akhauriyash/Code-Regression huggingface dataset:
A reversed arabic no is one whose digits have been written in the reversed order. However in this any trailing zeroes are omitted. The task at hand here is a simple one. You need to add two numbers which have been written in reversed arabic and return the output back in reversed arabic form, assuming no zeroes were lost while reversing.


-----Input-----
The input consists of N cases. The first line of the input contains only a positive integer N. Then follow the cases. Each case consists of exactly one line with two positive integers seperated by space. These are the reversednumbers you are to add.


-----Output-----
For each case, print exactly one line containing only one integer- the reversed sum of two reversed numbers. Omit any leading zeroes in the output.


-----Example-----
Input:
1
24 1

Output:
34

```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 = '#/usr/bin/python\n\ndef main():\n test = int(input())\n for i in range(test):\n  x = input()\n  l = x.split()\n  a = str(l[0])\n  b = str(l[1])\n  a = a[::-1]\n  b = b[::-1]\n  c = int(a) + int(b)\n  s = str(c)\n  s = s[::-1]\n  print(int(s))\n\ndef __starting_point():\n  main()\n\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13923
If　`a = 1, b = 2, c = 3 ... z = 26`

Then `l + o + v + e = 54`

and `f + r + i + e + n + d + s + h + i + p = 108`

So `friendship` is twice stronger than `love` :-)

The input will always be in lowercase and never be empty.

```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 words_to_marks(s):\n    return sum([ord(char) - 96 for char in s])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'words_to_marks'
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: 5362
# Convert number to reversed array of digits

Given a random non-negative number, you have to return the digits of this number within an array in reverse order.

## Example:

```
348597 => [7,9,5,8,4,3]
```

```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

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 digitize(n):\n    x = [int(i) for i in str(n)]\n    return [i for i in reversed(x)]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'digitize'
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: 5544
Raju has created a program to find the square root of a number. But his program can store only integers. Being a newbie, he didn't know about rounding the numbers. Hence his program returns the absolute value of the result if possible. For example, sqrt(3) = 1.73205080757……. His program will return 1
Given a number $N$, and it's integral square root $S$, His instructor will consider the answer correct if Difference between $N$ and the square of $S$ is within less than or equal to $X$% of $N$.

-----Input:-----
- First line contains $T$ no. of test cases and $X$ separated by space
- For every test case, a line contains an integer $N$

-----Output:-----
For every test case, print yes  if his programs return square root and (N-(S^2)) <= 0.01XN . For everything else, print no on a new line

-----Constraints-----
10 points:
- $1 \leq T \leq 10$
- $0\leq N \leq 10$
20 points:
- $1 \leq T \leq 30000$
- $-10^9 \leq N \leq 10^9$
70 points:
- $1 \leq T \leq 10^6$
- $-10^9 \leq N \leq 10^9$

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

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

-----EXPLANATION:-----
In #1, sqrt(5) = 2.2360679775. Taking integral value, S = 2.

S2 = 4. Difference=1 which is within 20% of 5
In #1, sqrt(3) = 1.73205080757. Taking integral value, S = 1.

S2 = 1. Difference=2  which is not within 20% of 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 = 'import math \nt,x=map(int,input().strip().split())\nfor l in range(t):\n n=int(input())\n if n>=0:\n  a=int(math.sqrt(n))\n  b=a*a\n  d=n-b\n  # print(a,b,d,int((x/100)*n))\n  if d<=int((x/100)*n):\n   print("yes")\n  else:\n   print("no")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13085
Very simple, given a number, find its opposite.

Examples:
```
1: -1
14: -14
-34: 34
```

~~~if:sql
You will be given a table: `opposite`, with a column: `number`. Return a table with a column: `res`.
~~~

```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 opposite(number):\n    return number * -1\n    #Nobody saw this\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'opposite'
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: 5272
You were strolling outside the restaurant at the end of the universe. On a metaspiral path you stumble upon a weird device which takes a three-digit number as input and processes it. The Hitchhiker's guide to the galaxy explains that it processes the input in the following manner: 
- Multiplies it with 13, followed by 11 and then 7          
- Outputs all the distinct three-digit numbers possible from the digits of the new number (each digit can only be used once)          
Your friend Zaphod is in a playful mood, and does the following with the device-           
- Given a three-digit positive number $K$, he feeds it to the device for processing.          
- He then takes the numbers it gives as output, and send each of them through the device and again collect all the numbers sent out.          
- Repeats the above step $N$ times.          
To test your wit, he challenges you to find the number of distinct 3-digit numbers which the device outputs over the $N$ steps. Can you?

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

-----Output:-----
For each testcase, output a single integer denoting the number of distinct 3-digit numbers which the device outputs over the $N$ steps.

-----Constraints-----
- $1 \leq T \leq 1000$ 
- $5 \leq N \leq 10^9$ 
- Each digit of $K$ is non-zero           

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

123 5         

-----Sample Output:-----
27

```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 a,b=map(int,input().split())\n a=set(str(a))\n print(len(a)**3)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12953
You have two arrays in this kata, every array contain only unique elements. Your task is to calculate number of elements in first array which also are in second array.

```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 = 'verbose,match_arrays=0,lambda a,b:sum(1for e in a if e in b)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'match_arrays'
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: 5354
Given N, count how many permutations of [1, 2, 3, ..., N] satisfy the following property.

Let P1, P2, ..., PN denote the permutation. The property we want to satisfy is that there exists an i between 2 and n-1 (inclusive) such that

- Pj > Pj + 1  ∀    i ≤ j ≤ N - 1.
- Pj > Pj - 1  ∀    2 ≤ j ≤ i.

-----Input-----
First line contains T, the number of test cases. Each test case consists of N in one line.

-----Output-----
For each test case, output the answer modulo 109+7.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 109

-----Subtasks-----
- Subtask #1(40 points): 1 ≤ N ≤ 1000
- Subtask #2(60 points): original constraints

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

Output:
0
2

-----Explanation-----

Test case 1:

No permutation satisfies.

Test case 2:

Permutations [1, 3, 2] and [2, 3, 1] satisfy the property.

```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 _ in range(int(input())):\n n = int(input())\n print(0) if(n==1) else print(pow(2,n-1,10**9+7)-2) '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12929
Chef is making polygon cakes in his kitchen today! 
Since the judge panel is very strict, Chef's cakes must be beautiful and have sharp and precise $internal$ angles in arithmetic progression. 
Given the number of sides, $N$, of the cake Chef is baking today and also the measure of its first angle(smallest angle), $A$, find the measure of the $K^{th}$ angle.

-----Input:-----
- The first line contains a single integer $T$, the number of test cases. 
- The next $T$ lines contain three space separated integers $N$, $A$ and $K$, the number of sides of polygon, the first angle and the $K^{th}$ angle respectively. 

-----Output:-----
For each test case, print two space separated integers $X$ and $Y$, such that the $K^{th}$ angle can be written in the form of $X/Y$ and $gcd(X, Y) = 1$

-----Constraints-----
- $1 \leq T \leq 50$
- $3 \leq N \leq 1000$
- $1 \leq A \leq 1000000000$
- $1 \leq K \leq N$
- It is guaranteed the answer is always valid.

-----Sample Input:-----
1
3 30 2

-----Sample Output:-----
60 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 = 'def gcd(d,s):\n if s==0:\n  return d\n else:\n  return gcd(s,d%s)\nfor _ in range(int(input())):\n n,a,k=[int(x) for x in input().split()]\n d = (360*(n-2)-2*a*n)*(k-1)\n \n s = n*(n-1)\n k = gcd(d,s)\n d = d//k\n s=s//k\n print(d+s*a,s)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13169
Let's call a sequence good if the sum of all its elements is $0$.
You have a sequence of integers $A_1, A_2, \ldots, A_N$. You may perform any number of operations on this sequence (including zero). In one operation, you should choose a valid index $i$ and decrease $A_i$ by $i$. Can you make the sequence good using these operations?

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

-----Output-----
For each test case, print a single line containing the string "YES" if it is possible to make the given sequence good or "NO" if it is impossible.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10$
- $|A_i| \le 100$ for each valid $i$

-----Subtasks-----
Subtask #1 (10 points): $N = 1$
Subtask #2 (30 points): $N \le 2$
Subtask #3 (60 points): original constraints

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

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

-----Explanation-----
Example case 2: We can perform two operations ― subtract $1$ from $A_1$ and $2$ from $A_2$.

```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 = 'T = int(input())\nfor i in range(0, T):\n n = int(input())\n arr = list(map(int, input().split()))\n flag=0\n if sum(arr)<0:\n  flag=1\n if flag==1:\n  print("NO")\n else:\n  print("YES")\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13035
Consider a currency system in which there are notes of six denominations, namely, Rs. 1, Rs. 2, Rs. 5, Rs. 10, Rs. 50, Rs. 100.
If the sum of Rs. N is input, write a program to computer smallest number of notes that will combine to give Rs. N.

-----Input-----

The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer N. 

-----Output-----
For each test case, display the smallest number of notes that will combine to give N, in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ N ≤ 1000000

-----Example-----
Input
3 
1200
500
242

Output
12
5
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 = '# cook your dish here\na=[100,50,10,5,2,1]\nfor i in range(int(input())):\n    n=int(input())\n    c=0\n    for i in a:\n        if n!=0:\n            if n//i!=0:\n                c+=n//i\n                n-=((n//i)*i)\n        else:\n            break \n    print(c)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13041
A Train started its journey at x=-infinity is travelling on the x-Coordinate Axis. Given n passengers and the coordinates $b_i$ and $d_i$ for each of the $ith$ passenger at which they board and leave from the train respectively. Due to current COVID-19 crisis, the train is monitored at each mile/coordinate. The infection degree of the train at each mile is equal to the total passengers present in the train at that mile/coordinate. The train stops its journey if no more passengers are there to board the train. The term infection severity of the journey is defined as the sum of infection degrees noted at each mile. Find the Infection severity of the journey. Note: A passenger is considered for calculation of infection degree at both boarding and leaving stations.

Since the answer can be very large, print it modulo $(10^9)+7$.

-----Input:-----
- First line will contain $N$, number of passengers. Then the $N$ lines follow. 
- $i$th line contains two integers $b_i, d_i$ , the boarding and departure mile of $i$th passenger.

-----Output:-----
Print a single value, the Infection Severity of the journey modulo $(10^9)+7$.

-----Constraints-----
- $0 \leq N \leq 100000$
- $-500000 \leq b_i \leq 500000$
- $-500000 \leq d_i \leq 500000$

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

0 2

1 3

-1 4  

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

-----EXPLANATION:-----
Infection degree at :

-1 is 1

0 is 2

1 is 3

2 is 3

3 is 2

4 is 1

Calculation started at mile -1 and ended at mile 4. Infection Severity = 1+2+3+3+2+1 =12

```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())\ns=0\nfor i in range(n):\n    l=list(map(int,input().split()))\n    k=l[1]+1-l[0]\n    if(l[0]<0 and l[1]<0):\n        k=l[0]-l[1]-1\n    s+=abs(k)\nm=10**9\nm+=7\nprint(s%m)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13101
You are given a string s of length n.
Does a tree with n vertices that satisfies the following conditions exist?
 - The vertices are numbered 1,2,..., n.
 - The edges are numbered 1,2,..., n-1, and Edge i connects Vertex u_i and v_i.
 - If the i-th character in s is 1, we can have a connected component of size i by removing one edge from the tree.
 - If the i-th character in s is 0, we cannot have a connected component of size i by removing any one edge from the tree.
If such a tree exists, construct one such tree.

-----Constraints-----
 - 2 \leq n \leq 10^5
 - s is a string of length n consisting of 0 and 1.

-----Input-----
Input is given from Standard Input in the following format:
s

-----Output-----
If a tree with n vertices that satisfies the conditions does not exist, print -1.
If a tree with n vertices that satisfies the conditions exist, print n-1 lines.
The i-th line should contain u_i and v_i with a space in between.
If there are multiple trees that satisfy the conditions, any such tree will be accepted.

-----Sample Input-----
1111

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

It is impossible to have a connected component of size n after removing one edge from a tree with n vertices.

```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 = input()\n\nif s[0] == '0' or s[-1] == '1' or s[:-1] != s[:-1][::-1]:\n    print((-1))\n    return\n\nedges = []\nhead = 0\nfor idx, i in enumerate(s[:-1]):\n    edges.append([head, idx + 1])\n    if i == '1':\n        head = idx + 1\nfor i, j in edges:\n    print((i + 1, j + 1))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes:
Hooray! Polycarp turned $n$ years old! The Technocup Team sincerely congratulates Polycarp!

Polycarp celebrated all of his $n$ birthdays: from the $1$-th to the $n$-th. At the moment, he is wondering: how many times he turned beautiful number of years?

According to Polycarp, a positive integer is beautiful if it consists of only one digit repeated one or more times. For example, the following numbers are beautiful: $1$, $77$, $777$, $44$ and $999999$. The following numbers are not beautiful: $12$, $11110$, $6969$ and $987654321$.

Of course, Polycarpus uses the decimal numeral system (i.e. radix is 10).

Help Polycarpus to find the number of numbers from $1$ to $n$ (inclusive) that are beautiful.


-----Input-----

The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases in the input. Then $t$ test cases follow.

Each test case consists of one line, which contains a positive integer $n$ ($1 \le n \le 10^9$) — how many years Polycarp has turned.


-----Output-----

Print $t$ integers — the answers to the given test cases in the order they are written in the test. Each answer is an integer: the number of beautiful years between $1$ and $n$, inclusive.


-----Example-----
Input
6
18
1
9
100500
33
1000000000

Output
10
1
9
45
12
81



-----Note-----

In the first test case of the example beautiful years are $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ and $11$.

```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 = 'tests = int(input())\nfor test in range(tests):\n    n = int(input())\n    l = len(str(n))\n    c = 0\n    for i in range(1, l+1):\n        for j in range(1, 10):\n            a = int(str(j)*i)\n            if a <= n:\n                c += 1\n    print(c)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13043
This is a peculiar functioning setup.
Two Tanks are separated from each other by a wall .There is a pipe in the wall which connects  both tanks  which allows flow of water between them . Due to this ,there is change in temperature of both tanks , every minute temperature of Tank with larger temperature among two decreases by one and temperature of Tank  with smaller temperature among two increases by two until equilibrium is reached , But there is a problem .
The pipe can't control this flow of water if there is Non-equilibrium (inequality of temperature  on  both sides )  even after $m$ minutes and the pipe will burst after it , your task is to predict whether the pipe will burst or not .
Note: If equilibrium cannot be reached the process will continue forever.
The initial temperature of Cold Tank is $Tc$ , of Hot Tank it is $Th$. 

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, three  integers $m, Tc,Th$. 

-----Output:-----
For each testcase, output in a single line answer "Yes" if Pipe will burst after m minutes "No" if pipe will not burst.

-----Constraints-----
- $1 \leq T \leq 100000$
- $1 \leq m,Tc,Th \leq 10^9$
- $Tc \leq Th $

-----Sample Input:-----
2
4 5 10
2 2 5

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

```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())\nflag=0\nfor i in range(t):\n m,tc,th=map(int,input().split())\n \n # for j in range(m):\n #     tc+=2\n #     th-=1\n #     if(tc==th):\n #         flag=1\n #         print('No')\n #         break\n #     if(tc>th):\n #         flag=0\n #         break\n  \n # if(flag==0):\n #     print('Yes')\n new_m=(th-tc)/3\n m2=int(new_m)\n if(new_m<=m and new_m==m2):\n  print('No')\n else:\n  print('Yes')"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12985
The statement of this problem is the same as the statement of problem C2. The only difference is that, in problem C1, $n$ is always even, and in C2, $n$ is always odd.

You are given a regular polygon with $2 \cdot n$ vertices (it's convex and has equal sides and equal angles) and all its sides have length $1$. Let's name it as $2n$-gon.

Your task is to find the square of the minimum size such that you can embed $2n$-gon in the square. Embedding $2n$-gon in the square means that you need to place $2n$-gon in the square in such way that each point which lies inside or on a border of $2n$-gon should also lie inside or on a border of the square.

You can rotate $2n$-gon and/or the square.


-----Input-----

The first line contains a single integer $T$ ($1 \le T \le 200$) — the number of test cases.

Next $T$ lines contain descriptions of test cases — one per line. Each line contains single even integer $n$ ($2 \le n \le 200$). Don't forget you need to embed $2n$-gon, not an $n$-gon.


-----Output-----

Print $T$ real numbers — one per test case. For each test case, print the minimum length of a side of the square $2n$-gon can be embedded in. Your answer will be considered correct if its absolute or relative error doesn't exceed $10^{-6}$.


-----Example-----
Input
3
2
4
200

Output
1.000000000
2.414213562
127.321336469

```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 math\nq = int(input())\nfor _ in range(q):\n\tn = int(input())\n\tn*=2\n\tprint(math.tan(math.pi/2-math.pi/n))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12949
Chef has an array of N natural numbers. Cheffina challenges the chef to choose the two numbers from the array and following the condition as the area of the rectangle formed from the two numbers is maximum. Cheffina also asks the chef to choose two numbers different from the previous two to form the rectangle with a minimum area.

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

-----Output:-----
For each test case, output in one line answers maximum and minimum area of a rectangle.

-----Constraints-----
- $1 \leq T \leq 10$
- $4 \leq N \leq 10^5$
- $1 \leq arr[i] \leq 10^6$

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

-----Sample Output:-----
20 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 = 'for _ in range(int(input())):\n    n=int(input())\n    l=list(map(int,input().split()))\n    l.sort()\n    mini,maxi=l[0]*l[1],l[-1]*l[-2]\n    print(maxi,mini)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13067