny and Powershell took their Piano Lessons and arrived at the Studio in different Trains.
Mr. Wilson, creative as usual, had created one single, long music track S. The track consisted of N musical notes. The beauty of each musical note was represented by a decimal digit from 0 to 9.
Mr. Wilson told them that he wanted to create multiple musical tracks out of this long song. Since Xenny and Powershell were more into the number theory part of music, they didn’t know much about their real workings. Mr. Wilson told them that a separator could be placed between 2 digits. After placing separators, the digits between 2 separators would be the constituents of this new track and the number formed by joining them together would represent the Quality Value of that track. He also wanted them to make sure that no number formed had greater than M digits.
Mr. Wilson had Y separators with him. He wanted Xenny and PowerShell to use at least X of those separators, otherwise he would have to ask them to Drive Home.
Xenny and PowerShell knew straight away that they had to put place separators in such a way that the Greatest Common Divisor (GCD) of all the Quality Values would eventually determine the success of this new album. Hence, they had to find a strategy to maximize the GCD.
If you find the maximum GCD of all Quality Values that can be obtained after placing the separators, Xenny and PowerShell shall present you with a Porcupine Tree.
Note:
-
You can read about GCD here.

-
Greatest Common Divisor of 0 and 0 is defined as 0.

-----Input-----
The first line of input consists of a single integer T - the number of testcases.
Each test case is of the following format:
First line contains a single integer N - the length of the long musical track.
Second line contains the string of digits S.
Third line contains 3 space-separated integers - M, X and Y - the maximum number of digits in a number, the minimum number of separators to be used and the maximum number of separators to be used.

-----Output-----
For each testcase, output a single integer on a new line - the maximum GCD possible after placing the separators.

-----Constraints-----
Subtask 1: 20 points

- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 18
- 1 ≤ M ≤ 2
- 1 ≤ X ≤ Y ≤ (N - 1)

Subtask 2: 80 points

- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 300
- 1 ≤ M ≤ 10
- 1 ≤ X ≤ Y ≤ (N - 1)

For both Subtask 1 and Subtask 2:

- 1 ≤ X ≤ Y ≤ (N - 1)
- M*(Y+1) ≥ N
- S may contain leading 0s.

-----Example-----Input:
2
3
474
2 1 1
34
6311861109697810998905373107116111
10 4 25

Output:
2
1

-----Explanation-----
Test case 1.
Since only 1 separator can be placed, we can only have 2 possibilities:

a. 4 | 74

The GCD in this case is 2.

b. 47 | 4

The GCD in this case is 1.

Hence, the maximum GCD is 2.
Test case 2.

One of the optimal partitions is:
63|118|61|109|69|78|109|98|90|53|73|107|116|111
Bonus: Decode the above partition to unlock a hidden treasure.


Pied Piper is a startup company trying to build a new Internet called Pipernet. Currently, they have $A$ users and they gain $X$ users everyday. There is also another company called Hooli, which has currently $B$ users and gains $Y$ users everyday.
Whichever company reaches $Z$ users first takes over Pipernet. In case both companies reach $Z$ users on the same day, Hooli takes over.
Hooli is a very evil company (like E-Corp in Mr. Robot or Innovative Online Industries in Ready Player One). Therefore, many people are trying to help Pied Piper gain some users.
Pied Piper has $N$ supporters with contribution values $C_1, C_2, \ldots, C_N$. For each valid $i$, when the $i$-th supporter contributes, Pied Piper gains $C_i$ users instantly. After contributing, the contribution value of the supporter is halved, i.e. $C_i$ changes to $\left\lfloor C_i / 2 \right\rfloor$. Each supporter may contribute any number of times, including zero. Supporters may contribute at any time until one of the companies takes over Pipernet, even during the current day.
Find the minimum number of times supporters must contribute (the minimum total number of contributions) so that Pied Piper gains control of Pipernet.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains six space-separated integers $N$, $A$, $B$, $X$, $Y$ and $Z$.
- The second line contains $N$ space-separated integers $C_1, C_2, \ldots, C_N$ — the initial contribution values.

-----Output-----
For each test case, if Hooli will always gain control of Pipernet, print a single line containing the string "RIP" (without quotes). Otherwise, print a single line containing one integer — the minimum number of times supporters must contribute.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A, B, X, Y, Z \le 10^9$
- $A, B < Z$
- $0 \le C_i \le 10^9$ for each valid $i$

-----Example Input-----
3
3 10 15 5 10 100
12 15 18
3 10 15 5 10 100
5 5 10
4 40 80 30 30 100
100 100 100 100

-----Example Output-----
4
RIP
1

-----Explanation-----
Example case 1: After $8$ days, Pied Piper will have $50$ users and Hooli will have $95$ users. Then, if each supporter contributes once, Pied Piper will also have $95$ users. After that, they still need $5$ more users, so supporter $3$ can contribute again, with $18/2 = 9$ more users. So the answer will be $4$.
Example case 2: There is no way to beat Hooli.


There's a tree and every one of its nodes has a cost associated with it. Some of these nodes are labelled special nodes. You are supposed to answer a few queries on this tree. In each query, a source and destination node (SNODE$SNODE$ and DNODE$DNODE$) is given along with a value W$W$. For a walk between SNODE$SNODE$ and DNODE$DNODE$ to be valid you have to choose a special node and call it the pivot P$P$. Now the path will be SNODE$SNODE$ ->P$ P$ -> DNODE$DNODE$. For any valid path, there is a path value (PV$PV$) attached to it. It is defined as follows:
Select a subset of nodes(can be empty)  in the path from SNODE$SNODE$ to P$P$ (both inclusive) such that sum of their costs (CTOT1$CTOT_{1}$) doesn't exceed W$W$.
Select a subset of nodes(can be empty) in the path from P$P$ to DNODE$DNODE$ (both inclusive) such that sum of their costs (CTOT2$CTOT_{2}$) doesn't exceed W$W$.
Now define PV=CTOT1+CTOT2$PV = CTOT_{1} + CTOT_{2}$ such that the absolute difference  x=|CTOT1−CTOT2|$x = |CTOT_{1} - CTOT_{2}|$ is as low as possible. If there are multiple pairs of subsets that give the same minimum absolute difference, the pair of subsets which maximize PV$PV$ should be chosen.
For each query, output the path value PV$PV$ minimizing x$x$ as defined above.
Note that the sum of costs of an empty subset is zero.

-----Input-----
- First line contains three integers N$N$ - number of vertices in the tree, NSP$NSP$ - number of special nodes in the tree and Q$Q$ - number of queries to answer.
- Second line contains N−1$N-1$ integers. If the i$i$th integer is Vi$V_i$ then there is an undirected edge between i+1$i + 1$ and Vi$V_i$ (i$i$ starts from 1$1$ and goes till N−1$N-1$).
- Third line contains N$N$ integers, the i$i$th integer represents cost of the i$i$th vertex.
- Fourth line contains NSP$NSP$ integers - these represent which nodes are the special nodes.
- Following Q$Q$ lines contains three integers each - SNODE$SNODE$, DNODE$DNODE$ and W$W$ for each query.

-----Output-----
For each query output a single line containing a single integer - the path value PV$PV$ between SNODE$SNODE$ and DNODE$DNODE$.

-----Constraints:-----
- 1≤$1 \leq $ Number of nodes ≤1000$ \leq 1000 $
- 0≤W≤1000$ 0 \leq W \leq 1000 $
- 1≤$ 1 \leq $ Number of special nodes ≤10$ \leq 10 $
- 0≤$ 0 \leq $ Cost of each node ≤1000$ \leq 1000 $
- 1≤$ 1 \leq $ Number of queries ≤1000$ \leq 1000 $

-----Sample Input-----
7 1 5

1 1 2 2 3 3

3 5 4 2 7 9 1

1

2 3 100

1 1 100

2 1 100

4 5 100

4 7 100

-----Sample Output:-----
6

6

6

20

16

-----Explanation:-----
Consider query 4$4$. The only path is 4−>2−>1−>2−>5$4->2->1->2->5$. The two sets defined for this path are {3,2,5${3,2,5}$} and {3,5,7${3,5,7}$}. Pick subsets {3,2,5${3,2,5}$} and {3,7${3,7}$} from each set which minimizes PV$PV$. Note that node 2$2$ can repeat as it is in different paths (both to and from the pivot).


Chef is baking a cake.

While baking, in each minute the size of cake doubles as compared to its previous size.

In this cake, baking of cake is directly proportional to its size.
You are given $a$, the total time taken(in minutes) to bake the whole cake.

Let cake be half baked at $k^{th}$ minute.
Your task is to find the value of $k+2$.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of T test cases follows.
- The first and only line of each test case contains a single integer $a$.

-----Output:-----
For each testcase , print one line, the value of $k+2$.

-----Constraints-----
- $1 \leq T \leq 8 $
- $2 \leq a \leq 10^{128}$

-----Sample Input:-----
1

2

-----Sample Output:-----
3

-----Explaination-----
Time was 1 min when cake was half baked by chef so answer is 1+2=3