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

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

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

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

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

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

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

```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 _ in range(t):\n    n = int(input())\n    ll = list(map(int, input().split()))\n    ss = 0\n    for ele in ll:\n        if ele <= 6:\n            ss += ele\n        else:\n            zz = ele % 6\n            if zz == 0:\n                ss += 6\n            else:\n                ss += zz\n    print(ss)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13041
Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen. 


-----Input-----

The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.

Then, k lines will follow. The i-th line will contain c_{i}, the number of balls of the i-th color (1 ≤ c_{i} ≤ 1000).

The total number of balls doesn't exceed 1000.


-----Output-----

A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007. 


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

Output
3

Input
4
1
2
3
4

Output
1680



-----Note-----

In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are: 

1 2 1 2 3

1 1 2 2 3

2 1 1 2 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 = 'k = int(input())\n\nh = []\n\nfor i in range(k):\n    h.append(int(input()))\n\n\nffs = [1]\ndef f(n):\n    if n < len(ffs):\n        return ffs[n]\n    v = n * f(n-1)\n    ffs.append(v)\n    return v\n\n\ndef c(k, n):\n    return f(n) // (f(k) * f(n-k))\n\ndef cc(k, n):\n    return c(n-1, n + k-1)\n\n\ndef solve(h):\n    if len(h) == 1:\n        return 1\n\n    hh = h[:-1]\n    hh_len = sum(hh)\n\n    return solve(hh) * cc(h[-1] -1, hh_len + 1)\n\n\nr = 1\nfor i in range(len(h)):\n    r *= cc(h[i] -1, sum(h[:i]) + 1)\n\nprint(r % 1000000007)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13097
Complete the function which takes two arguments and returns all numbers which are divisible by the given divisor. First argument is an array of `numbers` and the second is the `divisor`.

## Example

```python
divisible_by([1, 2, 3, 4, 5, 6], 2) == [2, 4, 6]
```

```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 divisible_by(l, d):\n    return [ n for n in l if not n%d ]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'divisible_by'
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: 5410
Given a number **n**, return the number of positive odd numbers below **n**, EASY!

Expect large Inputs!

```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 odd_count(n):\n    return round((n-1)/2) if n % 2 == 1 else n/2'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'odd_count'
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: 5356
Chef likes problems which using some math. Now he asks you to solve next one. You have 4 integers, Chef wondering is there non-empty subset which has sum equals 0.

-----Input-----
The first line of input contains T - number of test cases. 
Each of the next T lines containing four pairwise distinct integer numbers - a, b, c, d.

-----Output-----
For each test case output "Yes", if possible to get 0 by choosing non-empty subset of {a, b, c, d} with sum equal 0, or "No" in another case.

-----Constraints-----
- 1 ≤ T ≤ 103
- -106 ≤ a, b, c, d ≤ 106 

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

Output:
Yes
Yes
No

-----Explanation-----
Example case 1. We can choose subset {0} 
Example case 2. We can choose subset {-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 = "# cook your dish here\nt=int(input())\nwhile(t):\n a=[int(x) for x in input().split()]\n tot=1<<4\n flag=0\n for i in range(1,tot):\n  sum=0\n  for j in range(4):\n   f=1<<j\n   if(f&i):\n    sum+=a[j]\n  if(sum==0):\n   flag=1\n   break\n print( 'Yes' if sum==0 else 'No') \n t-=1"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13021
Complete the solution so that it reverses the string passed into it. 

```
'world'  =>  'dlrow'
```

```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 solution( param):\n    return param[::-1]\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'solution'
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: 5338
Determine the total number of digits in the integer (`n>=0`) given as input to the function. For example, 9 is a single digit, 66 has 2 digits and 128685 has 6 digits. Be careful to avoid overflows/underflows.

All inputs will be valid.

```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 digits(n):\n    # your code here\n    count=len(str(n))\n    return count'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'digits'
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: 5322
Chef had a sequence of positive integers with length $N + K$. He managed to calculate the arithmetic average of all elements of this sequence (let's denote it by $V$), but then, his little brother deleted $K$ elements from it. All deleted elements had the same value.
Chef still knows the remaining $N$ elements — a sequence $A_1, A_2, \ldots, A_N$. Help him with restoring the original sequence by finding the value of the deleted elements or deciding that there is some mistake and the described scenario is impossible.
Note that the if it is possible for the deleted elements to have the same value, then it can be proven that it is unique. Also note that this value must be a positive integer.

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

-----Output-----
For each test case, print a single line containing one integer — the value of the deleted elements, or $-1$ if there is a mistake.

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

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

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

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

```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 _ in range(t):\n \n n,k,v=list(map(int,input().split()))\n l=list(map(int,input().split()))\n count=sum(l)\n \n total=v*(n+k)\n \n num=total-count\n \n if(total<=count):\n  \n  print('-1')\n  \n elif(num%k != 0):\n  \n  print('-1')\n  \n else:\n  \n  print(int(num/k))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13173
Write a program to obtain a number $N$ and increment its value by 1 if the number is divisible by 4 $otherwise$ decrement its value by 1.

-----Input:-----
- First line will contain a number $N$.

-----Output:-----
Output a single line, the new value of the number.

-----Constraints-----
- $0 \leq N \leq 1000$

-----Sample Input:-----
5

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

-----EXPLANATION:-----
Since 5 is not divisible by 4 hence, its value is decreased by 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 = '# cook your dish here\na=int(input())\nif a%4==0:\n    print(a+1)\nelse:\n    print(a-1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12823
You are given an integer $D$. Find an integer sequence $A_1, A_2, \ldots, A_N$ such that the following conditions are satisfied:
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^5$ for each valid $i$
- $\sum_{i=1}^N \sum_{j=i}^N \left( \mathrm{min}(A_i, A_{i+1}, \ldots, A_j) - \mathrm{GCD}(A_i, A_{i+1}, \ldots, A_j) \right) = D$
It can be proved that a solution always exists under the given constraints.
Note: $\mathrm{GCD}(B_1, B_2, \ldots, B_M)$ is the greatest integer which divides all the integers $B_1, B_2, \ldots, B_M$.

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

-----Output-----
For each test case, print two lines. The first of these lines should contain a single integer $N$. The second line should contain $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
If there are multiple solutions, you may find any one of them.

-----Constraints-----
- $1 \le T \le 10$
- $0 \le D \le 10^9$

-----Example Input-----
4
2
5
200
13

-----Example Output-----
3
3 3 2 
5
2 8 5 1 10 
7
12 10 15 11 19 13 15
4
5 4 4 10

```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\nt=int(input())\nfor i in range(t):\n D=int(input())\n P=10**5-2\n ans=[]\n if(D==0):\n  ans.append(1)\n while(D>0):\n  P=min(P,D)\n  ans.append(P+2)\n  ans.append(P+1)\n  ans.append(1)\n  D-=P\n print(len(ans))\n print(*ans,sep=" ")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13141
=====Function Descriptions=====
inner

The inner tool returns the inner product of two arrays.

import numpy

A = numpy.array([0, 1])
B = numpy.array([3, 4])

print numpy.inner(A, B)     #Output : 4

outer

The outer tool returns the outer product of two arrays.

import numpy

A = numpy.array([0, 1])
B = numpy.array([3, 4])

print numpy.outer(A, B)     #Output : [[0 0]
                            #          [3 4]]

=====Problem Statement=====
You are given two arrays: A and B.
Your task is to compute their inner and outer product.

=====Input Format=====
The first line contains the space separated elements of array A.
The second line contains the space separated elements of array B.

=====Output Format=====
First, print the inner product.
Second, print the outer product.

```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 numpy as np\n\narr1 = np.array(list(map(int, input().strip().split())))\narr2 = np.array(list(map(int, input().strip().split())))\n\nprint((np.inner(arr1, arr2)))\nprint((np.outer(arr1, arr2)))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 6169837
Chef is playing a game with his brother Chefu. He asked Chefu to choose a positive integer $N$, multiply it by a given integer $A$, then choose a divisor of $N$ (possibly $N$ itself) and add it to the product. Let's denote the resulting integer by $M$; more formally, $M = A \cdot N + d$, where $d$ is some divisor of $N$.
Chefu told Chef the value of $M$ and now, Chef should guess $N$. Help him find all values of $N$ which Chefu could have chosen.

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

-----Output-----
For each test case, print two lines. The first line should contain a single integer $C$ denoting the number of possible values of $N$. The second line should contain $C$ space-separated integers denoting all possible values of $N$ in increasing order.
It is guaranteed that the sum of $C$ over all test cases does not exceed $10^7$.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le M \le 10^{10}$
- $1 \le A < M$

-----Subtasks-----
Subtask #1 (50 points):
- $M \le 10^6$
Subtask #2 (50 points): original constraints

-----Example Input-----
3
3 35
5 50
4 65

-----Example Output-----
1
10
0

3
13 15 16

```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\nfrom math import sqrt\ndef solve():\n a,m=list(map(int,input().split()))\n n=m//(a+1)\n\n all_vals=[]\n \n while(a*n<m or (a>=int(sqrt(m)) and n<=sqrt(m))):\n  if(a*n+((m-a*n)*(n%(m-a*n)==0))==m):\n   all_vals.append(n)\n  n+=1\n\n print(len(all_vals))\n if(len(all_vals)!=0):\n  print(*all_vals)\n\n  \n\nfor T in range(int(input())):\n solve()\n \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12975
Chef Two and Chef Ten are playing a game with a number $X$. In one turn, they can multiply $X$ by $2$. The goal of the game is to make $X$ divisible by $10$.
Help the Chefs find the smallest number of turns necessary to win the game (it may be possible to win in zero turns) or determine that it is impossible.

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

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

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

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

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

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

```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\ntest_case = int(input())\nfor i in range(test_case):\n num = int(input())\n if (num % 10 == 0):\n  print('0')\n elif (num * 2 % 10 == 0):\n  print('1')\n else:\n  print('-1')"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12931
Let's denote as $\text{popcount}(x)$ the number of bits set ('1' bits) in the binary representation of the non-negative integer x.

You are given multiple queries consisting of pairs of integers l and r. For each query, find the x, such that l ≤ x ≤ r, and $\text{popcount}(x)$ is maximum possible. If there are multiple such numbers find the smallest of them.


-----Input-----

The first line contains integer n — the number of queries (1 ≤ n ≤ 10000).

Each of the following n lines contain two integers l_{i}, r_{i} — the arguments for the corresponding query (0 ≤ l_{i} ≤ r_{i} ≤ 10^18).


-----Output-----

For each query print the answer in a separate line.


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

Output
1
3
7



-----Note-----

The binary representations of numbers from 1 to 10 are listed below:

1_10 = 1_2

2_10 = 10_2

3_10 = 11_2

4_10 = 100_2

5_10 = 101_2

6_10 = 110_2

7_10 = 111_2

8_10 = 1000_2

9_10 = 1001_2

10_10 = 1010_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 = 'n = int(input())\n\nfor i in range(n):\n\tl, r = list(map(int, input().split()))\n\tbits = 0\n\tresult = 0\n\twhile True:\n\t\tcount_bit = len(str(bin(r))) - 2\n\t\tif (1 << count_bit) - 1 == r:\n\t\t\tresult += (1 << count_bit) - 1\n\t\t\tbreak\n\t\texp = (1 << (count_bit - 1)) - 1\n\t\tif exp >= l:\n\t\t\tresult += exp\n\t\t\tbreak\n\t\telse:\n\t\t\tbits += 1\n\t\t\texp = 1 << (count_bit - 1)\n\t\t\tresult += exp\n\t\t\tl -= exp\n\t\t\tr -= exp\n\tprint(result)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13153
Mr. Pr and Ms. Ad are at $a$ and $b$ respectively on an infinite number line. Mr. Pr wants to meet Ms. Ad.
Mr. Pr can choose to move  $c$ or $d$ units in 1 second. If Mr. Pr moves $c$ units then Ms. Ad will move $d$ units and vice versa. (Both of them always moved in positive x-direction)
You have to determine if Mr. Pr can meet with Ms. Ad after some integral amount of time, given that Mr. Pr chooses optimally. Note that meeting after a fractional amount of time does not count.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains four space separated integers, $a$, $b$, $c$, and $d$.

-----Output:-----
- For each test case, output a single line containing "YES" if Mr. Pr meets with Ms. Ad, otherwise "NO".

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq a,b,c,d \leq 10^9$

-----Sample Input:-----
2
3 4 1 2
10 20 3 7

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

-----Explanation:-----
In the first test case, Mr. Pr will move 2 units in the first second and Ms. Ad moves 1 unit simultaneously and they meet. 
In the second test case, it is impossible to meet (fractional time is not allowed).

```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\nn=int(input())\nfor i in range(n):\n    l=list(map(int,input().split()))\n    a=min(l[0],l[1])\n    b=max(l[0],l[1])\n    c=min(l[2],l[3])\n    d=max(l[2],l[3])\n    if(d!=c):\n        d=d-c\n        t=(b-a)//d\n        a=a+(t*d)\n        if(a==b):\n            print("YES")\n        else:\n            print("NO")\n    else:\n        if(a!=b):\n            print("NO")\n        else:\n            print("YES")      \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13263
You are given a non-empty string s consisting of lowercase English letters. You have to pick exactly one non-empty substring of s and shift all its letters 'z' $\rightarrow$ 'y' $\rightarrow$ 'x' $\rightarrow \ldots \rightarrow$ 'b' $\rightarrow$ 'a' $\rightarrow$ 'z'. In other words, each character is replaced with the previous character of English alphabet and 'a' is replaced with 'z'.

What is the lexicographically minimum string that can be obtained from s by performing this shift exactly once?


-----Input-----

The only line of the input contains the string s (1 ≤ |s| ≤ 100 000) consisting of lowercase English letters.


-----Output-----

Print the lexicographically minimum string that can be obtained from s by shifting letters of exactly one non-empty substring.


-----Examples-----
Input
codeforces

Output
bncdenqbdr

Input
abacaba

Output
aaacaba



-----Note-----

String s is lexicographically smaller than some other string t of the same length if there exists some 1 ≤ i ≤ |s|, such that s_1 = t_1, s_2 = t_2, ..., s_{i} - 1 = t_{i} - 1, and s_{i} < t_{i}.

```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 shift():\n    word = input()\n    i = 0\n    shifted = ''\n    while i < len(word) - 1:\n        if word[i] != 'a':\n            break\n        shifted += word[i]\n        i += 1\n    if i == len(word) - 1 and word[i] == 'a':\n        shifted += 'z'\n        return shifted\n    while i < len(word):\n        if word[i] == 'a':\n            shifted += word[i:]\n            break\n        shifted += chr(ord(word[i]) - 1)\n        i += 1\n    return shifted\n\nprint(shift())\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13607
Chef Tobby is playing a rapid fire with Bhuvan. He gives Bhuvan a string S and each time, Bhuvan has to guess whether there exists 2 equal subsequences in the string or not.
Bhuvan got a perfect score in the game with Chef Tobby. However, Chef Tobby has now asked Bhuvan to write a program that will do this automatically given a string S. Bhuvan is an intelligent man but he does not know how to write a code. Can you help him?
Find two different subsequences such that they are equal in their value, more formally, find two sequences of indices (a1, a2, ..., ak-1, ak) and (b1, b2, ..., bk-1, bk) such that:

- 1≤ ai, bi ≤ |S|
- ai < ai+1 for all valid i
- bi < bi+1 for all valid i
- Sai = Sbi for all valid i
- there exist at least one i such that ai is not equal to bi

-----Input section-----
The first line contains T, the number of test cases.
Each of the next T lines contain one string S each.
Input will only consist of lowercase english characters

-----Output section-----
For each test case, output "yes" or "no" (without quotes) as the solution to the problem.

-----Input constraints-----
1 ≤ T ≤ 1000
1 ≤ length of S ≤ 100

-----Sample Input-----
4
likecs
venivedivici
bhuvan
codechef

-----Sample Output-----
no
yes
no
yes

-----Explanation-----
In test case 2, one of the possible equal subsequence is "vi" and "vi". (one at position {0, 3} and other at {4, 7}, assuming 0-based indexing).
In test case 4, one of the possible equal subsequence is "ce" and "ce". (one at position {0, 3} and other at {4, 6}, assuming 0-based indexing).

```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 i in range(t):\n a = input()\n b = list(a)\n c = 0\n for i in b:\n  if a.count(i) > 1:\n   c = c + 1\n if c >= 1:\n  print("yes")\n else:\n  print("no")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12955