Muennighoff/xP3x-sample huggingface dataset:
inputs: Solve in Python:
Suppose there is a $h \times w$ grid consisting of empty or full cells. Let's make some definitions:

  $r_{i}$ is the number of consecutive full cells connected to the left side in the $i$-th row ($1 \le i \le h$). In particular, $r_i=0$ if the leftmost cell of the $i$-th row is empty.  $c_{j}$ is the number of consecutive full cells connected to the top end in the $j$-th column ($1 \le j \le w$). In particular, $c_j=0$ if the topmost cell of the $j$-th column is empty. 

In other words, the $i$-th row starts exactly with $r_i$ full cells. Similarly, the $j$-th column starts exactly with $c_j$ full cells.

 [Image] These are the $r$ and $c$ values of some $3 \times 4$ grid. Black cells are full and white cells are empty. 

You have values of $r$ and $c$. Initially, all cells are empty. Find the number of ways to fill grid cells to satisfy values of $r$ and $c$. Since the answer can be very large, find the answer modulo $1000000007\,(10^{9} + 7)$. In other words, find the remainder after division of the answer by $1000000007\,(10^{9} + 7)$.


-----Input-----

The first line contains two integers $h$ and $w$ ($1 \le h, w \le 10^{3}$) — the height and width of the grid.

The second line contains $h$ integers $r_{1}, r_{2}, \ldots, r_{h}$ ($0 \le r_{i} \le w$) — the values of $r$.

The third line contains $w$ integers $c_{1}, c_{2}, \ldots, c_{w}$ ($0 \le c_{j} \le h$) — the values of $c$.


-----Output-----

Print the answer modulo $1000000007\,(10^{9} + 7)$.


-----Examples-----
Input
3 4
0 3 1
0 2 3 0

Output
2

Input
1 1
0
1

Output
0

Input
19 16
16 16 16 16 15 15 0 5 0 4 9 9 1 4 4 0 8 16 12
6 12 19 15 8 6 19 19 14 6 9 16 10 11 15 4

Output
797922655



-----Note-----

In the first example, this is the other possible case.

 [Image] 

In the second example, it's impossible to make a grid to satisfy such $r$, $c$ values.

In the third example, make sure to print answer modulo $(10^9 + 7)$.
targets: from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,copy,time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_str(): return list(sys.stdin.readline().split())

H,W = inpl()
rr = inpl()
cc = inpl()

MAP = [[-1]*W for _ in range(H)]

for x,c in enumerate(cc):
    for y in range(c):
        MAP[y][x] = 1
    if c < H:
        MAP[c][x] = 0


for y,r in enumerate(rr):
    for x in range(r):
        if MAP[y][x] == 0:
            print(0)
            return
        MAP[y][x] = 1
    if r < W:
        if MAP[y][r] == 1:
            print(0)
            return
        MAP[y][r] = 0

cnt = 0
for y in range(H):
    for x in range(W):
        if MAP[y][x] == -1:
            cnt += 1

print(pow(2,cnt,mod))
inputs: Solve in Python:
We are given a sequence of coplanar points and see all the possible triangles that may be generated which all combinations of three points.

We have the following list of points with the cartesian coordinates of each one:
```
Points [x, y]
   A   [1, 2]
   B   [3, 3]
   C   [4, 1]
   D   [1, 1]
   E   [4, -1]
```
With these points we may have the following triangles: ```ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.``` There are three special ones: ```ABC, ACD and CDE```, that have an angle of 90°. All is shown in the picture below:



We need to count all the rectangle triangles that may be formed by a given list of points.

The case decribed above will be:
```python
count_rect_triang([[1, 2],[3, 3],[4, 1],[1, 1],[4, -1]]) == 3
```

Observe this case:
```python
count_rect_triang([[1, 2],[4, -1],[3, 3],[4, -1],[4, 1],[1, 1],[4, -1], [4, -1], [3, 3], [1, 2]]) == 3
```
If no rectangle triangles may be generated the function will output ```0```.

Enjoy it!
targets: from itertools import combinations
def count_rect_triang(points):
    n=0
    points_set=set()
    for p in points:
        points_set.add(tuple(p))
    for (x1,y1),(x2,y2),(x3,y3) in combinations(points_set,3):
        l1,l2,l3=sorted([(x2-x1)**2+(y2-y1)**2,(x3-x2)**2+(y3-y2)**2,(x1-x3)**2+(y1-y3)**2])
        if l1+l2==l3:
            n+=1
    return n
inputs: I found an interesting problem on https://codeforces.com/problemset/problem/1353/C:
You are given a board of size $n \times n$, where $n$ is odd (not divisible by $2$). Initially, each cell of the board contains one figure.

In one move, you can select exactly one figure presented in some cell and move it to one of the cells sharing a side or a corner with the current cell, i.e. from the cell $(i, j)$ you can move the figure to cells:   $(i - 1, j - 1)$;  $(i - 1, j)$;  $(i - 1, j + 1)$;  $(i, j - 1)$;  $(i, j + 1)$;  $(i + 1, j - 1)$;  $(i + 1, j)$;  $(i + 1, j + 1)$; 

Of course, you can not move figures to cells out of the board. It is allowed that after a move there will be several figures in one cell.

Your task is to find the minimum number of moves needed to get all the figures into one cell (i.e. $n^2-1$ cells should contain $0$ figures and one cell should contain $n^2$ figures).

You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 200$) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ($1 \le n < 5 \cdot 10^5$) — the size of the board. It is guaranteed that $n$ is odd (not divisible by $2$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ ($\sum n \le 5 \cdot 10^5$).


-----Output-----

For each test case print the answer — the minimum number of moves needed to get all the figures into one cell.


-----Example-----
Input
3
1
5
499993

Output
0
40
41664916690999888

I tried it in Python, but could not do it. Can you solve it?
targets: t = int(input())
while t:
    n = int(input())
    ans = 0
    if n==1: print(0)
    else:
        for i in range(1, n//2 + 1):
            ans += 8*i*i
        print(ans)
    t -= 1
inputs: I found an interesting problem on https://www.codewars.com/kata/5254bd1357d59fbbe90001ec:
Have a look at the following numbers.

```
 n | score
---+-------
 1 |  50
 2 |  150
 3 |  300
 4 |  500
 5 |  750
```

Can you find a pattern in it? If so, then write a function `getScore(n)`/`get_score(n)`/`GetScore(n)` which returns the score for any positive number `n`:

```c++
int getScore(1) = return 50;
int getScore(2) = return 150;
int getScore(3) = return 300;
int getScore(4) = return 500;
int getScore(5) = return 750;
```

I tried it in Python, but could not do it. Can you solve it?
targets: def get_score(n):
    return 25 * n * (n + 1)
inputs: Solve in Python:
During quarantine chef’s friend invented a game. In this game there are two players, player 1 and Player 2. In center of garden there is one finish circle and both players are at different distances respectively $X$ and $Y$ from finish circle.
Between finish circle and Player 1 there are $X$ number of circles and between finish circle and Player 2 there are $Y$ number of circles. Both player wants to reach finish circle with minimum number of jumps. Player can jump one circle to another circle.
Both players can skip $2^0-1$ or $2^1- 1$ or …. or $2^N-1$ circles per jump. A player cannot skip same number of circles in a match more than once. If both players uses optimal way to reach finish circle what will be the difference of minimum jumps needed to reach finish circle by both players. 
If both players reach finish circle with same number of jumps answer will be $0$ $0$.

-----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 2 space separated integers $X$ and $Y$.

-----Output:-----
For each test case, print a single line containing 2 space-separated integers which player win and what is the difference between number of minimum jump required by both players to reach finish circle.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq X,Y \leq 2*10^7$

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

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

-----Explanation:-----
Test Case 1:

Test Case 2:
targets: import sys
input = sys.stdin.readline

T = int(input().strip())

for _ in range(T):
 X,Y = list(map(int,input().split()))
 x = X+1
 y = Y +1
 def bit(x):
  a = []
  while x>0:
   a.append(x&1)
   x = x//2

  return sum(a)
 
 count_x = bit(x)
 count_y = bit(y)


 # while(x>0):
 #   n = bit(x)
 #   # print('n_x ' , n)
 #   if x == 2**(n+1)-1:
 #       count_x += 1
 #       break
 #   elif 2**n -1 < x:
 #       x = (x-(2**n-1))
 #       count_x +=1
 #       if x != 1:
 #           x = x-1
 #       else:
 #           count_x += 1
 #           break
   
 
 # while y>0:
 #   n = bit(y)
 #   # print('n ' , n)
 #   if y == 2**(n+1)-1:
 #       count_y += 1
 #       break
 #   elif 2**n -1 < y:
 #       y = (y-(2**n-1))
 #       count_y += 1
 #       if y != 1:
 #           y = y-1
 #       else:
 #           count_y += 1
 #           break
 # print('x',count_x, count_y)

 if count_x < count_y:
  print('1',count_y-count_x)
 elif count_y < count_x:
  print('2',count_x-count_y)
 else:
  print('0','0')
inputs: Solve in Python:
Gru wants to distribute $N$ bananas to $K$ minions on his birthday.
Gru does not like to just give everyone the same number of bananas, so instead, he wants to distribute bananas in such a way that each minion gets a $distinct$ amount of bananas. That is, no two minions should get the same number of bananas.
Gru also loves $gcd$. The higher the $gcd$, the happier Gru and the minions get. So help Gru in distributing the bananas in such a way that each Minion gets a distinct amount of bananas and gcd of this distribution is highest possible. Output this maximum gcd. If such a distribution is not possible output $-1$.
Note: You have to distribute $all$ $N$ bananas. 

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

-----Output:-----
For each testcase, output in a single line the maximum gcd or -1.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N, K \leq 10^9$

-----Sample Input:-----
1
6 3

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

-----EXPLANATION:-----
The only possible distribution is $[1, 2, 3]$. So the answer is 1.
targets: def factors(x):
 result = []
 i = 1
 while i*i <= x:
  if x % i == 0:
   result.append(i)
   if x//i != i:
    result.append(x//i)
  i += 1
 return result

t = int(input())
for _ in range(t):
 n, k = map(int, input().split())
 a = factors(n)
 an = -1
 for i in a:
  c = ((i*k*(k+1))//2)
  if (c%i==0 and c<=n):
   an=max(an,i)
 print(an)
inputs: I found an interesting problem on https://www.codewars.com/kata/5aff237c578a14752d0035ae:
My grandfather always predicted how old people would get, and right before he passed away he revealed his secret!

In honor of my grandfather's memory we will write a function using his formula!

* Take a list of ages when each of your great-grandparent died.  
* Multiply each number by itself.  
* Add them all together.  
* Take the square root of the result.  
* Divide by two.

## Example

```R
predict_age(65, 60, 75, 55, 60, 63, 64, 45) == 86
```
```python
predict_age(65, 60, 75, 55, 60, 63, 64, 45) == 86
```

Note: the result should be rounded down to the nearest integer.

Some random tests might fail due to a bug in the JavaScript implementation. Simply resubmit if that happens to you.

I tried it in Python, but could not do it. Can you solve it?
targets: def predict_age(*age):
    return sum(a*a for a in age)**0.5//2
inputs: Solve in Python:
=====Function Descriptions=====
Python has built-in string validation methods for basic data. It can check if a string is composed of alphabetical characters, alphanumeric characters, digits, etc.

str.isalnum()
This method checks if all the characters of a string are alphanumeric (a-z, A-Z and 0-9).

>>> print 'ab123'.isalnum()
True
>>> print 'ab123#'.isalnum()
False

str.isalpha()
This method checks if all the characters of a string are alphabetical (a-z and A-Z).

>>> print 'abcD'.isalpha()
True
>>> print 'abcd1'.isalpha()
False

str.isdigit()
This method checks if all the characters of a string are digits (0-9).

>>> print '1234'.isdigit()
True
>>> print '123edsd'.isdigit()
False

str.islower()
This method checks if all the characters of a string are lowercase characters (a-z).

>>> print 'abcd123#'.islower()
True
>>> print 'Abcd123#'.islower()
False

str.isupper()
This method checks if all the characters of a string are uppercase characters (A-Z).

>>> print 'ABCD123#'.isupper()
True
>>> print 'Abcd123#'.isupper()
False

=====Problem Statement=====
You are given a string S.
Your task is to find out if the string S contains: alphanumeric characters, alphabetical characters, digits, lowercase and uppercase characters.

=====Input Format=====
A single line containing a string S.

=====Constraints=====
0 < len(S) < 1000

=====Output Format=====
In the first line, print True if S has any alphanumeric characters. Otherwise, print False.
In the second line, print True if S has any alphabetical characters. Otherwise, print False.
In the third line, print True if S has any digits. Otherwise, print False.
In the fourth line, print True if S has any lowercase characters. Otherwise, print False.
In the fifth line, print True if S has any uppercase characters. Otherwise, print False.
targets: # Enter your code here. Read input from STDIN. Print output to STDOUT
inputStr=input()
resalnum = False
resalpha = False
resdigit = False
reslower = False
resupper = False
for i in inputStr:
    if(i.isalnum()):
        resalnum=True
    if(i.isalpha()):
        resalpha=True
    if(i.isdigit()):
        resdigit=True
    if(i.islower()):
        reslower=True
    if(i.isupper()):
        resupper=True
    
print(resalnum)
print(resalpha)
print(resdigit)
print(reslower)
print(resupper)
inputs: Solve in Python:
The prime `149` has 3 permutations which are also primes: `419`, `491` and `941`.

There are 3 primes below `1000` with three prime permutations:
```python
149 ==> 419 ==> 491 ==> 941
179 ==> 197 ==> 719 ==> 971
379 ==> 397 ==> 739 ==> 937
```

But there are 9 primes below `1000` with two prime permutations:
```python
113 ==> 131 ==> 311
137 ==> 173 ==> 317
157 ==> 571 ==> 751
163 ==> 613 ==> 631
167 ==> 617 ==> 761
199 ==> 919 ==> 991
337 ==> 373 ==> 733
359 ==> 593 ==> 953
389 ==> 839 ==> 983
```

Finally, we can find 34 primes below `1000` with only one prime permutation: 
```python
[13, 17, 37, 79, 107, 127, 139, 181, 191, 239, 241, 251, 277, 281, 283, 313, 347, 349, 367, 457, 461, 463, 467, 479, 563, 569, 577, 587, 619, 683, 709, 769, 787, 797]
```

Each set of permuted primes are represented by its smallest value, for example the set `149, 419, 491, 941` is represented by `149`, and the set has 3 permutations.

**Notes**
* the original number (`149` in the above example) is **not** counted as a permutation;
* permutations with leading zeros are **not valid**

## Your Task

Your task is to create a function that takes two arguments:
* an upper limit (`n_max`) and
* the number of prime permutations (`k_perms`) that the primes should generate **below** `n_max`

The function should return the following three values as a list:
* the number of permutational primes below the given limit,
* the smallest prime such prime,
* and the largest such prime

If no eligible primes were found below the limit, the output should be `[0, 0, 0]`

## Examples

Let's see how it would be with the previous cases:
```python
permutational_primes(1000, 3) ==> [3, 149, 379]
''' 3 primes with 3 permutations below 1000, smallest: 149, largest: 379 '''

permutational_primes(1000, 2) ==> [9, 113, 389]
''' 9 primes with 2 permutations below 1000, smallest: 113, largest: 389 '''

permutational_primes(1000, 1) ==> [34, 13, 797]
''' 34 primes with 1 permutation below 1000, smallest: 13, largest: 797 '''
```

Happy coding!!
targets: from collections import defaultdict

# generate list of primes
SIEVE_LIMIT = 10**5
sieve = list(range(SIEVE_LIMIT))
sieve[1] = 0
# and store them based on used digits
cache = defaultdict(list)
for n in sieve:
    if n:
        digits = tuple(sorted(str(n)))
        cache[digits].append(n)
        for i in range(n*n, SIEVE_LIMIT, n):
            sieve[i] = 0


# return the number of items in arr below given limit
def items_below_limit(arr, limit):
    return sum( [x < limit for x in arr] )


# return number of primes with given permutations below limit
def find_prime_kPerm(limit, perms):
    res = []
    for k, v in list(cache.items()):
        if  items_below_limit(v, limit) == perms + 1:
            res.append(v[0])
    
    return [ len(res), min(res), max(res) ] if res else [0, 0, 0]
inputs: Solve in Python:
In the board game Talisman, when two players enter combat the outcome is decided by a combat score, equal to the players power plus any modifiers plus the roll of a standard 1-6 dice. The player with the highest combat score wins and the opposing player loses a life. In the case of a tie combat ends with neither player losing a life.

For example:
```
Player 1: 5 Power, 0 Modifier
Player 2: 3 Power, 2 Modifier

Player 1 rolls a 4, Player 2 rolls a 2.

(5 + 0 + 4) -> (3 + 2 + 2)
Player 1 wins (9 > 7)
```

Your task is to write a method that calculates the required roll for the player to win.

The player and enemy stats are given as an array in the format:
```python
[power, modifier]
```

For example for the examples used above the stats would be given as:
```python
get_required([5, 0], [3, 2]) # returns 'Random'
```

If the player has at least 6 more power (including modifiers) than the enemy they automatically wins the fight, as the enemy's combat score couldn't possibly exceed the player's. In this instance the method should return "Auto-win".

For example:
```python
get_required([9, 0], [2, 1]) # returns 'Auto-win' as the enemy can't possibly win
```

If the enemy has at least 6 more power (including modifiers) than the player they automatically wins the fight, as the player's combat score couldn't possibly exceed the enemy's. In this instance the method should return "Auto-lose".

For example:
```python
get_required([2, 1], [9, 0]) # returns 'Auto-lose' as the player can't possibly win
```

If the player and enemy have the same power (including modifiers) the outcome is purely down to the dice roll, and hence would be considered completely random. In this instance the method should return "Random".

For example (as above):
```python
get_required([5, 0], [3, 2]) # returns 'Random' as it is purely down to the dice roll
```

If the player has greater power than the enemy (including modifiers) the player could guarantee a win by rolling a high enough number on the dice. In this instance the method should...
targets: def get_required(player, enemy):
    p = sum(player)
    e = sum(enemy)
    if p==e: 
        return 'Random'
    elif p+6<=e: 
        return "Auto-lose"
    elif p>=e+6: 
        return "Auto-win"
    elif p+6==e+1: 
        return "Pray for a tie!"
    elif p>e: 
        return f'({6+e-p+1}..6)'
    else: 
        return f'(1..{6+p-e-1})'
inputs: Solve in Python:
Vanya has a table consisting of 100 rows, each row contains 100 cells. The rows are numbered by integers from 1 to 100 from bottom to top, the columns are numbered from 1 to 100 from left to right. 

In this table, Vanya chose n rectangles with sides that go along borders of squares (some rectangles probably occur multiple times). After that for each cell of the table he counted the number of rectangles it belongs to and wrote this number into it. Now he wants to find the sum of values in all cells of the table and as the table is too large, he asks you to help him find the result.


-----Input-----

The first line contains integer n (1 ≤ n ≤ 100) — the number of rectangles.

Each of the following n lines contains four integers x_1, y_1, x_2, y_2 (1 ≤ x_1 ≤ x_2 ≤ 100, 1 ≤ y_1 ≤ y_2 ≤ 100), where x_1 and y_1 are the number of the column and row of the lower left cell and x_2 and y_2 are the number of the column and row of the upper right cell of a rectangle.


-----Output-----

In a single line print the sum of all values in the cells of the table.


-----Examples-----
Input
2
1 1 2 3
2 2 3 3

Output
10

Input
2
1 1 3 3
1 1 3 3

Output
18



-----Note-----

Note to the first sample test:

Values of the table in the first three rows and columns will be as follows:

121

121

110

So, the sum of values will be equal to 10.

Note to the second sample test:

Values of the table in the first three rows and columns will be as follows:

222

222

222

So, the sum of values will be equal to 18.
targets: a = int(input())
summ = 0
for i in range(a):
    p = [int(x) for x in input().split()]
    summ += (p[2] - p[0] + 1) * (p[3] - p[1] + 1)
print(summ)
inputs: Solve in Python:
You are given N non-negative integers A_1, A_2, ..., A_N and another non-negative integer K.
For a integer X between 0 and K (inclusive), let f(X) = (X XOR A_1) + (X XOR A_2) + ... + (X XOR A_N).
Here, for non-negative integers a and b, a XOR b denotes the bitwise exclusive OR of a and b.
Find the maximum value of f.
What is XOR?
The bitwise exclusive OR of a and b, X, is defined as follows:
 - When X is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if, when written in base two, exactly one of A and B has 1 in the 2^k's place, and 0 otherwise.
For example, 3 XOR 5 = 6. (When written in base two: 011 XOR 101 = 110.)

-----Constraints-----
 - All values in input are integers.
 - 1 \leq N \leq 10^5
 - 0 \leq K \leq 10^{12}
 - 0 \leq A_i \leq 10^{12}

-----Input-----
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N

-----Output-----
Print the maximum value of f.

-----Sample Input-----
3 7
1 6 3

-----Sample Output-----
14

The maximum value is: f(4) = (4 XOR 1) + (4 XOR 6) + (4 XOR 3) = 5 + 2 + 7 = 14.
targets: N, K = list(map(int, input().split()))
A = list(map(int, input().split()))

less = -float('inf')
eq = 0

for d in range(60)[::-1]:
    mask = (1 << d)

    one = len([0 for a in A if (a & mask) != 0])
    zero = N - one

    l = less + mask * max(one, zero)

    if (K & mask) != 0:
        l = max(l, eq + mask * one)

    less = l
    eq += mask * (one if (K & mask == 0) else zero)

print((max(less, eq)))
inputs: Solve in Python:
We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.
The i-th edge connects Vertex U_i and Vertex V_i.
The time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).
Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible.
Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.

-----Constraints-----
 - 1 \leq N \leq 100 000
 - 1 \leq M \leq 200 000
 - 1 \leq S, T \leq N
 - S \neq T
 - 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
 - 1 \leq D_i \leq 10^9 (1 \leq i \leq M)
 - If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
 - U_i \neq V_i (1 \leq i \leq M)
 - D_i are integers.
 - The given graph is connected.

-----Input-----
Input is given from Standard Input in the following format:
N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M

-----Output-----
Print the answer.

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

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

There are two ways to choose shortest paths that satisfies the condition:
 - Takahashi chooses the path 1 \rightarrow 2 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 4 \rightarrow 1.
 - Takahashi chooses the path 1 \rightarrow 4 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 2 \rightarrow 1.
targets: from heapq import*
def f(s):
 a=[1<<50]*N;a[s]=0;p=[(0,s)];c=[0]*N;c[s]=1
 while p:
  d,v=heappop(p)
  if d<=a[v]:
   for u,w in G[v]:
    if a[u]>d+w:a[u]=d+w;heappush(p,(d+w,u));c[u]=0
    if a[u]==d+w:c[u]+=c[v]
 return a,c
n=lambda:map(int,input().split());N,M=n();N+=1;S,T=n();G=[[]for _ in[0]*N]
for _ in[0]*M:U,V,D=n();G[U]+=[(V,D)];G[V]+=[(U,D)]
P,X=f(S);Q,Y=f(T);s=P[T];print((X[T]**2--~s%2*sum((X[i]*Y[i])**2for i in range(N)if P[i]==Q[i]==s//2)-sum((P[i]+d+Q[j]==s)*(P[i]<Q[i])*(Q[j]<P[j])*(X[i]*Y[j])**2for i in range(N)for j,d in G[i]))%(10**9+7))
inputs: I found an interesting problem on https://www.codechef.com/problems/BIT2C:
Chef is playing with an expression which consists of integer operands and the following binary
Bitwise operators -  AND, OR and XOR. He is trying to figure out that what could be the Maximum possible answer of the expression, given that he can perform the operation in any order i.e not necessarily follow the rule of Precedence of operators while evaluating the expression.
After some time of consistent work Chef starts feeling exhausted and wants you to automate this process for him. Can you help him out?
The expression has Bitwise operators in symbol format:
- &  stands for AND 
- |   stands for OR
- ^   stands for XOR
NOTE : It is guaranteed that the expression will always be valid, also each OPERATOR will always be preceded and succeeded by an OPERAND.

-----Input:-----
- The first line of input contains a single integer $T$ denoting the number of test cases.
- The only line of input for each test case is a $string$ which is the Chef's expression to evaluate.

-----Output:-----
For each test case print a single integer i.e the maximum possible value of Chef's expression.

-----Constraints-----
- $1 \leq T \leq 100$.
- The number of OPERATORS in the expression will be atleast 1 and atmost 10.
- Each OPERAND may range from 0 to $10^9$.

-----Subtasks-----
- 10 points : The number of OPERATORS in the expression will be atmost 5.
- 20 points : The number of OPERATORS in the expression will be atmost 8.
- 70 points : Original constraints.

-----Sample Input:-----
2
3^40|10^2

92^95|56&2&3

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

95

-----EXPLANATION:-----CASE 2 :
- If we first compute (56 & 2), the expression becomes 92^95|0&3, since (56 & 2) yields $0$.
- Now on computing (95 | 0), the expression becomes 92^95&3.
- Further on computing (95 & 3), the expression becomes 92^3.
- Finally (92 ^ 3) yields 95, which is the maximum value of the expression.

I tried it in Python, but could not do it. Can you solve it?
targets: def extract(s):
	arr = []
	news = ''
	for x in s:
		try:
			x = int(x)
			news += str(x)
		except:
			arr += [news]
			news = ''
			arr += [x]
	arr += [news]
	return arr

t = int(input())
for _ in range(t):
	s = input()
	arr = extract(s)
	n = len(arr)//2 + 1
	dp = [[0]*n for j in range(n)]
	for i in range(n):
		dp[i][i] = [int(arr[2*i])]

	n = len(arr)
	for i in range(3, n+1, 2):
		for j in range(0, n-i+1, 2):
			ans = []
			for k in range(j+2, i+j+1, 2):
				for x in dp[j//2][(k-1)//2]:
					for y in dp[k//2][(i+j)//2]:
						ans += [eval(str(x) + arr[k-1] + str(y))]

			if i != n:
				dp[j//2][k//2] = ans[:]
			else:
				print(max(ans))
inputs: I found an interesting problem on https://www.codewars.com/kata/59b2883c5e2308b54d000013:
An onion array is an array that satisfies the following condition for all values of `j` and `k`:

If all of the following are `true`:

* `j >= 0`
* `k >= 0`
* `j + k = array.length - 1`
* `j != k`
  
then:

* `a[j] + a[k] <= 10`

### Examples:

```
[1, 2, 19, 4, 5]   =>  true  (as 1+5 <= 10 and 2+4 <= 10)
[1, 2, 19, 4, 10]  =>  false (as 1+10 > 10)
```

Write a function named `isOnionArray`/`IsOnionArray`/`is_onion_array()` that returns `true` if its argument is an onion array and returns `false` if it is not.

~~~if:php
Your solution should at least be moderately efficient.  Make sure you don't do any unnecessary looping ;)
~~~

I tried it in Python, but could not do it. Can you solve it?
targets: def is_onion_array(a):
    for j in range(len(a)//2):
        if a[j] + a[-j-1] > 10:
            return False
    return True
inputs: I found an interesting problem on https://atcoder.jp/contests/arc104/tasks/arc104_d:
Given positive integers N, K and M, solve the following problem for every integer x between 1 and N (inclusive):
 - Find the number, modulo M, of non-empty multisets containing between 0 and K (inclusive) instances of each of the integers 1, 2, 3 \cdots, N such that the average of the elements is x.

-----Constraints-----
 - 1 \leq N, K \leq 100
 - 10^8 \leq M \leq 10^9 + 9
 - M is prime.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N K M

-----Output-----
Use the following format:
c_1
c_2
:
c_N

Here, c_x should be the number, modulo M, of multisets such that the average of the elements is x.

-----Sample Input-----
3 1 998244353

-----Sample Output-----
1
3
1

Consider non-empty multisets containing between 0 and 1 instance(s) of each of the integers between 1 and 3. Among them, there are:
 - one multiset such that the average of the elements is k = 1: \{1\};
 - three multisets such that the average of the elements is k = 2: \{2\}, \{1, 3\}, \{1, 2, 3\};
 - one multiset such that the average of the elements is k = 3: \{3\}.

I tried it in Python, but could not do it. Can you solve it?
targets: import sys
readline = sys.stdin.readline

N, K, MOD = list(map(int, readline().split()))

MAX = K*(N//2)*(N//2+1)//2+1


table = [[1]]

for idx in range(1, N+1):
    dp = table[-1]
    dp2 = dp + [0]*(idx*(K+1))
    s = idx*(K+1)
    for i in range(min(len(dp), len(dp2)-s)):
        dp2[i+s] = (dp2[i+s] + -dp[i])%MOD
    for i in range(len(dp2)-idx):
        dp2[i+idx] = (dp2[i+idx]+dp2[i])%MOD
    
    if len(dp2) > MAX:
        dp2 = dp2[:MAX]
    table.append(dp2)

Ans = [None]*(N+1)
for x in range(1, N+1):
    if N-x < x:
        Ans[x] = Ans[N+1-x]
    ans = 0
    for i in range(min(len(table[x-1]), len(table[N-x]))):
        ans = (ans + table[x-1][i]*table[N-x][i])%MOD
    ans = (ans*(K+1)-1)%MOD
    Ans[x] = ans
print(('\n'.join(map(str, Ans[1:]))))
inputs: I found an interesting problem on https://www.codewars.com/kata/5b817c2a0ce070ace8002be0:
Do you have in mind the good old TicTacToe?

Assuming that you get all the data in one array, you put a space around each value, `|` as a columns separator and multiple `-` as rows separator, with something like `["O", "X", " ", " ", "X", " ", "X", "O", " "]` you should be returning this structure (inclusive of new lines):

```
 O | X |   
-----------
   | X |   
-----------
 X | O |   
```

Now, to spice up things a bit, we are going to expand our board well beyond a trivial `3` x `3` square and we will accept rectangles of big sizes, still all as a long linear array.

For example, for `"O", "X", " ", " ", "X", " ", "X", "O", " ", "O"]` (same as above, just one extra `"O"`) and knowing that the length of each row is `5`, you will be returning

```
 O | X |   |   | X 
-------------------
   | X | O |   | O 
```

And worry not about missing elements, as the array/list/vector length is always going to be a multiple of the width.

I tried it in Python, but could not do it. Can you solve it?
targets: def display_board(board, width):
    lines = [' ' + ' | '.join(board[i:i+width]) + ' ' for i in range(0, len(board), width)]
    return ('\n' + '-' * len(lines[0]) + '\n').join(lines)
inputs: Solve in Python:
You play your favourite game yet another time. You chose the character you didn't play before. It has $str$ points of strength and $int$ points of intelligence. Also, at start, the character has $exp$ free experience points you can invest either in strength or in intelligence (by investing one point you can either raise strength by $1$ or raise intelligence by $1$).

Since you'd like to make some fun you want to create a jock character, so it has more strength than intelligence points (resulting strength is strictly greater than the resulting intelligence).

Calculate the number of different character builds you can create (for the purpose of replayability) if you must invest all free points. Two character builds are different if their strength and/or intellect are different.


-----Input-----

The first line contains the single integer $T$ ($1 \le T \le 100$) — the number of queries. Next $T$ lines contain descriptions of queries — one per line.

This line contains three integers $str$, $int$ and $exp$ ($1 \le str, int \le 10^8$, $0 \le exp \le 10^8$) — the initial strength and intelligence of the character and the number of free points, respectively.


-----Output-----

Print $T$ integers — one per query. For each query print the number of different character builds you can create.


-----Example-----
Input
4
5 3 4
2 1 0
3 5 5
4 10 6

Output
3
1
2
0



-----Note-----

In the first query there are only three appropriate character builds: $(str = 7, int = 5)$, $(8, 4)$ and $(9, 3)$. All other builds are either too smart or don't use all free points.

In the second query there is only one possible build: $(2, 1)$.

In the third query there are two appropriate builds: $(7, 6)$, $(8, 5)$.

In the fourth query all builds have too much brains.
targets: T = int(input())
for i in range(T):
    s, k, f = map(int, input().split())
    print(min(f + 1, max(0, (s + f - k + 1) // 2)))
inputs: I found an interesting problem on https://leetcode.com/problems/factorial-trailing-zeroes/:
Given an integer n, return the number of trailing zeroes in n!.

Example 1:


Input: 3
Output: 0
Explanation: 3! = 6, no trailing zero.

Example 2:


Input: 5
Output: 1
Explanation: 5! = 120, one trailing zero.

Note: Your solution should be in logarithmic time complexity.

I tried it in Python, but could not do it. Can you solve it?
targets: class Solution:
     def trailingZeroes(self, n):
         """
         :type n: int
         :rtype: int
         """
         c=0
         while n>0:
             n//=5
             c+=n
         return c
inputs: Solve in Python:
Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.

Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).

What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?


-----Input-----

Single line of the input contains three integers x, y and m ( - 10^18 ≤ x, y, m ≤ 10^18).

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.


-----Output-----

Print the minimum number of operations or "-1" (without quotes), if it is impossible to transform the given pair to the m-perfect one.


-----Examples-----
Input
1 2 5

Output
2

Input
-1 4 15

Output
4

Input
0 -1 5

Output
-1



-----Note-----

In the first sample the following sequence of operations is suitable: (1, 2) $\rightarrow$ (3, 2) $\rightarrow$ (5, 2).

In the second sample: (-1, 4) $\rightarrow$ (3, 4) $\rightarrow$ (7, 4) $\rightarrow$ (11, 4) $\rightarrow$ (15, 4).

Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations.
targets: x, y, m = list(map(int, input().split()))
if max(x, y) >= m:
    print(0)
elif m < 0 or max(x, y) <= 0:
    print(-1)
else:
    if x + y < 0:
        cnt = (max(x, y) - min(x, y)) // max(x, y)
        x, y = min(x, y) + max(x, y) * cnt, max(x, y)
    else:
        cnt = 0
    while max(x, y) < m:
        x, y = max(x, y), x + y
        cnt += 1
    print(cnt)
inputs: I found an interesting problem on https://codeforces.com/problemset/problem/1062/B:
JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer $n$, you can perform the following operations zero or more times:  mul $x$: multiplies $n$ by $x$ (where $x$ is an arbitrary positive integer).  sqrt: replaces $n$ with $\sqrt{n}$ (to apply this operation, $\sqrt{n}$ must be an integer). 

You can perform these operations as many times as you like. What is the minimum value of $n$, that can be achieved and what is the minimum number of operations, to achieve that minimum value?

Apparently, no one in the class knows the answer to this problem, maybe you can help them?


-----Input-----

The only line of the input contains a single integer $n$ ($1 \le n \le 10^6$) — the initial number.


-----Output-----

Print two integers: the minimum integer $n$ that can be achieved using the described operations and the minimum number of operations required.


-----Examples-----
Input
20

Output
10 2
Input
5184

Output
6 4


-----Note-----

In the first example, you can apply the operation mul $5$ to get $100$ and then sqrt to get $10$.

In the second example, you can first apply sqrt to get $72$, then mul $18$ to get $1296$ and finally two more sqrt and you get $6$.

Note, that even if the initial value of $n$ is less or equal $10^6$, it can still become greater than $10^6$ after applying one or more operations.

I tried it in Python, but could not do it. Can you solve it?
targets: n = int(input())
fac = {}
nn = n
maxe = 1
while nn%2 == 0:
    fac[2] = fac.get(2, 0) + 1
    nn >>= 1
for i in range(3, nn+1, 2):
    if i*i > nn:
        break
    while nn%i == 0:
        fac[i] = fac.get(i, 0) + 1
        nn //= i
if nn > 1:
    fac[nn] = 1
# print(nn)
# print(fac)

maxe = 1
mine = n
prod = 1
for f in fac:
    if fac[f] > maxe:
        maxe = fac[f]
    if fac[f] < mine:
        mine = fac[f]
    prod *= f
ops = 0
t = 1
while t < maxe:
    t <<= 1
    ops += 1
if mine < t:
    ops += 1
print(prod, ops)
inputs: I found an interesting problem on https://codeforces.com/problemset/problem/1183/A:
Polycarp knows that if the sum of the digits of a number is divisible by $3$, then the number itself is divisible by $3$. He assumes that the numbers, the sum of the digits of which is divisible by $4$, are also somewhat interesting. Thus, he considers a positive integer $n$ interesting if its sum of digits is divisible by $4$.

Help Polycarp find the nearest larger or equal interesting number for the given number $a$. That is, find the interesting number $n$ such that $n \ge a$ and $n$ is minimal.


-----Input-----

The only line in the input contains an integer $a$ ($1 \le a \le 1000$).


-----Output-----

Print the nearest greater or equal interesting number for the given number $a$. In other words, print the interesting number $n$ such that $n \ge a$ and $n$ is minimal.


-----Examples-----
Input
432

Output
435

Input
99

Output
103

Input
237

Output
237

Input
42

Output
44

I tried it in Python, but could not do it. Can you solve it?
targets: n = int(input())
def s(n):
    k = 0
    for i in str(n):
        k += int(i)
    return k
while s(n) % 4 != 0:
    n += 1
print(n)
inputs: I found an interesting problem on https://www.codechef.com/NEWB2020/problems/CNFCT:
Oliver and Nova are true lovers. Inspite of knowing that Nova will die Oliver married her at the lake where they met. But they had a conflict about even and odd numbers. Nova likes the odd numbers and Oliver prefers even. One day they went to a fair where Oliver bought some square shaped marshmallows and Nova bought some round shaped. Then they decided to play a game. They will pick a natural number N . Nova will sum up the odd numbers from 1 to N and and she will notedown LCM of R(R is defined in the picture) and the sum she calculated before. And Oliver will sum up the even numbers from 1 to N and and he will notedown LCM of S(S is defined in the picture) and the sum he calculated before. You must use the ceil value of R and S.

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

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

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

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

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

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

I tried it in Python, but could not do it. Can you solve it?
targets: import math

def lcm(a, b):
    return (a*b)//gcd(a, b)

def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a%b)    
    
for _ in range(int(input())):
    n = int(input())

    na = math.ceil((2*n)/math.acos(-1))
    nb = ((n+1)//2)**2

    nlcm = lcm(na, nb)

    oa = math.ceil(n/2)
    ob = (n//2)*(n//2+1)

    olcm = lcm(oa, ob)

    if olcm > nlcm:
        print("Nova's gonna kill me")
    else:
        print("YESS(sunglass emo)")

# cook your dish here
inputs: I found an interesting problem on https://www.codechef.com/problems/MAXSC:
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.

I tried it in Python, but could not do it. Can you solve it?
targets: # cook your dish here
t=int(input())
for cases in range(t):
 n=int(input())
 lis=[]
 for i in range(n):
  lis1=sorted(list(map(int,input().split())))
  lis.append(lis1)
 summ=lis[-1][-1]
 maxx=summ
 c=1
 for i in range(n-2,-1,-1):
  for j in range(n-1,-1,-1):
   if lis[i][j]<maxx:
    maxx=lis[i][j]
    c+=1
    summ+=lis[i][j]
    break
 if c==n:
  print(summ)
 else:
  print(-1)
 print()
inputs: Solve in Python:
Omkar is building a waterslide in his water park, and he needs your help to ensure that he does it as efficiently as possible.

Omkar currently has $n$ supports arranged in a line, the $i$-th of which has height $a_i$. Omkar wants to build his waterslide from the right to the left, so his supports must be nondecreasing in height in order to support the waterslide. In $1$ operation, Omkar can do the following: take any contiguous subsegment of supports which is nondecreasing by heights and add $1$ to each of their heights. 

Help Omkar find the minimum number of operations he needs to perform to make his supports able to support his waterslide!

An array $b$ is a subsegment of an array $c$ if $b$ can be obtained from $c$ by deletion of several (possibly zero or all) elements from the beginning and several (possibly zero or all) elements from the end.

An array $b_1, b_2, \dots, b_n$ is called nondecreasing if $b_i\le b_{i+1}$ for every $i$ from $1$ to $n-1$.


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 100$). Description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of supports Omkar has.

The second line of each test case contains $n$ integers $a_{1},a_{2},...,a_{n}$ $(0 \leq a_{i} \leq 10^9)$ — the heights of the supports.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.


-----Output-----

For each test case, output a single integer — the minimum number of operations Omkar needs to perform to make his supports able to support his waterslide.


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

Output
3
2
0



-----Note-----

The subarray with which Omkar performs the operation is bolded.

In the first test case:

First operation:

$[5, 3, \textbf{2}, 5] \to [5, 3, \textbf{3}, 5]$

Second operation:

$[5, \textbf{3}, \textbf{3}, 5] \to [5, \textbf{4}, \textbf{4}, 5]$

Third operation:

$[5,...
targets: for _ in range(int(input())):
    n=int(input())
    a=list(map(int,input().split()))
    ans=0
    for i in range(1,n):
        if a[i]<a[i-1]:
            ans+=a[i-1]-a[i]
    print(ans)
inputs: Solve in Python:
The chef was busy in solving algebra, he found some interesting results, that there are many numbers which can be formed by sum of some numbers which are prime. Chef wrote those numbers in dairy. Cheffina came and saw what the chef was doing. Cheffina immediately closed chef's dairy and for testing chef's memory, she starts asking numbers and chef needs to answer wheater given number N can be formed by the sum of K prime numbers if it yes 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, two integers $N, K$.

-----Output:-----
For each test case, output in a single line answer as 1 or 0.

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

-----Sample Input:-----
2
12 2
11 2

-----Sample Output:-----
1
0
targets: from math import sqrt

def isprime(n):
    if (n % 2 == 0 and n > 2) or n == 1: return 0
    else:
        s = int(sqrt(n)) + 1
        for i in range(3, s, 2):
            if n % i == 0:
                return 0
        return 1

def find(N, K): 
    if (N < 2 * K): 
        return 0
    if (K == 1): 
        return isprime(N) 
    if (K == 2): 
        if (N % 2 == 0): 
            return 1
        return isprime(N - 2); 
    return 1

for _ in range(int(input())):
    n, k = list(map(int, input().split()))
    print(find(n, k))
inputs: Solve in Python:
# Task
 A noob programmer was given two simple tasks: sum and sort the elements of the given array `arr` = [a1, a2, ..., an]. 
 
 He started with summing and did it easily, but decided to store the sum he found in some random position of the original array which was a bad idea. Now he needs to cope with the second task, sorting the original array arr, and it's giving him trouble since he modified it.

 Given the array `shuffled`, consisting of elements a1, a2, ..., an, and their sumvalue in random order, return the sorted array of original elements a1, a2, ..., an.

# Example

 For `shuffled = [1, 12, 3, 6, 2]`, the output should be `[1, 2, 3, 6]`.

 `1 + 3 + 6 + 2 = 12`, which means that 1, 3, 6 and 2 are original elements of the array.

 For `shuffled = [1, -3, -5, 7, 2]`, the output should be `[-5, -3, 2, 7]`.

# Input/Output


 - `[input]` integer array `shuffled`

    Array of at least two integers. It is guaranteed that there is an index i such that shuffled[i] = shuffled[0] + ... + shuffled[i - 1] + shuffled[i + 1] + ... + shuffled[n].

    Constraints:

    `2 ≤ shuffled.length ≤ 30,`

    `-300 ≤ shuffled[i] ≤ 300.`


 - `[output]` an integer array

    A `sorted` array of shuffled.length - 1 elements.
targets: def shuffled_array(a):
    a.remove(sum(a) / 2)
    return sorted(a)