akhauriyash/Code-Regression huggingface dataset:
Chef has a garden with $N$ plants arranged in a line in decreasing order of height. Initially the height of the plants are $A_1, A_2, ..., A_N$.
The plants are growing, after each hour the height of the $i$-th plant increases by $i$ millimeters. Find the minimum number of integer hours that Chef must wait to have two plants of the same height.

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

-----Output:-----
For each test case print a single line containing one integer, the minimum number of integer hours that Chef must wait to have two plants of the same height.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq N \leq 10^5$
- $0\leq A_i \leq 10^{18}$
- $A_i >A_{i+1}$, for each valid $i$
- The Sum of $N$ over all test cases does not exceed $10^6$

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

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

-----EXPLANATION:-----
After $2$ hours there are two plants with the same height. 
$[8,4,2] \rightarrow [9,6,5] \rightarrow [10,8,8]$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nfor i in range(int(input())):\n n=int(input())\n arr=list(map(int,input().split()))\n ans=arr[0]\n i=0\n while(i<n-1):\n  ans=min(ans,arr[i]-arr[i+1])\n  i+=1 \n print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13081
Chef Zidane likes the number 9. He has a number N, and he wants to turn it into a multiple of 9. He cannot add or remove digits, and he can only change one digit at a time. The only allowed operation is to increment or decrement a digit by one, and doing this takes exactly one second. Note that he cannot increase a digit 9 or decrease a digit 0, and the resulting number must not contain any leading zeroes unless N has a single digit.

Chef Zidane wants to know the minimum amount of time (in seconds) needed to accomplish this. Please help him, before his kitchen gets overwhelmed with mist!

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

-----Output-----
For each test case, output a single line containing the answer.

-----Constraints-----
- 1 ≤ T ≤ 105
- 1 ≤ N ≤ 10105
- N will not contain leading zeroes.
- Each test file is at most 3Mb in size.

-----Example-----
Input:4
1989
86236
90210
99999999999999999999999999999999999999988

Output:0
2
3
2

-----Explanation-----
Example case 1. 1989 is already divisible by 9, so no operations are needed to be performed.
Example case 2. 86236 can be turned into a multiple of 9 by incrementing the first and third digit (from the left), to get 96336. This takes 2 seconds.
Example case 3. 90210 can be turned into a multiple of 9 by decrementing the third digit twice and the fourth digit once, to get 90000. This takes 3 seconds.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 's=int(input())\nwhile(s>0):\n s-=1\n a=input()\n c=0\n for x in a:\n  c+=int(x)\n if(c<9 and len(a)!=1):\n  print(9-c%9)\n else:\n  print(min(9-c%9,c%9))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13007
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:   $f(0) = a$;  $f(1) = b$;  $f(n) = f(n-1) \oplus f(n-2)$ when $n > 1$, where $\oplus$ denotes the bitwise XOR operation. 

You are given three integers $a$, $b$, and $n$, calculate $f(n)$.

You have to answer for $T$ independent test cases.


-----Input-----

The input contains one or more independent test cases.

The first line of input contains a single integer $T$ ($1 \le T \le 10^3$), the number of test cases.

Each of the $T$ following lines contains three space-separated integers $a$, $b$, and $n$ ($0 \le a, b, n \le 10^9$) respectively.


-----Output-----

For each test case, output $f(n)$.


-----Example-----
Input
3
3 4 2
4 5 0
325 265 1231232

Output
7
4
76



-----Note-----

In the first example, $f(2) = f(0) \oplus f(1) = 3 \oplus 4 = 7$.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from sys import stdin\nt=int(stdin.readline().strip())\nfor i in range(t):\n    a,b,n=list(map(int,stdin.readline().strip().split()))\n    x=a^b\n    arr=[a,b,x]\n    n=n%3\n    print(arr[n])\n    \n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13147
Devu loves to play with his dear mouse Jerry.  One day they play a game on 2 dimensional grid of dimensions n * n (n ≥ 2). Jerry is currently at coordinates (sx, sy) and wants to move to location (ex, ey) where cheese is placed by Devu. Also Devu is very cunning and has placed a bomb at location (bx, by). All these three locations are distinct. 

In a single move, Jerry can go either up, down, left or right in the grid such that it never goes out of the grid. Also, it has to avoid the bomb. Find out minimum number of moves Jerry needs. It is guaranteed that it is always possible to do so.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows."
- The first line of each test case contains seven space separated integers n, sx, sy , ex, ey, bx, by. 

-----Output-----
- For each test case, output a single line containing an integer corresponding to minimum number of moves Jerry needs.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 2 ≤ n ≤ 20
-  1 ≤ sx, sy , ex, ey, bx, by ≤ n 
- No two or more poitns in the three points are same.

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

Output:
2
4

-----Explanation-----
Example case 1. ...
Jerry will move directly (1, 1) to (2, 1) and then to (2, 2) in total 2 moves.

Example case 2. ...

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\n\ndef main():\n t=int(sys.stdin.readline())\n for _ in range(t):\n  n,sx,sy,dx,dy,bx,by=list(map(int,sys.stdin.readline().strip().split()))\n  if (sx==bx==dx) and (min(sy,dy)<by) and (by<max(sy,dy)): \n   print(abs(dx-sx)+abs(dy-sy)+2)\n  elif (sy==by==dy) and(min(sx,dx)<bx) and (bx<max(sx,dx)):\n   print(abs(dx-sx)+abs(dy-sy)+2)\n  else:\n   print(abs(dx-sx)+abs(dy-sy))\nmain()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14107
When Serezha was three years old, he was given a set of cards with letters for his birthday. They were arranged into words in the way which formed the boy's mother favorite number in binary notation. Serezha started playing with them immediately and shuffled them because he wasn't yet able to read. His father decided to rearrange them. Help him restore the original number, on condition that it was the maximum possible one. 


-----Input-----

The first line contains a single integer $n$ ($1 \leqslant n \leqslant 10^5$) — the length of the string. The second line contains a string consisting of English lowercase letters: 'z', 'e', 'r', 'o' and 'n'.

It is guaranteed that it is possible to rearrange the letters in such a way that they form a sequence of words, each being either "zero" which corresponds to the digit $0$ or "one" which corresponds to the digit $1$.


-----Output-----

Print the maximum possible number in binary notation. Print binary digits separated by a space. The leading zeroes are allowed.


-----Examples-----
Input
4
ezor

Output
0 

Input
10
nznooeeoer

Output
1 1 0 



-----Note-----

In the first example, the correct initial ordering is "zero".

In the second example, the correct initial ordering is "oneonezero".

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'n = int(input())\ns = input()\nfor i in range(s.count(\'n\')):\n    print(1,end = " ")\nfor i in range(s.count(\'z\')):\n    print(0, end =" ")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12957
You'll be given a string, and have to return the total of all the unicode characters as an int. Should be able to handle any characters sent at it. 

examples:

uniTotal("a") == 97
uniTotal("aaa") == 291

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def uni_total(string):\n    #your code here\n    s=0\n    for x in string:\n        s+=ord(x)\n    return s'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'uni_total'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5316
Chef recently learned about ratios and proportions. He wrote some positive integers a, b, c, d on a paper. Chef wants to know whether he can shuffle these numbers so as to make some proportion? Formally, four numbers x, y, z, w are said to make a proportion if ratio of x : y is same as that of z : w.

-----Input-----
Only line of the input contains four space separated positive integers - a, b, c, d.

-----Output-----
Print "Possible" if it is possible to shuffle a, b, c, d to make proportion, otherwise "Impossible" (without quotes).

-----Constraints-----
- 1 ≤ a, b, c, d  ≤ 1000

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

Output:
Possible

-----Explanation-----
By swapping 4 and the second 2, we get 1 2 2 4. Note that 1 2 2 4 make proportion as 1 : 2 = 2 : 4. Hence answer is "Possible"

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def permutate(arr):\n if len(arr) == 1:\n  yield arr\n for x in range(len(arr)):\n  for perm in permutate(arr[:x] + arr[x+1:]):\n   yield [arr[x]] + perm\n\nvals = [int(x) for x in input().split()]\n\nfounded = False\nfor val in permutate(vals):\n if (val[0] / float(val[1]) == val[2] / float(val[3])):\n  print("Possible")\n  founded = True \n  break\nif not founded:\n print("Impossible")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13317
=====Function Descriptions=====
any()
This expression returns True if any element of the iterable is true. If the iterable is empty, it will return False.

Code
>>> any([1>0,1==0,1<0])
True
>>> any([1<0,2<1,3<2])
False

all()
This expression returns True if all of the elements of the iterable are true. If the iterable is empty, it will return True.

Code
>>> all(['a'<'b','b'<'c'])
True
>>> all(['a'<'b','c'<'b'])
False

=====Problem Statement=====
You are given a space separated list of integers. If all the integers are positive, then you need to check if any integer is a palindromic integer.

=====Input Format=====
The first line contains an integer N. N is the total number of integers in the list. The second line contains the space separated list of N integers.

=====Constraints=====
0<N<100

=====Output Format=====
Print True if all the conditions of the problem statement are satisfied. Otherwise, print False.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def __starting_point():\n    num_cnt = int(input().strip())\n    arr = list(input().strip().split())\n    print(all([all([int(x) > 0 for x in arr]), any([x == x[::-1] for x in arr])]))\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13467
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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nfor _ in range(int(input())):\n    n,k=list(map(int,input().split()))\n    x=list(map(int,input().split()))\n    x=x[-(k):]+x\n    y=sum(x[0:k])\n    z=sum(x[0:k])\n    for i in range(k,len(x)):\n        z=(z-x[i-k])+x[i]\n        y=max(y,z)\n    print(y)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13239
Mike is the president of country What-The-Fatherland. There are n bears living in this country besides Mike. All of them are standing in a line and they are numbered from 1 to n from left to right. i-th bear is exactly a_{i} feet high. 

 [Image] 

A group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strength of a group is the minimum height of the bear in that group.

Mike is a curious to know for each x such that 1 ≤ x ≤ n the maximum strength among all groups of size x.


-----Input-----

The first line of input contains integer n (1 ≤ n ≤ 2 × 10^5), the number of bears.

The second line contains n integers separated by space, a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9), heights of bears.


-----Output-----

Print n integers in one line. For each x from 1 to n, print the maximum strength among all groups of size x.


-----Examples-----
Input
10
1 2 3 4 5 4 3 2 1 6

Output
6 4 4 3 3 2 2 1 1 1

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '\nn=int(input())\na=[int(o) for o in input().split()]\nl=[-1]*n\nr=[(n)]*n\nstack=[]\nfor i in range(n):\n  #  print(stack)\n    while stack and a[stack[-1]]>=a[i]:\n        stack.pop()\n    if stack:\n        l[i]=stack[-1]\n    stack.append(i)\nstack=[]\nfor i in range(n-1,-1,-1):\n   # print(stack)\n    while stack and a[stack[-1]]>=a[i]:\n        stack.pop()\n    if stack:\n        r[i]=stack[-1]\n    stack.append(i)\nanswers=[min(a)]*n\n#print(l)\n#print(r)\n\nfor i in range(n):\n  #  print(r,l)\n    lw=r[i]-l[i]-2\n    #print(lw)\n    \n    answers[lw]=max(answers[lw],a[i])\n    \nans=min(a)\nanswers[0]=max(a)\nfor i in range(n-1,-1,-1):\n    ans=max(ans,answers[i])\n    answers[i]=ans\nprint(*answers)\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13655
The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K(odd) to form a new pattern. Help the chef to code this pattern problem.

-----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, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 50$
- $1 \leq K \leq 50$

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

-----Sample Output:-----
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*

-----EXPLANATION:-----
No need, else pattern can be decode easily.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = lambda: sys.stdin.readline().rstrip("\\r\\n")\nfor _ in range(int(input())):\n    n = int(input())\n    k = 0\n    for i in range(n//2+1):\n        for i in range(k):\n            print(" ", end ="")\n        print("*")\n        k = k+1\n    #print("*")\n    k = k-2\n    for i in range(n//2):\n        for i in range(k):\n            print(" ",end="")\n        print("*")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13579
Little chef has just been introduced to the world of numbers! While experimenting with addition and multiplication operations, the little chef came up with the following problem:

Given an array A of non-negative integers, how many pairs of indices i and j exist such that  A[i]*A[j] > A[i]+A[j]  where  i < j .

Now being a learner, little chef isn't able to solve this problem efficiently and hence turns to you for help. 

-----Input-----
First line of input contains an integer T denoting the number of test cases. For each test case, the first line contains an integer N denoting the number of integers in the array. The next line contains N space separated integers where the ith integer represents A[i]. 
Note : There may be trailing spaces on each line of input. 

-----Output-----
For each test, print the required number of pairs in a single line.

-----Constraints-----
-  1 ≤ T ≤ 10 
-  2 ≤ N ≤ 100000 (105) 
-  0 ≤ A[i] ≤ 1000000 (106)

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

Output:
3
0

-----Explanation-----

Example case 1.

All pairs of numbers satisfy the criteria. Total number of pairs equals 3.

Example case 2.

No pair of numbers satisfy the criteria.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nfor _ in range(int(input())):\n \n n = int(input())\n l = list(map(int,input().split()))\n \n c2=0\n c=0\n for i in l:\n  \n  if i==2:\n   c2+=1\n  if i>2:\n   c+=1\n   \n    \n print(c2*c + (c*(c-1))//2)\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13047
Define a function that removes duplicates from an array of numbers and returns it as a result.

The order of the sequence has to stay the same.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def distinct(seq):\n    arr = []\n    used = set()\n    \n    for n in seq:\n        if n not in used:\n          arr.append(n)\n          used.add(n)\n          \n    return arr'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'distinct'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5488
Andre has very specific tastes. Recently he started falling in love with arrays.

Andre calls an nonempty array $b$ good, if sum of its elements is divisible by the length of this array. For example, array $[2, 3, 1]$ is good, as sum of its elements — $6$ — is divisible by $3$, but array $[1, 1, 2, 3]$ isn't good, as $7$ isn't divisible by $4$. 

Andre calls an array $a$ of length $n$ perfect if the following conditions hold:   Every nonempty subarray of this array is good.  For every $i$ ($1 \le i \le n$), $1 \leq a_i \leq 100$. 

Given a positive integer $n$, output any perfect array of length $n$. We can show that for the given constraints such an array always exists.

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


-----Input-----

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

The first and only line of every test case contains a single integer $n$ ($1 \le n \le 100$).


-----Output-----

For every test, output any perfect array of length $n$ on a separate line. 


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

Output
24
19 33
7 37 79 49



-----Note-----

Array $[19, 33]$ is perfect as all $3$ its subarrays: $[19]$, $[33]$, $[19, 33]$, have sums divisible by their lengths, and therefore are good.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't=int(input())\nfor you in range(t):\n    n=int(input())\n    for i in range(n):\n        print(1,end=" ")\n    print()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12901
Given an integer N, Chef wants to find the smallest positive integer M such that the bitwise XOR of M and M+1 is N. If no such M exists output -1.

-----Input-----
The first line of input contain an integer T denoting the number of test cases. Each of the following T lines contains an integer N for that test case.

-----Output-----
For each test case, output a single line containing the number M or -1 as described above.

-----Constraints-----
- 1 ≤ T ≤ 5000
- 1 ≤ N ≤ 230

-----Example-----
Input:
1
3

Output:
1

-----Explanation-----First Example :  M desired in the problem would be 1. As bitwise XOR of 1 and 2 is equal to 3.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "for i in range(int(input())):\n N = int(input())\n binary = (bin(N)[2:])\n if N == 1 :\n  print(2)\n else :\n  if '0' in binary:\n   print(-1)\n  else:\n   print((N-1)//2)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12963
Complete the method that takes a boolean value and return a `"Yes"` string for `true`, or a `"No"` string for `false`.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def bool_to_word(boolean):\n    if boolean == True:\n        return "Yes"\n    elif boolean == False:\n        return "No"\n    else:\n        return "error, neither True nor False"'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'bool_to_word'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5298