Not everyone probably knows that Chef has younder brother Jeff. Currently Jeff learns to read.
He knows some subset of the letter of Latin alphabet. In order to help Jeff to study, Chef gave him a book with the text consisting of N words. Jeff can read a word iff it consists only of the letters he knows.
Now Chef is curious about which words his brother will be able to read, and which are not. Please help him!

-----Input-----
The first line of the input contains a lowercase Latin letter string S, consisting of the letters Jeff can read. Every letter will appear in S no more than once.
The second line of the input contains an integer N denoting the number of words in the book.
Each of the following N lines contains a single lowecase Latin letter string Wi, denoting the ith word in the book.

-----Output-----
For each of the words, output "Yes" (without quotes) in case Jeff can read it, and "No" (without quotes) otherwise.

-----Constraints-----
- 1 ≤ |S| ≤ 26
- 1 ≤ N ≤ 1000
- 1 ≤ |Wi| ≤ 12
- Each letter will appear in S no more than once.
- S, Wi consist only of lowercase Latin letters.

-----Subtasks-----
- Subtask #1 (31 point): |S| = 1, i.e. Jeff knows only one letter.
- Subtask #2 (69 point)	: no additional constraints

-----Example-----
Input:act
2
cat
dog

Output:Yes
No

-----Explanation-----
The first word can be read.
The second word contains the letters d, o and g that aren't known by Jeff.


You are an evil sorcerer at a round table with $N$ sorcerers (including yourself). You can cast $M$ spells which have distinct powers $p_1, p_2, \ldots, p_M$.
You may perform the following operation any number of times (possibly zero):
- Assign a living sorcerer to each positive integer cyclically to your left starting from yourself ― the closest living sorcerer to your left is assigned to $1$, the next living sorcerer to the left is assigned to $2$ and so on. Note that each living sorcerer (including yourself) is assigned to an infinite number of integers.
- Choose a spell $j$ (possibly a spell you have chosen before) and kill the living sorcerer assigned to $p_j$. You may not cast a spell to kill yourself.

What is the maximum number of sorcerers you can kill using zero or more operations?

-----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 space-separated integers $N$ and $M$.
- The second line contains $M$ space-separated integers $p_1, p_2, \ldots, p_M$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum number of sorcerers you can kill.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^9$
- $1 \le M \le 3 \cdot 10^5$
- $1 \le p_i \le 10^9$ for each valid $i$
- $p_1, p_2, \ldots, p_N$ are pairwise distinct
- the sum of $M$ over all test cases does not exceed $3 \cdot 10^5$

-----Example Input-----
5
4 1
5
6 2
2 4
1 4
7 16 8 29
1000000000 1
998244353
1 1
20201220

-----Example Output-----
3
4
0
1755647
0

-----Explanation-----
Example case 1: The initial state is shown in the figure from the statement. We can first use spell $1$ and kill the $5$-th sorcerer to our left, i.e. sorcerer $2$. Now there are $3$ living sorcerers and the state is as shown in the following figure:

We can use spell $1$ again and kill the current $5$-th living sorcerer to our left, i.e. sorcerer $4$. Now there are $2$ living sorcerers and the state is:

Finally, we can use spell $1$ again and kill the only other living sorcerer, i.e. sorcerer $3$. Now, none of the other sorcerers are alive. As we cannot cast a spell to kill ourselves, we cannot improve the answer any further.
Example case 2: We can perform $4$ operations using the spell $p_1 = 2$ each time. We can also instead use $p_2 = 4$ in the first two operations and $p_1 = 2$ in the last two operations. Note that there may be multiple valid sequences of operations that lead to the best answer.
Example case 3: We cannot perform any operations using any of the given spells, so we are unable to kill any sorcerers.
Example case 4: We can perform $1,755,647$ operations, each of them using the spell $p_1 = 998,244,353$.

question_and_tests_only_no_solution_or_reasoning; test_cases are the VERIFIER not an answer


Ganesh lives in Gopalmath. He is looking for Jojo. So he decides to collect Aadhar Card Information of all the citizens of India from UIDAI.
Someone told Ganesh that the sum of all the digits of Jojo’s Aadhar number is divisible by 10 and it is greater than zero. After finding all Aadhar numbers which are divisible by 10, Jojo’s Aadhar number is $N$th smallest Aadhar number. Hence, Ganesh wants to find Jojo’s  Aadhar number which satisfies all of the above conditions. (In this chaotic world, Aadhar numbers can be any natural number.)
However, Guruji refused Ganesh to carry out this task, because he is weak in Maths. Therefore, Ganesh assigns this task to Paritoshbhai who possesses excellent Mathematical skills. Since Paritoshbhai is busy in his jewellery business, help him in this task.

-----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 Aadhar number of Jojo.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^{100,000}$

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

-----Sample Output:-----
37


Chef just got a box of chocolates as his birthday gift. The box contains $N$ chocolates in a row (numbered $1$ through $N$), where $N$ is even. For each valid $i$, the $i$-th chocolate has a sweetness value $W_i$.
Chef wants to eat all the chocolates in the first half of the box and leave all chocolates in the second half uneaten. Since he does not like chocolates that are too sweet, he will be unhappy if at least one of the chocolates he eats has the maximum sweetness among all the chocolates in the box.
A right cyclic shift by $k$ chocolates ($0 \le k < N$) consists of moving the last $k$ chocolates in the row to the beginning in the same order and moving each of the remaining $N-k$ chocolates $k$ places to the right. Before eating the first half of the chocolates, Chef wants to perform some right cyclic shift in such a way that he will not be unhappy after eating them. Find the number of ways to do this, i.e. the number of valid integers $k$ such that if Chef performs the right cyclic shift by $k$ chocolates and then eats the first half of the chocolates in the box, he does not become unhappy.

-----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 $W_1, W_2, \ldots, W_N$.

-----Output-----
For each test case, print a single line containing one integer ― the number of shifts for which Chef does not become unhappy.

-----Constraints-----
- $1 \le T \le 5$
- $1 \le N \le 10^5$
- $N$ is even
- $1 \le W_i \le 10^5$ for each valid $i$

-----Example Input-----
2
6
1 1 2 1 1 1
6
1 1 2 1 1 2

-----Example Output-----
3
0

-----Explanation-----
Example case 1: The three valid right shifts and the contents of the box for these shifts are:
- shift by $k = 1$: $(1, 1, 1, 2, 1, 1)$
- shift by $k = 2$: $(1, 1, 1, 1, 2, 1)$
- shift by $k = 3$: $(1, 1, 1, 1, 1, 2)$


Consider the infinite x$x$ axis. There are N$N$ impacts on this X-axis at integral points (X1$X_1$,X2$X_2$,....XN$X_N$)  (all distinct) . An impact at a point X$X$i propagates such that at a point X$X$0, the effect of the impact is K|Xi−X0|$K^{|X_i - X_0|}$. Given the point X0$X_0$, N$N$ and K$K$. Assume the total impact on X0$X_0$ is M$M$, find if it is possible to do so.Note: You are not required to find the set X

Formally print "yes" if this is possible and "no" if not possible.

-----Input:-----
- First line will contain T$T$, number of testcases. Then the testcases follow.
-  Each testcase contains of a single line of input, four integers N$N$,K$K$,M$M$,X$X$0

-----Output:-----
-  The output of each test case is either "yes" or "no"

-----Constraints -----
-  1≤T≤1000$1\leq T \leq 1000$
-  1≤N≤100$1\leq N \leq 100$
-  1≤K≤1000$1\leq K \leq 1000$
-  1≤M≤1018$1\leq M \leq 10^{18}$
-  −109≤X0≤109$-10^9 \leq X_0 \leq 10^9$

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

4 3 10 10

2 3 10 10

-----Sample Output:-----
	no

yes


-----Problem-----

			Nikki's latest work is writing a story of letters. However, she finds writing story so boring that, after working for three hours, she realized that all she has written are M long words consisting entirely of letters A and B. Having accepted that she will never finish the story in time, Nikki has decided to at least have some fun with it by counting bubbly words.

			Now Nikki is connecting pairs of identical letters (A with A, B with B) by drawing lines above the word. A given word is bubbly if each letter can be connected to exactly one other letter in such a way that no two lines intersect. So here is your task. Help Nikki count how many words are bubbly.

-----Input-----
-
			The first line of input contains the positive integer M, the number of words written down by Nikki.

-
			Each of the following M lines contains a single word consisting of letters A and B, with length

			between 2 and 10^5, inclusive. The sum of lengths of all words doesn't exceed 10^6.

-----Output-----

			The first and only line of output must contain the number of bubbly words.

-----Constraints-----
-
			1 ≤ M ≤ 100

-----Sample Input-----

3

ABAB

AABB

ABBA

-----Sample Output-----
2

-----Explanation-----
-
					 ABAB - It is not bubbly as A(indexed 1) will connect to A(indexed 3) by a line and when we try to connect B(indexed 2) with B(indexed 4) by a line then it will intersect with the line b/w A and A.

-
					AABB - It is bubbly as line b/w A and A will not intersect with the line b/w B and B.

-
ABBA -It is also bubbly as lines will not intersect. We can draw line b/w A and A above the line b/w B and B.
				 p { text-align:justify }


Dexter, being irritated by DD, gave her a lucrative game to play to keep her busy.
There are $N$ bags numbered $1$ to $N$. The $i_{th}$ bag contains $A_i$ coins. The bags are placed in a circular order such that the $N_{th}$ bag is adjacent to the $1^{st}$ bag.
DD can select $K$ consecutive adjacent bags and take all the coins in them.   Help her find the maximum number of coins she can take by making the ideal choice.
Note that the selected bags must be consecutive. Since they are placed in circular order, bag number $1$ and $N$ are considered to be consecutive.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- First-line contains $N$ and $K$.
- Second-line contains $N$ numbers $A_1, A_2,...,A_N$,

-----Output:-----
For each test case, output in a single line, the maximum money that can be collected by DD.

-----Constraints-----
- $1 \leq T \leq 100$
- $5 \leq N \leq 10^5$
- $1 \leq K < N$
- $1 \leq A_i \leq 10^5$
Sum of $N$ over all test cases is less than $10^6$

-----Sample Input:-----
1
5 3
8 6 9 4 10

-----Sample Output:-----
24

-----EXPLANATION:-----
The ideal choice would be to take the last bag with $10$ coins and the first $2$ bags with $8$ and $6$ coins.


Shaun is very much interested in Subarrays. Shaun wants to count the number of subarrays in his chosen array with sum being a multiple of $10^9$. Since, Shaun is interested in huge numbers.He chose his array such that it contains only $10^8$ and $9*10^8$ as its elements.
Help shaun to count the number of required subarrays.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- First line of each testcase contains one integer $N$,size of array $A$.
- Second line of each testcase contains $N$ space separated array elements

-----Output:-----
For each testcase, output in a single line number of subarrays with sum being multiple of $10^9$.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $A[i]$=$10^8$ , $9*10^8$

-----Sample Input:-----
2
3
100000000 900000000 100000000
1
900000000

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


Chef is given a sequence of prime numbers $A_1, A_2, \ldots, A_N$. This sequence has exactly $2^N$ subsequences. A subsequence of $A$ is good if it does not contain any two identical numbers; in particular, the empty sequence is good.
Chef has to find the number of good subsequences which contain at most $K$ numbers. Since he does not know much about subsequences, help him find the answer. This number could be very large, so compute it modulo $1,000,000,007$.

-----Input-----
- The first line of the input contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
Print a single line containing one integer ― the number of good subsequences with size at most $K$, modulo $1,000,000,007$.

-----Constraints-----
- $1 \le K \le N \le 10^5$
- $2 \le A_i \le 8,000$ for each valid $i$

-----Subtasks-----
Subtask #1 (40 points): $A_1, A_2, \ldots, A_N$ are pairwise distinct
Subtask #2 (60 points): original constraints

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

-----Example Output-----
18

-----Explanation-----
There is $1$ good subsequence with length $0$, $5$ good subsequences with length $1$, $8$ good subsequences with length $2$ and $4$ good subsequences with length $3$.


Chef made two laddus with sweetness X and Y respectively. Cheffina comes and sees the chef created two laddus with different sweetness (might be same). Cheffina has the magical power to make the sweetness of laddus equal. Cheffina requires 1 unit of power to increase the sweetness of laddu by its original value i.e. 1 unit to convert Z to 2Z and 2 unit to convert Z to 3Z and so on… How many units of power does cheffina want to make the sweetness equal?

-----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, two integers $X, Y$.

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

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq X,Y \leq 10^5$

-----Sample Input:-----
2
2 2
4 6

-----Sample Output:-----
0
3

-----EXPLANATION:-----
For 1) Sweetness are same so no need to use power.
For 2)
1st laddu
2 Unit power = 4 -> 12
2nd Laddu
1 Unit power = 6 -> 12
After using total 3 unit power sweetness of both laddus are same.


Chef has $K$ chocolates and he wants to distribute them to $N$ people (numbered $1$ through $N$). These people are standing in a line in such a way that for each $i$ ($1 \le i \le N-1$), person $i$ and person $i+1$ are adjacent.
First, consider some way to distribute chocolates such that for each valid $i$, the number of chocolates the $i$-th person would receive from Chef is $A_i$ and the sum $S_1 = \sum_{i=1}^{N-1} \left|A_i - A_{i+1}\right|$ is minimum possible. Of course, each person must receive a non-negative integer number of chocolates.
Then, Chef wants to create a new sequence $B_1, B_2, \ldots, B_N$ by rearranging (permuting) the elements of the sequence $A_1, A_2, \ldots, A_N$. For each valid $i$, the number of chocolates the $i$-th person actually receives from Chef is $B_i$. Chef wants to distribute the chocolates (choose $B_1, B_2, \ldots, B_N$ by permuting the sequence $A$ and give $B_i$ chocolates to the $i$-th person for each valid $i$) in such a way that $S_2 = \sum_{i=1}^{N-1} \left|B_i – B_{i+1}\right|$ is maximum possible. You need to find the maximum value of $S_2$.
It is guaranteed that $S_2$ does not depend on the exact choice of the sequence $A_1, A_2, \ldots, A_N$, as long as it is a sequence that minimises $S_1$.

-----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 a single integer $K$.

-----Output-----
For each test case, print a single line containing one integer — the maximum value of the sum $S_2$.

-----Constraints-----
- $1 \le T \le 10$
- $2 \le N \le 10^5$
- $2 \le K \le 10^{100,000}$

-----Subtasks-----
Subtask #1 (30 points): $2 \le N, K \le 1,000$
Subtask #2 (70 points): original constraints

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

-----Example Output-----
2

-----Explanation-----
Example case 1: To minimise $S_1$, Chef could give $1$ chocolate to person $1$ and $1$ chocolate to person $2$, so $S_1 = |1-1| + |1-0| = 1$.
To maximise $S_2$, Chef can give $1$ chocolate to person $1$ and $1$ chocolate to person $3$, since the sequence $B = (1, 0, 1)$ is a permutation of $A = (1, 1, 0)$. Then, $S_2 = |1-0| + |0-1| = 2$.


Chef is the event manager of his college. He has been assigned the task to manage the upcoming tech fest. There are $K$ rooms where the event can take place, and at a particular time only one event can be organized in a room for a particular time interval.
Each event coordinator has their strictly preferred room $P_i$, and if the room is already occupied he simply cancels that event.Chef wants to maximize the total number of events,and so he allows or disallows certain events in order to achieve the task . Chef is busy handling his events so the chef needs your help .
Given a list of $N$ events with their start time $S_i$,end time $E_i$ and preferred room $P_i$,you need to calculate the maximum number of events that can take place.
Note that the $i$th event wants to occupy the $p_i$ room from [$s_i$, $f_i$) .

-----Input:-----
The first line contains an integer $T$ denoting the number of test cases . Each of the next $T$ lines contains two integers $N$ and $K$ , the number of events and the number of rooms respectively . Each of the next $N$ lines contains three integers $s_i$ ,$e_i$ and $p_i$,the start time ,end time and the preferred room of ith event.

-----Output:-----
Print the maximum number of events that can take place.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^3$
- $1 \leq  K \leq 10^5$
- $1 \leq  Si <  Ei \leq 10^9$
- $1 \leq Pi \leq K$

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

4 2
1 10 1
10 20 2
15 50 2
20 30 2

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

-----EXPLANATION:-----
Chef can allow events 1st ,2nd and 4th,to get the maximum 3.


Chef had a sequence of positive integers with length $N + K$. He managed to calculate the arithmetic average of all elements of this sequence (let's denote it by $V$), but then, his little brother deleted $K$ elements from it. All deleted elements had the same value.
Chef still knows the remaining $N$ elements — a sequence $A_1, A_2, \ldots, A_N$. Help him with restoring the original sequence by finding the value of the deleted elements or deciding that there is some mistake and the described scenario is impossible.
Note that the if it is possible for the deleted elements to have the same value, then it can be proven that it is unique. Also note that this value must be a positive integer.

-----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 three space-separated integers $N$, $K$ and $V$.
- 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 value of the deleted elements, or $-1$ if there is a mistake.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, K \le 100$
- $1 \le V \le 10^5$
- $1 \le A_i \le 10^5$ for each valid $i$

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

-----Example Input-----
3
3 3 4
2 7 3
3 1 4
7 6 5
3 3 4
2 8 3

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


Kabir wants to impress Tara by showing her his problem solving skills. He has decided to give the correct answer to the next question which will be asked by his Algorithms teacher.
The question asked is:
Find the sum of alternate consecutive d$d$ odd numbers from the range L$L$ to R$R$ inclusive.
if d$d$ is 3 and L$L$ is 10 and R$R$ is 34, then the odd numbers between 10 and 34 are 11,13,15,17,19,21,23,25,27,29,31,33$11,13,15,17,19,21,23,25,27,29,31,33$, and the d$d$ alternate odd numbers are 11,13,15,23,25,27$11,13,15,23,25,27$.
You are a friend of Kabir, help him solve the question.
Note:$Note:$ Number of odd number between L$L$ and R$R$ (both inclusive) is a multiple of d$d$.

-----Input:-----
- First line will contain T$T$, number of test cases.
- First line of each test case contains one integer d$d$ .
- Second line of each test case contains two space separated integer L$L$ and R$R$.

-----Output:-----
For each test case, print the sum modulo 1000000007.

-----Constraints:-----
- 1≤T≤106$1 \leq T \leq 10^6$
- 1≤d≤103$1 \leq d \leq 10^3$
- 1≤L<R≤106$1 \leq L < R \leq 10^6$

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

10 33

-----Sample Output:-----
114

-----EXPLANATION:-----
Sum of alternate odd numbers i.e, 11,13,15,23,25,27 is 114


Diana is planning to make a very long journey. Her journey consists of $N$ bus routes, numbered from $1 to N$ in the order she must take them. The buses themselves are very fast but do not run often. The $i-th$ bus route only runs every $Xi$ days.

More specifically, she can only take the $i-th$ bus on day $Xi, 2Xi, 3Xi$, and so on. Since the buses are very fast, she can take multiple buses on the same day.

Diana must finish her journey by day D, but she would like to start the journey as late as possible. What is the latest day she could take the first bus, and still finish her journey by day $D$?
It is guaranteed that it is possible for Diana to finish her journey by day $D$.

-----Input:-----
The first line of the input gives the number of test cases, $T$. $T$ test cases follow. Each test case begins with a line containing the two integers N and D. Then, another line follows containing $N$ integers, the $i-th$ one is $Xi$.

-----Output:-----
For each test case, output one line containing an integer $Y$, where $Y$ is the latest day she could take the first bus, and still finish her journey by day $D$.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq Xi \leq D.$
- $1 \leq N \leq 1000.$
It is guaranteed that it is possible for Diana to finish her journey by day $D$.

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

3 10

3 7 2

4 100

11 10 5 50

1 1

1

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

99

1

-----EXPLANATION:-----
In Sample $Case 1$, there are $N = 3$ bus routes and Bucket must arrive by day $D = 10$. She could:
- Take the 1st bus on day 6 $(X1 = 3)$,
- Take the 2nd bus on day 7 $(X2 = 7)$ and
- Take the 3rd bus on day 8 $(X3 = 2)$.
In Sample $Case 2$, there are $N = 4$ bus routes and Bucket must arrive by day $D = 100$. She could:
- Take the 1st bus on day 99 $(X1 = 11)$,
- Take the 2nd bus on day 100$ (X2 = 10)$,
- Take the 3rd bus on day 100 $(X3 = 5)$ and
- Take the 4th bus on day 100 $(X4 = 50)$,
In Sample Case 3, there is $N = 1$ bus route, and Bucket must arrive by day $D = 1$. She could:
- Take the 1st bus on day 1 $(X1 = 1)$.


In my town ,there live a coder named Chef . He is a cool programmer . One day , he participate in a programming contest ,the contest give him only one problem . If he can’t solve the problem ,the problem setter will kill him . But the round allow you to help Chef. Can you save the life of Chef from problem setter ? :p
You are given two point of a straightline in X and Y axis and they are A(x1 , y1) and B(x2 ,y2) . Problem setter will give you another point C(x3 , y3) . If C exist in AB straightline ,then print “YES” . Otherwise ,print “NO” in first line and print the minimum distance from C to AB straightline in second line .
Please , save the life of Chef .
Note : It is not possible that A and B point is similar .

-----Input:-----
The first line of the input contains a single integer t (1≤t≤100) — the number of test cases .
Each test case starts with four integers( x1, y1 , x2 , y2 ) in first line .
Next line contains a single number q ,the number of queries . Each query contains two integers ( x3 ,y3 )

-----Output:-----
Print , q number of “YES” or “NO” (as it mentioned above) in each test case .For every test case , print “Test case : i ” ( 1<= i <=T )

-----Constraints-----
-1000 <=  x1 , y1 , x2 , y2 , x3 , y3 <= 1000

-----Sample Input:-----
2
3  5  6  5
2
4  5
6  8
3  4  7  10
1
7  4

-----Sample Output:-----
Test case : 1
YES
NO
3.000000
Test case : 2
NO
3.328201

Test case : 1
YES
NO
3.000000
Test case : 2
NO
3.328201


Rohit collects coins: he has exactly one coin for every year from 1 to n. Naturally, Rohit keeps all the coins in his collection in the order in which they were released. Once Rohit's younger brother made a change — he took all the coins whose release year dated from l to r inclusively and put them in the reverse order. That is, he took a certain segment [l, r] and reversed it. At that, the segment's endpoints did not coincide. For example, if n = 8, then initially Rohit's coins were kept in the order 1 2 3 4 5 6 7 8. If Rohit's younger brother chose the segment [2, 6], then after the reversal the coin order will change to 1 6 5 4 3 2 7 8. Rohit suspects that someone else could have spoilt the permutation after his brother. Help him to find that out. Check if the given permutation can be obtained from the permutation 1 2 … n using exactly one segment reversal. If it is possible, find the segment itself.

-----Input:-----
- The first line contains an integer N which is the number of coins in Rohit's collection.
- The second line contains space-separated n integers which are the spoilt sequence of coins. It is guaranteed that the given sequence is a permutation, i.e. it contains only integers from 1 to n, and every number is used exactly 1 time.

-----Output:-----
If it is impossible to obtain the given permutation from the original one in exactly one action, print 0 0. Otherwise, print two numbers l, r (1 ≤ l < r ≤ n) which are the endpoints of the segment that needs to be reversed to obtain from permutation 1 2 … n the given one.

-----Constraints-----
- $1 \leq N \leq 1000$
- $1 \leq A[N] \leq 10^9$

-----Sample Input:-----
8
1 6 5 4 3 2 7 8

-----Sample Output:-----
2 6


In africa jungle , there were zebra's who liked to spit.
There owner watched them for whole day and noted in his sheet where each zebra spitted.
Now he's in a confusion and wants to know if in the jungle there are two zebra's which spitted at each other.
Help him solve this task.
If the zebra is present in position a spits b metres right , he can hit only zebra in position a+b , if such a zebra exists.

-----Input:-----
- The first line contains integer t(1<=t<100)- amount of zebras in jungle.
- Each of following t lines contains two integers a(i) and b(i)(-10^4<=x(i)<=10^4,1<|d(i)|<=2.10^4) - records in owner sheet.
- a(i) is the position of i-th zebra and b(i) is distance at which the i-th camel spitted.
Positive values of d(i) correspond to spits right, negative values correspond to spit left.No two zebras may stand in the same position.

-----Output:-----
If there are two zebras , which spitted at each other , output YES, otherwise , output NO.

-----Sample Input:-----
2
0 1
1 -1

-----Sample Output:-----
YES


The MarkiT online virtual market startup wants to organize its grand opening in NIT Patna.
but they want maximum crowd for their inauguration. So the manager told  this  to Praveen a student in NITP who suggested them:
The first-year students come to campus  every x hour,
Second-year students come to campus every y hour,
Third-year students come to campus every z hour and
Fourth-year is very busy so they don't come regularly.
So Praveen being very clever told him the no of times in n days he can have an audience of all year student (1st,2nd & 3rd) at max. So can you code what Praveen has done?

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a 2 line of input, first line contain one  integers $N$ (No of Days).
-Next line contain 3 space separated integer the  value of x y z

-----Output:-----
For each testcase, output in a single line answer the no of times audience consists of all year.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^8$
- $1 \leq x,y,z \leq 10^5$

-----Sample Input:-----
1
10
8 10 6

-----Sample Output:-----
2

-----EXPLANATION:-----
First favourable condition will come on 5th day and Second on 10th day.


Now-a-days, Manish is becoming  famous for bank robbery in the country because of his cleverness, he never robs own his own.He has four workers A , B, C, and D , all working under him.All of the four take some amount for that. There are total N banks in the country and Manish wants to rob all the banks with minimum

amount spent on workers.Only one worker is allowed to rob the ith bank but following a condition that if one worker robs ith bank, then he can't rob (i+1) th bank.

So ,Manish wants you to calculate minimum amount that he has to spend on all workers to rob all N banks.

-----Input Format-----
First line consists number of test cases T.For each test case,

first line consists an integer N, number of banks in the country

and the next N line consists 4 integers amount taken by A,B,C and D respectively to rob ith bank.

-----Output format-----
For each test case ,output an integer, minimum amount paid  by Manish in separate line .

-----Constraint-----
- 1<=T<=1000
- 1<=N<=100000
- 1<=amount<=100000

-----Subtasks-----
Subtask-1 (10 points)
- 1<=T<=5
- 1<=N<=10
- 1<=amount<=10
Subtask-1 (30 points)
- 1<=T<=100
- 1<=N<=1000
- 1<=amount<=1000
Subtask-1 (60 points)
Original Constraints
Sample Input
1
3
4 7 2 9
5 6 4 7
2 6 4 3

Sample Output
10


A city of dimension N x N is constructed with grid of lanes. These lanes are fenced by government so that no one can cross any grid diagonally. Although a train
line runs diagonally from (0,0) to (N,N).
Our chef has a weird kind of phobia and is very afraid to cross the railway line. He is at point (0,0) and wants to get to the point (N,N). Calculate number of path
through which it is possible to reach to its destination travelling the minimum distance. .
Note that:

1. Since he is already at position (0,0) he can go to either part of grid (i.e. left or right part - divided by diagonal) but he will remain in that part for the whole path.
2. He is only afraid to "cross" the line, i.e. during the route he can go to position (m,m) where 0
3. You have to calculate the number of path possible. If there is more than one path then you have to print the number of path of minimum distances.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases, for each test case enter the grid size i.e value of N.

-----Output-----
For each test case, output a single line with number of such paths possible.
(Note : If no such path possible print 0)

-----Constraints-----
- 1 <= T <= 100
- 0 <= N <= 30

-----Example-----
Input:
2
2
5
Output:
4
84


Blob is a computer science student. He recently got an internship from Chef's enterprise. Along with the programming he has various other skills too like graphic designing, digital marketing and social media management. Looking at his skills Chef has provided him different tasks A[1…N] which have their own scores. Blog wants to maximize the  value of the expression A[d]-A[c]+A[b]-A[a] such that d>c>b>a.

Can you help him in this?

-----Input:-----
- The first line contain the integer N
- The second line contains N space separated integers representing A[1], A[2] … A[N]

-----Output:-----
The maximum score that is possible

-----Constraints-----
- $4 \leq N \leq 10^4$
- $0 \leq A[i] \leq 10^5$

-----Sample Input:-----
6

3 9 10 1 30 40

-----Sample Output:-----
46


Today is rose day, batch mates of Kabir and Tara decided to celebrate this day by exchanging roses with each other.
Note:$Note:$ exchanging means both the boy and the girl will give rose to each other.
In the class there are B$B$ boys and G$G$ girls.
Exchange of rose will take place if and only if at least one of them hasn't received a rose from anyone else and a rose can be exchanged only once.
Tara has to bring maximum sufficient roses for everyone and is confused as she don't know how many roses to buy.You are a friend of Kabir, so help him to solve the problem so that he can impress Tara by helping her.

-----Input:-----
- First line will contain T$T$, number of test cases.
- Each test case contains two space separated integers B$B$ (Number of boys) and  G$G$ (Number of Girls).

-----Output:-----
For each test case, output in a single line the total number of roses exchanged.

-----Constraints:-----
- 1≤T≤105$1 \leq T \leq 10^5$
- 1≤B≤109$1 \leq B \leq 10^{9}$
- 1≤G≤109$1 \leq G \leq 10^{9}$

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

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


Today, Chef decided to cook some delicious meals from the ingredients in his kitchen. There are $N$ ingredients, represented by strings $S_1, S_2, \ldots, S_N$. Chef took all the ingredients, put them into a cauldron and mixed them up.
In the cauldron, the letters of the strings representing the ingredients completely mixed, so each letter appears in the cauldron as many times as it appeared in all the strings in total; now, any number of times, Chef can take one letter out of the cauldron (if this letter appears in the cauldron multiple times, it can be taken out that many times) and use it in a meal. A complete meal is the string "codechef". Help Chef find the maximum number of complete meals he can make!

-----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 a single string $S_i$.

-----Output-----
For each test case, print a single line containing one integer — the maximum number of complete meals Chef can create.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 100$
- $|S_1| + |S_2| + \ldots + |S_N| \le 1,000$
- each string contains only lowercase English letters

-----Example Input-----
3
6
cplusplus
oscar
deck
fee
hat
near
5
code
hacker
chef
chaby
dumbofe
5
codechef
chefcode
fehcedoc
cceeohfd
codechef

-----Example Output-----
1
2
5

-----Explanation-----
Example case 1: After mixing, the cauldron contains the letter 'c' 3 times, the letter 'e' 4 times, and each of the letters 'o', 'd', 'h' and 'f' once. Clearly, this is only enough for one "codechef" meal.
Example case 2: After mixing, the cauldron contains the letter 'c' 4 times, 'o' 2 times, 'd' 2 times, 'e' 4 times, 'h' 3 times and 'f' 2 times, which is enough to make 2 meals.


Given a string consisting of only lowercase English alphabets, your task is to find the smallest palindromic substring.
In case there are multiple palindromic substrings of the same length present, print the lexicographically smallest substring.
Formally, a substring is a contiguous sequence of characters within a string. So in a string "abcdef", "abc" is a substring whereas "adf" is not a substring.
A palindrome is a word, phrase, or sequence that reads the same backwards as forwards, e.g. madam or mom.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains of two lines of input, two integers.
- First, we have a single integer $N$ which signifies the length of the substring.
- Next, we have a string of length $N$ that only has lowercase English alphabets.

-----Output:-----
For each testcase, output in a single line the shortest palindromic substring.

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq N \leq 10^5$

-----Sample Input:-----
2
2
zy
1
cd

-----Sample Output:-----
y
c

-----EXPLANATION:-----
There are only two possibilities. "z" and "y". Since both of them have the same length. We print the lexicographically smaller substring which is y.


Calculate the power of an army of numbers from 1 to $N$, both included.

-----Input:-----
- First line will contain a single integer $N$.

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

-----Constraints-----
- $1 \leq N \leq 5000$

-----Sample Input:-----
24

-----Sample Output:-----
5


Yesterday, Chef found $K$ empty boxes in the cooler and decided to fill them with apples. He ordered $N$ apples, where $N$ is a multiple of $K$. Now, he just needs to hire someone who will distribute the apples into the boxes with professional passion.
Only two candidates passed all the interviews for the box filling job. In one minute, each candidate can put $K$ apples into boxes, but they do it in different ways: the first candidate puts exactly one apple in each box, while the second one chooses a random box with the smallest number of apples and puts $K$ apples in it.
Chef is wondering if the final distribution of apples can even depend on which candidate he hires. Can you answer that question?
Note: The boxes are distinguishable (labeled), while the apples are not. Therefore, two distributions of apples are different if there is a box such that the number of apples in it when the first candidate finishes working can be different from the number of apples in it when the second candidate finishes working.

-----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 $K$.

-----Output-----
For each test case, print a single line containing the string "YES" if the final distributions of apples can be different or "NO" if they will be the same (without quotes).

-----Constraints-----
- $1 \le T \le 250$
- $1 \le N, K \le 10^{18}$
- $N$ is divisible by $K$

-----Subtasks-----
Subtask #1 (30 points): $1 \le N, K \le 10^5$
Subtask #2 (70 points): original constraints

-----Example Input-----
3
5 1
4 2
10 10

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

-----Explanation-----
Example case 1: No matter who is hired, all apples will be in the only box at the end.
Example case 2: At the end, there will be two apples in each box.
Example case 3: If we hire the first candidate, there will be one apple in each box, but if we hire the second one, there will be $10$ apples in one box and none in all other boxes.


Chef has a number N, Cheffina challenges the chef to check the divisibility of all the permutation of N by 2. If any of the permutations is divisible by 2 then print 1 else print 0.

-----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 1 or 0.

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

-----Sample Input:-----
2
19
385

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


Sereja has a string A consisting of n lower case English letters.

Sereja calls two strings X and Y each of length n similar if they can be made equal by applying the following operation at most once in each of them.

- Chose any two position i, j in the string (i can be equal to j too). Swap the characters at position i with character at position j.

For example strings "abcd" and "acbd" are similar, strings "ab" and "ab" are similar, but strings "abcde" and "bcdea" are not similar. Note that strings  "abc" and "cab" are also similar, as you can swap 'a' and 'c' in the first string to get "cba" and 'a' and 'b' in the second string to get "cba".

Now Sereja is interested in finding number of ordered pairs of non similar strings X and Y such that they can be constructed from a given string A by permutation of its characters. As answer could be large, please output your answer modulo  (109 + 7).

Note

A string s (of size n) is said to be constructed from string t (also of size n) by permutation of its characters if there exists a permutation P (of length n), such that s[i] = t[P[i]] for each i from 1 to n.

-----Input-----
- First line contain integer T - number of test cases.
- For each of the next T lines:

- Each line contains a string A as defined in the problem.

-----Output-----
For each test case, output answer modulo 1000000007 (109 + 7) in separate line.

-----Constraints-----
- 1 ≤ T ≤  10
- 1 ≤ n ≤  10^5

-----Constraints-----
- Subtask #1: 1 ≤ n ≤  10  (25 points)
- Subtask #2: 1 ≤ n ≤  100  (25 points)
- Subtask #3: 1 ≤ n ≤  1000  (25 points)
- Subtask #4: original constraints (25 points)

-----Example-----
Input:
2
z
abcd

Output:
0
144


The MEX of a set of integers is defined as the smallest non-negative integer that does not belong to this set. For example, $\mathrm{MEX}(\{0,2,3\}) = 1$ and $\mathrm{MEX}(\{1,3\}) = 0$.
Chef has a tree with $N$ nodes (numbered $1$ through $N$). The tree is rooted at node $1$. Chef wants to assign a non-negative integer to each node in such a way that each integer between $0$ and $N-1$ (inclusive) is assigned to exactly one node.
For each node $u$, consider the integers assigned to the nodes in the subtree of $u$ (including $u$); let $a_u$ denote the MEX of these integers. Chef wants $a_1 + a_2 + \ldots + a_N$ to be as large as possible. Find the maximum possible value of this sum.

-----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 $N-1$ space-separated integers $p_1, p_2, \ldots, p_{N-1}$. For each valid $i$, the node $p_i$ is the parent of the node $i+1$.

-----Output-----
For each test case, print a single line containing one integer ― the maximum sum of subtree MEX-s which can be obtained if you assign the weights optimally.

-----Constraints-----
- $1 \le T \le 5$
- $2 \le N \le 10^5$
- $1 \le p_i < i$ for each valid $i$

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

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

-----Example Output-----
4
9


A permutation of length n is an array of size n consisting of n distinct integers in the range [1, n]. For example, (3, 2, 4, 1) is a permutation of length 4, but (3, 3, 1, 4) and (2, 3, 4, 5) are not, as (3, 3, 1, 4) contains duplicate elements, and (2, 3, 4, 5) contains elements not in range [1,4].
A permutation p of length n is good if and only if for any 1 ≤ i ≤ n, pi ≠ i.
Please find the lexicographically smallest good permutation p.
Definition for "lexicographically smaller":
For two permutations p and q, we say that p is lexicographically smaller than q if and only if there exists a index 1 ≤ l ≤ n such that:
- For any 1 ≤ i < l, pi = qi. Note that if l = 1, this constraint means nothing.
- and, pl < ql.

For example, (2, 3, 1, 4) < (2, 3, 4, 1) < (3, 4, 1, 2). The lexicographically smallest permutation is, of course, (1, 2, ..., n), though this one is not good.

-----Input-----
First line of the input contains an integer T denoting number of test cases.
For each test case, the only line contains an integer n.

-----Output-----
For each test case, output the lexicographically smallest good permutation of length n. It's guaranteed that this permutation exists.

-----Constraints-----
- 1 ≤ T ≤ 10
- 2 ≤ n ≤ 105

-----Subtasks-----
- Subtask #1 (17 points): 2 ≤ n ≤ 9
- Subtask #2 (83 points): Original Constraints

-----Example-----
Input:
4
2
3
5
6

Output:
2 1
2 3 1
2 1 4 5 3
2 1 4 3 6 5

-----Explanation-----
Example case 1. The only good permutation of length 2 is (2, 1).
Example case 2. Consider all permutations of length 3, they are(in lexicographically order):
- p = (1, 2, 3), it's not good since p[1] = 1, p[2] = 2 and p[3] = 3;
- p = (1, 3, 2), it's not good since p[1] = 1;
- p = (2, 1, 3), it's not good since p[3] = 3;
- p = (2, 3, 1), it's good since p[1] ≠ 1, p[2] ≠ 2 and p[3] ≠ 3;
- p = (3, 1, 2), it's good since p[1] ≠ 1, p[2] ≠ 2 and p[3] ≠ 3;
- p = (3, 2, 1), it's not good since p[2] = 2.
Thus the minimum good one is (2, 3, 1).
Example case 3. Consider two good permutations for third test case: p=(2, 1, 4, 5, 3) and q=(2, 4, 1, 5, 3), then p < q. You can check lexicographically condition as follows. Find the first index where the entries of two permutations are different, and compare those entries. For example, in this case, the first position where the entries differ is index 2. You can see that p[2] < q[2], as 1 < 4, so p is lexicographically smaller than q.


"Ring Ring!!"
Sherlock's phone suddenly started ringing. And it was none other than Jim Moriarty..
"Long time no see ! You miss me right ? Anyway we'll talk about it later . Let me first tell you something. Dr.Watson is with me . And you've got only one chance to save him . Here's your challenge:.
Given a number N and another number M, tell if the remainder of N%M is odd or even. If it's odd, then print "ODD" else print "EVEN"

If Sherlock can answer the query correctly, then Watson will be set free. He has approached you for help since you being a programmer.Can you help him?

-----Input-----
The first line contains, T, the number of test cases..
Each test case contains an integer, N and M

-----Output-----
Output the minimum value for each test case

-----Constraints-----
1 = T = 20
1 <= N <= 10^18
1 <= M<= 10^9

-----Subtasks-----
Subtask #1 : (20 points)
1 = T = 20
1 <= N <= 100
1 <= M<= 100

Subtask 2 : (80 points)

1 = T = 20
1 <= N <= 10^18
1 <= M<= 10^9

-----Example-----
Input:
2
4 4
6 5

Output:
EVEN
ODD


The chef was not happy with the binary number system, so he designed a new machine which is having 6 different states, i.e. in binary there is a total of 2 states as 0 and 1. Now, the chef is confused about how to correlate this machine to get an interaction with Integer numbers, when N(Integer number) is provided to the system, what will be the Nth number that system will return(in Integer form), help the chef to design this system.

-----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 given by the system.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^5$

-----Sample Input:-----
2
3
5

-----Sample Output:-----
7
37

-----EXPLANATION:-----
Initial numbers for system = [1, 6, 7, 36, 37, 42, 43, 216, …..
For 1) 3rd Number for the system will be 7.
For 2) 5th Number for the system will be 37.


As lockdown is going on so no is allowed to go outside , so Chef has come with an innovative idea for food home delivery using drone.  But there is an issue with it , the drone can move forward or backward a fix number of steps $x$ .
All the houses and chef restaurant are all in a straight line . Homes which need delivery are located at $H[i]$ and chef is located at $y$ coordinate .
If Drone is at a location $R$, then it can move to $R-x$ or $R+x$ .
Help chef find maximum value of $x$ to complete all the deliveries as he is busy managing the orders.

-----Input:-----
- First line will contain $n$ and $R$, number of houses that need delivery and the correct coordinate of chef (Drone).
- Second line contains $n$ integers , the coordinate of all homes that need delivery.

-----Output:-----
- The maximum value of $x$ , so that drone delivers to all houses.

-----Constraints-----
- $1 \leq n \leq 1000$
- $1 \leq R \leq 10^9$
- $1 \leq hi \leq 10^9$
- $1 \leq x  \leq 10^9$

-----Sample Input:-----
3 1
3 5 11

-----Sample Output:-----
2

-----EXPLANATION:-----
Chef's drone is at 1 initially and he needs to visit 3,5,11 , so optimal solution will be (maximum value of x ) equal to 2.


Chef has provided with a sequence of integers of length $N$ arranged in an unsorted fashion.
The elements of the sequence are ordered as ${A1,A2,A3.....A'N}$
The task of the chef is to identify the highest and lowest value among the given sequence. It is assured that the sequence given contains the highest and the lowest value always
Please help chef in finding the desired value.

-----Input:-----
- First line will contain $N$, number of elements in the sequence.
- Next line contains  $N$ integers of the sequence  .

-----Output:-----
Print the HIGHEST and  LOWEST value of the sequence respectively.

-----Constraints-----
- $1 \leq N \leq 100$
- $2 \leq  {A1,A2,A3.....A'N}  \leq 10^4$

-----Sample Input:-----
5
3 2 7 9 4

-----Sample Output:-----
9 2

-----EXPLANATION:-----
This list is :
[3,2,7,9,4]  so the highest value is 9 and lowest is 2 respectively.


One day Chef was playing with numbers. He loves Lowest Common Multiple (LCM) too much and he is a very curious guy. He always try to do new things. Now he want to make a large number with it. But he doesn't want to take too many numbers.

He is willing to take only three numbers less than or equal to N (not necessarily distinct ) and from those three number he want get the maximum number by taking LCM of the numbers.

As he is busy in playing some more tricks of maths, he assign this task to you.

-----Input-----
First line of input contains an integer t ( t<=1000 ), Number of test cases.

t line follows an integer N

-----Output-----
Print t lines contains a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than N.

-----Constraints-----
1<= N <= 10^6

-----Example-----
Input:
2
9
7

Output:
504
210

-----Explanation-----
Example case 2. For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7•6•5 = 210. It is the maximum value we can get.


This is another problem about Indraneel's library. His library has one long shelf. His books are numbered and he identifies the books by their number. Each book has a distinct number.
He has lost many books, since many of his friends borrow his books and never bother to return them. He does not want to lose any more books and has decided to keep a record of all books that he lends to his friends. To make the task of borrowing a book a little difficult, he has given the following instructions to his friends: when they borrow a book, they must record in a register its position from the left among the books currently on the shelf.
Suppose there are $5$ books in the library and they are arranged as follows:
261421532614215326 \quad 1 \quad 42 \quad 15 \quad 3
If someone walks in and borrows the book $42$, then he will record $3$ in the register because this book is the third from the left on the shelf. Now the shelf looks like this:
26115326115326 \quad 1 \quad 15 \quad 3
If the next person borrow the book $3$, he writes down $4$ in the register since this is currently the fourth book from the left on the shelf, and so on.
Indraneel knows the initial arrangement of the books in his library at the time that he introduced the register system. After a while he examines his register and would like to know which books have been borrowed. Your task is to write a program to help Indraneel solve this problem.

-----Input:-----
The first line of the input contains a single integer $M$ indicating the number of books in Indraneel's library. The next line contains $M$ distinct positive integers describing the sequence in which the books are arranged on the library shelf. The third line of input contains a single integer $N$ indicating the number of entries in the register. This, in turn, is followed by $N$ lines (lines $4$ to $N+3$), each containing one positive integer. The integer on line $3+i$ indicates the position from left of the book ith book borrowed. (You may assume that the number on line $3+i$ is at most $M-i+1$.)

-----Output:-----
$N$ lines with one positive integer on each line. The number on line $i$ is the book borrowed by the ith borrower.

-----Constraints:-----
- $1 \leq M \leq 1000000$.
- $1 \leq N \leq 4000$.

-----Sample Input-----
5
26 1 42 15 3
2
3
4

-----Sample Output-----
42
3


Doubleville, a small town in Texas, was attacked by the aliens. They have abducted some of the residents and taken them to the a spaceship orbiting around earth. After some (quite unpleasant) human experiments, the aliens cloned the victims, and released multiple copies of them back in Doubleville. So now it might happen that there are 6 identical person named Hugh F. Bumblebee: the original person and its 5 copies. The Federal Bureau of Unauthorized Cloning (FBUC) charged you with the task of determining how many copies were made from each person. To help you in your task, FBUC have collected a DNA sample from each person. All copies of the same person have the same DNA sequence, and different people have different sequences (we know that there are no identical twins in the town, this is not an issue).

-----Input-----

The input contains several blocks of test cases. Each case begins with a line containing two integers: the number 1 <= n <= 20000 people, and the length 1 <= m <= 20 of the DNA sequences. The next n lines contain the DNA sequences: each line contains a sequence of m characters, where each character is either 'A', 'C', 'G' or 'T'.

The input is terminated by a block with n = m = 0 .

-----Output-----
For each test case, you have to output n lines, each line containing a single integer. The first line contains the number of different people that were not copied. The second line contains the number of people that were copied only once (i.e., there are two identical copies for each such person.) The third line contains the number of people that are present in three identical copies, and so on: the i -th line contains the number of persons that are present in i identical copies. For example, if there are 11 samples, one of them is from John Smith, and all the others are from copies of Joe Foobar, then you have to print '1' in the first and the tenth lines, and '0' in all the other lines.

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

9 6
AAAAAA
ACACAC
GTTTTG
ACACAC
GTTTTG
ACACAC
ACACAC
TCCCCC
TCCCCC
0 0

Output:

1
2
0
1
0
0
0
0
0


Chef lives in a big apartment in Chefland. The apartment charges maintenance fees that he is supposed to pay monthly on time. But Chef is a lazy person and sometimes misses the deadlines. The apartment charges 1000 Rs per month as maintenance fees. Also, they also charge a one-time fine of 100 Rs for each of the late payments. It does not matter how late the payment is done, the fine is fixed to be Rs.100.
Chef has been living in the apartment for N months. Now, he wants to switch the apartment, so he has to pay the entire dues to the apartment. The deadline for the N-th month is also over. From his bank statement, he finds the information whether he paid apartment rent for a particular month for not. You are given this information by an array A of size N, where Ai (can be either 0 or 1) specifies whether he has paid the 1000Rs in the i-th month or not. Assume that Chef paid the fees in the i-th month, then this fees will be considered for the earliest month for which Chef has not yet paid the fees.

For example, assume Chef did not pay any money in first month and 1000Rs in the second month. Then this rent of 1000Rs will be considered for 1st month. But this counts as late payment for the first month's fees, and hence he will have to pay Rs. 100 for that. And since the payment he made in the second month is not accounted for the second month, but rather for the first month, he will incur a fine of Rs.100 even for the second month.

He has not paid any of the fines so far. Can you please help in finding Chef total due (all the fines, plus all the unpaid maintenance fees) that he has to pay to apartment?

-----Input-----
First line of the input contains an integer T denoting number of test cases. The description of T test cases follows.
The first line of each test cases contains an integer N denoting the number of months for which you have to calculate the total amount of money that Chef has to pay at the end of the n month to clear all of his dues.
Next line of each test case contains N space separated integers (each of them can be either 0 or 1) denoting whether Chef paid the 1000Rs fees in the corresponding month or not. If the corresponding integer is 1, it means that Chef paid the maintenance fees for that month, whereas 0 will mean that Chef did not pay the maintenance fees that month.

-----Output-----
For each test case, output a single integer denoting the total amount including fine that Chef has to pay.

-----Constraints-----Constraints
- 1 ≤ T ≤ 25
- 0 ≤ Ai ≤ 1

-----Subtasks-----
Subtask #1 (30 points)
- 1 ≤ N ≤ 103

Subtask #2 (70 points)
- 1 ≤ N ≤ 105

-----Example-----
Input
4
2
1 1
2
0 0
3
0 1 0
2
0 1

Output
0
2200
2300
1200

-----Explanation-----
Example case 1. Chef paid maintenance fees for both the months. So, he does not have any dues left.
Example case 2. Chef did not pay the maintenance fees for any of the months. For the first month, he has to pay 1000Rs, and 100Rs fine as a late payment. For second month payments, he just have to pay 1100Rs. So, in total he has a due of 1100 + 1100 = 2200 Rs.
Example case 3. In the first month, Chef did not pay his maintenance fees. He paid the maintenance of first in the second month. So, he paid a fine of 100Rs for first month. For second and third month, Chef did not pay the maintenance fees. So, he has to pay 1000Rs + 100Rs (of fine) for second month and only 1000Rs + 100Rs (of fine) for third month. In total, Chef has got to pay 100 + 1100 + 1100 = 2300 Rs.
Example case 4. In the first month, Chef did not pay his maintenance fees. He paid the maintenance of first in the second month. So, he paid a fine of 100Rs for first month. For second month, Chef did not pay the maintenance fees. So, he has to pay 1000Rs + 100Rs (of fine) for second month. In total, Chef has got to pay 100 + 1100 = 1200 Rs.


Chef is stuck in a two dimensional maze having N rows and M columns. He needs to get out of the maze as soon as possible and arrive at the kitchen in order to serve his hungry customers. But, he can get out of the maze only if he is able to successfully find any magical path in the given maze.

A path is defined as magical if it starts from any of the cell (a,b) of the maze and ends at the cell (c,d) such that the following conditions are satisfied :-
- |a - c| + |b - d| = 1
- All the cells in the maze are traversed exactly once.
- It is allowed to move only in the four directions - up, down, left and right from the current cell.

-----Input-----
- First line of the input contains an integer T denoting the number of different types of scenarios.
- Each of the next T lines will contain two integers N, M denoting the dimensions of the maze.

-----Output-----
For each of the T scenarios, output a single line containing "Yes" or "No" (without quotes) denoting whether the Chef can get out of the maze or not.

-----Constraints-----
- 1 ≤ T ≤ 105
- 1 ≤ N, M ≤ 1018

-----Subtasks-----
Subtask #1 : (30 points)
- 1 ≤ T ≤ 100
- 1 ≤ N, M ≤ 10

Subtask #2 : (70 points)

Original Constraints

-----Example-----
Input:
1
2 2

Output:
Yes

-----Explanation-----
Example case 1.

Chef can start from (1,1), move down to (2,1), then move right to (2,2) and finally move upwards to reach (1,2). As, he is able to visit all the cells exactly once and sum of absolute differences of corresponding x and y dimension is 1, we can call this path a magical path.


You are given N integer sequences A1, A2, ..., AN. Each of these sequences contains N elements. You should pick N elements, one from each sequence; let's denote the element picked from sequence Ai by Ei. For each i (2 ≤ i ≤ N), Ei should be strictly greater than Ei-1.
Compute the maximum possible value of E1 + E2 + ... + EN. If it's impossible to pick the elements E1, E2, ..., EN, print -1 instead.

-----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 valid i, the i-th of these lines contains N space-separated integers Ai1, Ai2, ..., AiN denoting the elements of the sequence Ai.

-----Output-----
For each test case, print a single line containing one integer — the maximum sum of picked elements.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 700
- 1 ≤ sum of N in all test-cases ≤ 3700
- 1 ≤ Aij ≤ 109 for each valid i, j

-----Subtasks-----
Subtask #1 (18 points): 1 ≤ Aij ≤ N for each valid i, j
Subtask #2 (82 points): original constraints

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

1
3
1 2 3
4 5 6
7 8 9

Output:

18

-----Explanation-----
Example case 1: To maximise the score, pick 3 from the first row, 6 from the second row and 9 from the third row. The resulting sum is E1+E2+E3 = 3+6+9 = 18.


We all know how great ABD aka AB-DE-VILLIERS is. However his team mates were jealous of him and posed a problem for him to solve.The problem description is as follows :

Given an array of integers,find the length of the largest subarray(contiguous) of the given array with the maximum possible GCD (Greatest Common Divisor).

For info on GCD ,see this link: https://en.wikipedia.org/wiki/Greatest_common_divisor

GCD of the subarray is defined as the GCD of all the elements of the subarray.
As ABD is not aware of competitive programming he asks your help. Help him!

-----Input-----
First line will contain integer N denoting the size of array.

Second line will contain N integers denoting array elements.

-----Output-----
The answer as specified in the problem statement .

-----Constraints-----
1 <= N <= 1000000

1 <= array[i] <=100000000000

-----Example-----
Input:
4
2 4 8 3

Output:
1

Explanation
GCD of all possible subarrays of the given array are : 2 , 2 , 2 , 1 , 4 , 4, 1 , 8 , 1 , 3

Largest GCD possible : 8

Length of the largest subarray with GCD as 8 is 1

Hence answer is 1 .


You are given a dataset consisting of $N$ items. Each item is a pair of a word and a boolean denoting whether the given word is a spam word or not.
We want to use this dataset for training our latest machine learning model. Thus we want to choose some subset of this dataset as training dataset. We want to make sure that there are no contradictions in our training set, i.e. there shouldn't be a word included in the training set that's marked both as spam and not-spam. For example item {"fck", 1}, and item {"fck, 0"} can't be present in the training set, because first item says the word "fck" is a spam, whereas the second item says it is not, which is a contradiction.
Your task is to select the maximum number of items in the training set.
Note that same pair of {word, bool} can appear multiple times in input. The training set can also contain the same pair multiple times.

-----Input-----
- First line will contain $T$, number of test cases. Then the test cases follow.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains a string $w_i$, followed by a space and an integer(boolean) $s_i$, denoting the $i$-th item.

-----Output-----
For each test case, output an integer corresponding to the maximum number of items that can be included in the training set in a single line.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 25,000$
- $1 \le |w_i| \le 5$ for each valid $i$
- $0 \le s_i \le 1$ for each valid $i$
- $w_1, w_2, \ldots, w_N$ contain only lowercase English letters

-----Example Input-----
3
3
abc 0
abc 1
efg 1
7
fck 1
fck 0
fck 1
body 0
body 0
body 0
ram 0
5
vv 1
vv 0
vv 0
vv 1
vv 1

-----Example Output-----
2
6
3

-----Explanation-----
Example case 1: You can include either of the first and the second item, but not both. The third item can also be taken. This way the training set can contain at the very max 2 items.
Example case 2: You can include all the items except the second item in the training set.


Recall the definition of the Fibonacci numbers:

f1 := 1

f2 := 2

fn := fn-1 + fn-2 (n>=3)

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a,b].

-----Input-----

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a=b=0. Otherwise, a<=b<=10^100. The numbers a and b are given with no superfluous leading zeros.

-----Output-----

For each test case output on a single line the number of Fibonacci numbers fi with a<=fi<=b.

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

10 100
1234567890 9876543210
0 0

Output:

5
4


For her next karate demonstration, Ada will break some bricks.
Ada stacked three bricks on top of each other. Initially, their widths (from top to bottom) are W1,W2,W3.
Ada's strength is S. Whenever she hits a stack of bricks, consider the largest k≥0 such that the sum of widths of the topmost k bricks does not exceed S; the topmost k bricks break and are removed from the stack. Before each hit, Ada may also decide to reverse the current stack of bricks, with no cost.
Find the minimum number of hits Ada needs in order to break all bricks if she performs the reversals optimally. You are not required to minimise the number of reversals.
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 four space-separated integers S, W1, W2 and W3.Output
For each test case, print a single line containing one integer ― the minimum required number of hits.Constraints
- 1≤T≤64
- 1≤S≤8
- 1≤Wi≤2 for each valid i
it is guaranteed that Ada can break all bricksExample Input

3

3 1 2 2

2 1 1 1

3 2 2 1
Example Output

2

2

2
Explanation

Example case 1:

Ada can reverse the stack and then hit it two times. Before the first hit, the widths of bricks in the stack (from top to bottom) are (2,2,1). After the first hit, the topmost brick breaks and the stack becomes (2,1). The second hit breaks both remaining bricks.

In this particular case, it is also possible to hit the stack two times without reversing. Before the first hit, it is (1,2,2). The first hit breaks the two bricks at the top (so the stack becomes (2)) and the second hit breaks the last brick.


Appy and Chef are participating in a contest. There are $N$ problems in this contest; each problem has a unique problem code between $1$ and $N$ inclusive. Appy and Chef decided to split the problems to solve between them ― Appy should solve the problems whose problem codes are divisible by $A$ but not divisible by $B$, and Chef should solve the problems whose problem codes are divisible by $B$ but not divisible by $A$ (they decided to not solve the problems whose codes are divisible by both $A$ and $B$).
To win, it is necessary to solve at least $K$ problems. You have to tell Appy whether they are going to win or lose.

-----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 four space-separated integers $N$, $A$, $B$ and $K$.

-----Output-----
For each test case, print a single line containing the string "Win" if they can solve at least $K$ problems or "Lose" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 15$
- $1 \le K \le N \le 10^{18}$
- $1 \le A, B \le 10^9$

-----Subtasks-----
Subtask #1 (15 points):
- $1 \le T \le 15$
- $1 \le K \le N \le 10^6$
- $1 \le A, B \le 10^3$
Subtask #2 (85 points): original constraints

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

-----Example Output-----
Win

-----Explanation-----
Example case 1: Appy is solving the problems with codes $2$ and $4$, Chef is solving the problem with code $3$. Nobody is solving problem $6$, since $6$ is divisible by both $2$ and $3$. Therefore, they can solve $3$ problems and win.


There is a big staircase with $N$ steps (numbered $1$ through $N$) in ChefLand. Let's denote the height of the top of step $i$ by $h_i$. Chef Ada is currently under the staircase at height $0$ and she wants to reach the top of the staircase (the top of the last step). However, she can only jump from height $h_i$ to the top of a step at height $h_f$ if $h_f-h_i \le K$. To help Ada, we are going to construct some intermediate steps; each of them may be constructed between any two steps, or before the first step, and have any height. What is the minimum number of steps that need to be added to the staircase so that Ada could reach the top?

-----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 space-separated integers $N$ and $K$.
- The second line contains $N$ space-seperated integers $h_1, h_2, \dots, h_N$.

-----Output-----
For each test case, print a single line containing one integer — the minimum required number of steps.

-----Constraints-----
- $1 \le T \le 64$
- $1 \le N \le 128$
- $1 \le K \le 1,024$
- $1 \le h_i \le 1,024$ for each valid $i$
- $h_i < h_{i+1}$ for each valid $i$

-----Example Input-----
1
4 3
2 4 8 16

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


Write a program that reads two numbers $X$ and $K$. The program first finds the factors of $X$ and then gives the sum of $K$th power of every factor. The program also finds the factor of $k$ and outputs the sum of $X$ times of every factor.

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

-----Output:-----
For each testcase, output in a single line the factors of $X$ and the $K$th power of every factor, seperated by a space.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq X, K \leq 10^9$

-----Sample Input:-----
1
8 6

-----Sample Output:-----
266304 88

-----EXPLANATION:-----
Factors of x = 8 are 2, 4, and 8. Also, factors of k = 6 are 2, 3, and 6.
2^6 + 4^6 + 8^6 = 266304 and 2 × 8 + 3 × 8 + 6 × 8 = 88.
(Where a ^b denotes a raised to the power of b).


Chef is a brilliant university student that does not attend lectures because he believes that they are boring and coding is life! However, his university follows certain rules and regulations, and a student may only take an exam for a course if he has attended at least 75% of lectures for this course.
Since you are Chef's best friend, you want to help him reach the attendance he needs to take exams. Unfortunately, Chef is still focused on his code and refuses to attend more lectures, so the only option is to have some of his friends mark him as present by proxy. This trick is well-known in the university, but only few have the talent to pull it off.
In a certain course, there is exactly one lesson per day over the course of $D$ days (numbered $1$ through $D$). You are given a string $S$ with length $D$ describing the lessons Chef attended — for each valid $i$, the $i$-th character of this string is either 'A' if Chef was absent on day $i$ or 'P' if Chef was actually present on day $i$.
For each day $d$ when Chef is absent, one of Chef's friends can mark him as present by proxy on this day only if he was present (if he was really present, not just marked as present) on at least one of the previous two days, i.e. days $d-1$ and $d-2$, and on at least one of the following two days, i.e. days $d+1$ and $d+2$. However, it is impossible to mark him as present by proxy on the first two days and the last two days.
Find the minimum number of times Chef has to be marked as present by proxy so that his attendance becomes at least 75% ($0.75$). Chef's attendance is number of days when he was marked as present, either by proxy or by actually being present, divided by $D$.

-----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 $D$.
- The second line contains a single string $S$ with length $D$.

-----Output-----
For each test case, print a single line containing one integer — the minimum number of times Chef needs to be marked as present by proxy, or $-1$ if it is impossible to make Chef achieve 75% attendance.

-----Constraints-----
- $1 \le T \le 200$
- $1 \le D \le 1,000$
- $S$ contains only characters 'A' and 'P'

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

-----Example Input-----
1
9
PAAPPAPPP

-----Example Output-----
1

-----Explanation-----
Example case 1: With a proxy on the third day, the attendance string is "PAPPPAPPP". Now, Chef's attendance is at least 75%, so the minimum number of times Chef needs to be marked as present by proxy is $1$.


Chef wants to teach a lesson of sharing to the students.
There are $N$ students (numbered from $1$ to $N$ from left to right) who are asked to stand in a row. Initially Chef gave $A$$i$ candies to the $i$$th$ child. In one operation any child can give any number of candies to the child standing to his immediate left (i.e. $i$$th$ child can give any amount of candies to the $(i-1)$$th$ child. In particular 1st child cannot give his candies to anyone).
He asked them to minimize the maximum value of candies a student can possess after performing any number of operations (possibly zero).
Help the students finding such maximum 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.
- First line of each test case contains a single integer $N$ denoting the number of students.
- Second line contains $N$ space-separated integers $A$$1$,$A$$2$,$.....$ $A$$N$ denoting the initial amount of candies chef gave to them.

-----Output:-----
- For each test case, print a single line containing one integer ― maximum value after sharing.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^5$
- $0$ $\leq$ $A$$i$ $\leq$ $10^9$
- Sum of $N$ over all Test Cases does not exceed $10^5$

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

-----Sample Output-----
3
5

-----Explanation-----
-
For First Test Case:
The $5$$th$ student will give $2$ candies to $4$$th$ student and $4$$th$ will give $3$ candies to $3$$rd$ and $3$$rd$ will give $3$ candies to $2$$nd$ and $2$$nd$ will give $2$ candies to $1$$st$. So finally the number of candies that they will have are
$[3,3,3,3,3]$ and the value of maximum candies is $3$.
-
For Second Test Case:
Sharing to the left student will not change the maximum value as $1$$st$ cannot share to anyone. So the maximum value will remain $5$.


The most dangerous cyborg Jenish is finally entrapped on a narrow bridge over a valley. The bridge is $N$ meters long. For convenience, position $i$ represents a portion of bridge between whose left border is at distance $i-1$ meters from left end and right border is at distance $i$ meters from left end.
There are $N$ batteries placed at positions $1,2...N$. The $i^{th}$ one has energy $a[i]$.
There are two tanks of strength $X$ at positions $0$ and $N+1$. Initially Jenish has $0$ energy.
From now at any second $t$ starting from $1$,
first, Jenish can select any battery placed at position $i$ such that $(t \leq i \leq N-t+1)$ and add $a[i]$ to his energy (every battery can be used atmost once).
Then both the tanks move one meter towards each other. If there are still any batteries present at positions where the tanks are heading, the battery gets destroyed.
At any moment if Jenish's total energy is greater than or equal to $X$, he destroys both the tanks and he escapes the cops. If by the end of $\lfloor \frac {(n+1)}{2}\rfloor^{th}$ second, he can't destroy the tanks, he himself gets destroyed. Find out if he can escape.

-----Input:-----
- The first line consists of a single integer $T$, the number of test cases.
- The first line of each test case contains two space separated integers which represents $N$ and $X$ for that test case respectively.
- The second line of each test case contains $N$ space separated integers, $i^{th}$ of which represents $a[i]$.

-----Output:-----
For each test case, print in a single line, $YES$ if Jenish can escape or $NO$ if he gets destroyed.

-----Constraints:-----
- $1 \leq  X \leq 10^9$
- $0 \leq a[i] \leq 10^6$
- $ 1 \leq N \leq 10^5$
- $\Sigma$ $N$ over all the test cases does not exceed $10^5$

-----Sample Input:-----
3
4 8
5 1 4 2
3 4
3 1 2
2 7
5 5

-----Sample Output:-----
YES
YES
NO

-----Explanation-----
For test $1$, in the 1st second, first Jenish will select battery at index $1$ and then the tanks from either side will move one meter closer, thus destroying the battery at index $4$.Then, in the next second, Jenish will select battery at index $3$.Then,tanks will move one meter closer again to destroy the remaining battery at index $2$.But now, Jenish has a total energy of $9$ units which is more than enough to destroy the tanks.
For test $2$, Jenish can use batteries at index $1$ and $2$ to get a total energy of $4$ units.
For test $3$, Jenish can use batteries at index $1$ or $2$ and get a maximum of $5$ units of energy which is less than required.


There is a building with $N$ floors (numbered $1$ through $N$ from bottom to top); on each floor, there are $M$ windows (numbered $1$ through $M$ from left to right). Let's denote the $j$-th window on the $i$-th floor by $(i, j)$.
All windows in the building need to be cleaned one by one in a specific order. You are given this order as a matrix $A$ with $N$ rows and $M$ columns; for each valid $i$ and $j$, the window $(i, j)$ must be cleaned on the $A_{N-i+1,j}$-th turn.
Whenever we clean a window $(i, j)$, it becomes clean, but the dirty water used for cleaning it flows down to windows $(i-1, j-1)$, $(i-1, j)$ and $(i-1, j+1)$ (more precisely, to all of these windows which exist), so these windows become dirty again. Then, the water flows further down, so the same applies for other windows below: whenever a window $(i, j)$ becomes dirty, windows $(i-1, j-1)$, $(i-1, j)$ and $(i-1, j+1)$ become dirty as well. For example, cleaning a window $(5, 3)$ will make the window $(3, 2)$ dirty. The next window is cleaned only after water flows down completely. Note that each window is cleaned only once and there may be dirty windows at the end.
For each window, determine whether it will be clean after the cleaning process ends.

-----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 space-separated integers $N$ and $M$.
- $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$-th of these lines contains $M$ space-separated integers $A_{i, 1}, A_{i, 2}, \ldots, A_{i, M}$.

-----Output-----
For each test case, print $N$ lines; each of them should contain a string with length $M$. For each valid $i$ and $j$, the $j$-th character on the $i$-th line should be '1' if the window $(N-i+1, j)$ is clean or '0' if it is dirty.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N, M \le 10^3$
- $1 \le A_{i, j} \le N \cdot M$ for each valid $i, j$
- the elements of the matrix $A$ are pairwise distinct
- the sum of $N \cdot M$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $N, M \le 25$
- the sum of $N \cdot M$ over all test cases does not exceed $625$
Subtask #2 (50 points): original constraints

-----Example Input-----
1
3 4
1 3 7 10
9 2 4 11
8 12 5 6

-----Example Output-----
1111
1001
0100


Doctor Kunj installed new software on cyborg Shresth.
This software introduced Shresth to range minimum queries.
Cyborg Shresth thought of T$T$ different problems in each of which you will be given
an array A$A$ of length N$N$ and an array B$B$ of length M$M$. In each of these problems, you have to calculate:
∑mi=1∑mj=irangeMin(B[i],B[j])$\sum_{i=1}^m \sum_{j=i}^m rangeMin(B[i],B[j])$
Where rangeMin(i,j)$rangeMin(i,j)$ returns the minimum element in the range of indices i$i$ to j$j$ (both included) in array A$A$.
It is given that array B$B$ consists of pairwise distinct elements and is in ascending order.

-----Input Format:-----
- First line will contain T$T$, the number of different problems Cyborg Shresth thought of.
- Each problem's input data will be given in three different lines.
- The first line will contain N$N$ and M$M$, the length of array A$A$ and B$B$ respectively.
- The second line will contain N$N$ space separated positive integers, which form the array A$A$. -
- The third line will contain M$M$ space separated positive integers, which form the array B$B$.

-----Output Format:-----
- For each different problem, print on a new line the answer to the problem, i.e. the value of ∑mi=1∑mj=irangeMin(B[i],B[j])$\sum_{i=1}^m \sum_{j=i}^m rangeMin(B[i],B[j])$ .

-----Constraints:-----
- 1≤T≤105$1 \leq T \leq {10}^5$
- 1≤N≤105$1 \leq N \leq {10}^5$
- 1≤M≤105$1 \leq M \leq {10}^5$
- 1≤A[i]≤109$1 \leq A[i] \leq 10^9$
- 1≤B[i]≤N$1 \leq B[i] \leq N$
It is guaranteed that the sum of N$N$ over all test cases does not exceed 106${10}^6$ .

-----Sample Input:-----
1
7 3
10 3 7 9 1 19 2
1 4 6

-----Sample Output:-----
43

-----Explanation:-----
For the given array A$A$, we have to calculate rangeMin(1,1)+rangeMin(1,4)+rangeMin(1,6)+rangeMin(4,4)+rangeMin(4,6)+rangeMin(6,6)$rangeMin(1,1) + rangeMin(1,4) + rangeMin(1,6) + rangeMin(4,4) + rangeMin(4,6) + rangeMin(6,6) $.
This is equal to 10+3+1+9+1+19=43$10 + 3 + 1 + 9 + 1 +19 = 43$.


Being a crewmate in the Among Us game, you will have to solve a task to win against the imposter.
The task : You are given a certain number of bulbs(Say n) which are initially in OFF position.
The bulbs are numbered from 1 to n. There will be n current fluctuations in such a way that in the 1st fluctuation all bulbs are toggled, in the 2nd fluctuation every 2nd bulb is toggled, in the 3rd fluctuation every 3rd bulb is toggled and so on.
Your job as a crewmate is to find the number of bulbs which are ON at the end of n fluctuations. But, the imposter has a special power which alerts it when a bulb with a number divisible by 3 is kept ON at the end of n fluctuations.
So, you will have to switch off the bulbs with numbers divisible by 3 and give the final result to complete the task and win the game.

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

-----Output:-----
- For each testcase, output a single integer - the number of bulbs that will remain ON after $n$ fluctuations.

-----Constraints :-----
- $1 \leq T \leq 1000$
- $2 \leq n \leq 10^9$

-----Sample Input:-----
2
2
20

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

3


Chef Two and Chef Ten are playing a game with a number $X$. In one turn, they can multiply $X$ by $2$. The goal of the game is to make $X$ divisible by $10$.
Help the Chefs find the smallest number of turns necessary to win the game (it may be possible to win in zero turns) or determine that it is impossible.

-----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 denoting the initial value of $X$.

-----Output-----
For each test case, print a single line containing one integer — the minimum required number of turns or $-1$ if there is no way to win the game.

-----Constraints-----
- $1 \le T \le 1000$
- $0 \le X \le 10^9$

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

-----Example Input-----
3
10
25
1

-----Example Output-----
0
1
-1


Chef has a circular plot of land of radius $R$ on which he wants to construct a swimming pool.
He wants the swimming pool to be square in shape with maximum possible area,so that he along
with his friends can enjoy themselves during their summer vacations.
Help Chef to find out the maximum area of the swimming pool that can be constructed in his
circular plot.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input,  $R$ i.e the radius of the plot.

-----Output:-----
For each testcase, output in a single line answer displaying the maximum possible area of the swimming pool.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq R \leq 10^8$

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

5

10

-----Sample Output:-----
50

200


In this problem we are concerned with words constructed using the lowercase letters of the English alphabet - that is, a,b,c,…,z. These words need not necessarily be meaningful: any sequence of letters forms a word. For example, abbca is a word.
We say that we can "hop" from the word $w_1$ to the word $w_2$ if they are "sufficiently close". We define $w_2$ to be sufficiently close to $w_1$ if one of the following holds:
- $w_2$ is obtained from $w_1$ by deleting one letter.
- $w_2$ is obtained from $w_1$ by replacing one of the letters in $w_1$ by some letter that appears to its right in $w_1$ and which is also to its right in alphabetical order.
For example, we can hop from abbca to abca by deleting the second (or third letter). We can hop from aabca to abbca by replacing the a in the second position by the letter b that appears to the right of the a in aabca and which is also to its right in alphabetical order. On the other hand we cannot hop from abbca to aabca since we would need to replace the b in the second position by a, but a is to the left of b in alphabetical order.
You will be given a collection of words $W$. Your task is to find the length of the longest sequence $w_1, w_2, \ldots $ of distinct words from $W$ such that we may hop from $w_1$ to $w_2$, $w_2$ to $w_3$ and so on. We call this the hopping number for this set.
For example, if
$W$ = {abacd, bcdada, dd, abcd,bcdd, adcd, addd, aa, ccd, add, ad}
then, the hopping number is 7 corresponding to the sequence
abacd, abcd, adcd, addd, add, ad, dd

-----Input Format:-----
- The first line of the input contains one integer $N$ indicating the number of words in the input.
- This is followed by $N$ lines of input, lines 2, 3,…, $N$+1, each containing one word over the letters {a,b,…, z}.

-----Output Format:-----
The output should be a single integer, indicating the hopping number of the given set of words.

-----Test Data:-----
- $N \leq 100$
- You may assume that each word has at most 10 letters.

-----Sample Input:-----
11
abacd
bcdada
dd
abcd
bcdd
adcd
addd
aa
ccd
add
ad

-----Sample Output:-----
7


Chef has  $N$ doggo (dogs) , Lets number them $1$ to $N$.

Chef decided to build houses for each, but he soon realizes that keeping so many dogs at one place may be messy. So he decided to divide them into several groups called doggo communities. Let the total no. of groups be $K$ . In a community, paths between pairs of houses can be made so that doggo can play with each other. But there cannot be a path between two houses of different communities for sure. Chef wanted to make maximum no. of paths such that the total path is not greater then $K$.
Let’s visualize this problem in an engineer's way :)
The problem is to design a graph with max edge possible such that the total no. of edges should not be greater than the total no. of connected components.

-----INPUT FORMAT-----
- First line of each test case file contain $T$ , denoting total number of test cases.
- $ith$ test case contain only one line with a single integer $N$ , denoting the number of dogs(vertex)

-----OUTPUT FORMAT-----
- For each test case print a line with a integer , denoting the maximum possible path possible.

-----Constraints-----
- $1 \leq T \leq 10000$
- $1 \leq N \leq 10^9$

-----Sub-Tasks-----
- $20 Points$
- $1 \leq N \leq 10^6$

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

4

-----Sample Output-----
2

-----Explanation-----
4 houses can be made with  like this:

community #1  : [1 - 2  ]

community #2 :  [3 - 4 ]

or  [1 - 2 - 3]  , [ 4 ]

In both cases the maximum possible path is 2.


The chef has one array of N natural numbers (might be in sorted order). Cheffina challenges chef to find the total number of inversions in the array.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains two lines of input, $N$.
- N space-separated natural numbers.

-----Output:-----
For each test case, output in a single line answer as the total number of inversions.

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

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

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


You may have helped Chef and prevented Doof from destroying the even numbers. But, it has only angered Dr Doof even further. However, for his next plan, he needs some time. Therefore, Doof has built $N$ walls to prevent Chef from interrupting him. You have to help Chef by telling him the number of walls he needs to destroy in order to reach Dr Doof.
Formally, the whole area can be represented as the first quadrant with the origin at the bottom-left corner. Dr. Doof is located at the origin $(0, 0)$. There are $N$ walls, the i-th wall is a straight line segment joining the points $(a_i, 0)$ and $(0, a_i)$. For every initial position of Chef $(x_j, y_j)$, find the number of walls he needs to break before reaching Doof. Obviously, chef can't start from a point on the wall. Therefore, if $(x_j, y_j)$ lies on any of the given walls, print $-1$ in a new line.

-----Input-----
- First line contains $T$, denoting the number of testcases.
- The first line of every test case contains a single integer $N$ denoting the number of walls Dr Doof has built.
- The next line contains $N$ space separated distinct integers each denoting $a_i$.
- The next line contains a single integer $Q$ denoting the number of times Chef asks for your help.
- The next $Q$ lines contains two space separated integers $x_j$ and $y_j$, each denoting the co-ordinates of the starting point of Chef.

-----Output-----
For each query, print the number of walls Chef needs to break in order to reach Dr Doof in a separate line. If Chef tries to start from a point on any of the walls, print $-1$.

-----Constraints-----
- $1 \leq T \leq 2 * 10^2$
- $1 \leq N, Q \leq 2 * 10^5$
- $1 \leq a_i \leq 10^9$
- $0 \leq x_j, y_j \leq 10^9$
- $a_1 < a_2 < a_3 < .... < a_N$
- Sum of $N$ and $Q$ over all testcases for a particular test file does not exceed $2 * 10^5$

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

-----Sample Output-----
0
1
2
1
-1

-----Explanation-----
The sample input can be represented by the graph given below:

If Chef starts from $(0, 0)$, he can reach Dr Doof without destroying any wall.

If Chef starts from $(2, 0)$, he has to destroy the $1st$ wall.

If Chef starts from $(0, 4)$, he has to destroy both the walls.

If Chef starts from $(1, 1)$, he has to destroy the $1st$ wall.

As $(1, 2)$ lies on the second wall, the answer is $-1$ for the last query.


The ZCO scholarship contest offers scholarships to first time ZCO participants. You are participating in it for the first time. So you want to know the number of participants who'll get the scholarship.
You know that the maximum number of scholarships offered is $R$ and there are a total of $N$ participants numbered from $1$ to $N$. Out of these, you know the set of people (denoted by $X$) who you know, had participated in previous year ZCOs and hence, they shall not get the scholarship.
Further, as the world isn't free from plagiarism, so is the case with the scholarship contest. And from your secret sources, you also know the set of people (denoted by set $Y$) who were involved in plagiarism and therefore aren't eligible for scholarship either.
Find out the number of participants who shall get the scholarship.
PS: Don't ask how so many scholarships are being offered when you see the constraints on $R$. You never questioned it when in mathematics classes, some person bought $80$ watermelons twice just to compare them and save $₹1$.

-----Input:-----
- The first line will contain a single integer, $T$, the number of testcases. Then the testcases follow.
- The first line of each test case contains four integers; $N$, $R$, $|X|$ and $|Y|$ denoting the number of participants, maximum number of scholarships offered, number of old participants, and the number of participants involved in plagiarism, respectively.
- The second line of each test case contains $|X|$ space separated integers $x_1, x_2 \ldots x_{|X|}$ denoting the indices of people who participated in previous years. If $X$ is empty, this line is skipped and no empty line is in the input.
- The third line of each test case contains $|Y|$ space separated integers $y_1, y_2 \ldots y_{|Y|}$  denoting the indices of people who are involved in plagiarism. If $Y$ is empty, this line is skipped and no empty line is in input.

-----Output:-----
For each testcase, print a single integer in a new line, denoting the number of participants who shall get the scholarship.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^{15}$
- $0 \leq R \leq 10^{15}$
- $0 \leq |X|, |Y| \leq min(N, 2*10^5)$
- $1 \leq x_i, y_i \leq N$
- All $x_i$ are distinct
- All $y_i$ are distinct
- Sum of $|X|$ over all test cases does not exceed $5*10^5$
- Sum of $|Y|$ over all test cases does not exceed $5*10^5$

-----Subtasks-----
- 20 points : $1 \leq N \leq 10^3$, and the sum of $N$ over all test cases does not exceed $3*10^3$
- 30 points : $1 \leq N \leq 2*10^5$, and the sum of $N$ over all test cases does not exceed $5*10^5$
- 50 points: Original constraints

-----Sample Input:-----
3
5 3 0 1
4
10 2 4 6
3 1 7 6
4 3 1 5 9 7
10 4 4 6
3 1 7 6
4 3 1 5 9 7

-----Sample Output:-----
3
2
3

-----EXPLANATION:-----
- In the first testcase, only participant $4$ is involved in plagiarism, and thus not eligible for the scholarship. No user has participated in previous years, and so no empty line is there in the sample. All participants except participant $4$ are eligible for the scholarship, but only three of them get it because $R = 3$.
- Both second and third testcases are the same, except for $R$. In both samples, only participants $2$, $8$ and $10$ are eligible for scholarships.
- In the second testcase, since the maximum number of scholarships is $2$, only $2$ participants get scholarships.
- In the third testcase, all three eligible participants get scholarships.


Special Numbers
Mani has encountered a problem on Special numbers in Bytecode. A number S is called a special number if its digits are in an arithmetic progression modulo 10. He has an array consisting of all numbers from 1 to N and needs your help to find the number of special numbers in the array. He has promised you a significant share of the prize money if he wins the contest :p
Note:
123,99,802 are special numbers.
146 is not a special number

-----Input-----

Input consists of 1 integer - the value of N

-----Output-----
Print one integer in the first line - the solution to this problem

-----Constraints-----
- 1 ≤ Number of digits in N ≤ 105

Example

Input

123

Output

102


You are given a sequence of non-negative integers $A_1, A_2, \ldots, A_N$. At most once, you may choose a non-negative integer $X$ and for each valid $i$, change $A_i$ to $A_i \oplus X$ ($\oplus$ denotes bitwise XOR).
Find the minimum possible value of the sum of all elements of the resulting sequence.

-----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 $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum possible sum.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $1 \le N \le 10^3$
- $1 \le A_i \le 10^3$ for each valid $i$
Subtask #2 (50 points): original constraints

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

-----Example Output-----
14
0
2

-----Explanation-----
Example case 1: If we choose $X = 6$, the sequence becomes $(4, 5, 2, 3, 0)$.
Example case 2: We can choose $X = 7$ to make all elements of the resulting sequence equal to $0$.
Example case 3: We can choose $X = 1$. The sequence becomes $(0, 0, 2)$, with sum $2$.


You are given an integer sequence $A_1, A_2, \ldots, A_N$ and an integer $X$. Consider a $N \times N$ matrix $B$, where $B_{i,j} = A_i + A_j$ for each valid $i$ and $j$.
You need to find the number of square submatrices of $B$ such that the sum of their elements is $X$. Formally, find the number of quartets $(x_1, y_1, x_2, y_2)$ such that $1 \le x_1 \le x_2 \le N$, $1 \le y_1 \le y_2 \le N$, $x_2-x_1 = y_2-y_1$ and $\sum_{i=x_1}^{x_2}\sum_{j=y_1}^{y_2} B_{i,j} = X$.

-----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 space-separated integers $N$ and $X$.
- 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 number of square submatrices with sum $X$.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le X \le 10^6$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points): the sum of $N$ over all test cases does not exceed $1,000$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
5 36
1 2 3 1 12
4 54
3 3 3 3

-----Example Output-----
6
4