akhauriyash/Code-Regression huggingface dataset:
Consider a number X on which K Mag-Inc operations are to be performed. In a Mag-Inc operation, the number X undergoes an increment of A/B times of X where A and B are two integers.

There is a numerator and a denominator array of size K which contain the ith values of A and B. After K Mag-Inc operations, the number X turns to M.

Now your job is to find what percentage of M is to be decremented from M if it has to be converted back to X. Let this percentage be denoted by Z.

Print the integral part of Z.

-----Input:-----

First line contains an integer T denoting the number of test cases.

First line of every test case contains two space separated integers X and K.

The second and third line of every test case will contain K space separated integers 

denoting the Numerator and Denominator array.

-----Output:-----

For each test case, print the required result in a single line.

-----Constraints:-----
1 ≤ T ≤ 100
1 ≤ K, A, B ≤ 40000
1≤X≤10^100

-----Example:-----Input:
2
100 1
1 
4
100 2
1 1
2 3Output:
20
50

-----Explanation:-----

Case 2: 100 undergoes an increment of (1/2)*100. Therefore M = 100 + 50.

Now M = 150.

Now again, 

M undergoes an increment of (1/3)*150. Therefore, M = 150 + 50. 

Now as we want to revert back M = 200 to X i.e. 100, we need to decrement it by a value 

of 100 and we know that 100 is 50% of 200.

Hence, we print 50.

```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=eval(input())\nwhile t:\n t-=1\n x,k=list(map(int,input().split()))\n a=list(map(float,input().split()))\n b=list(map(float,input().split()))\n rat = 1.0\n for i in range(k):\n  rat = rat*((a[i]+b[i])/b[i])\n rat = ((rat-1)/rat)*100.0\n print(int(rat))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16881
Vasya's got a birthday coming up and his mom decided to give him an array of positive integers a of length n.

Vasya thinks that an array's beauty is the greatest common divisor of all its elements. His mom, of course, wants to give him as beautiful an array as possible (with largest possible beauty). Unfortunately, the shop has only one array a left. On the plus side, the seller said that he could decrease some numbers in the array (no more than by k for each number).

The seller can obtain array b from array a if the following conditions hold: b_{i} > 0; 0 ≤ a_{i} - b_{i} ≤ k for all 1 ≤ i ≤ n.

Help mom find the maximum possible beauty of the array she will give to Vasya (that seller can obtain).


-----Input-----

The first line contains two integers n and k (1 ≤ n ≤ 3·10^5; 1 ≤ k ≤ 10^6). The second line contains n integers a_{i} (1 ≤ a_{i} ≤ 10^6) — array a.


-----Output-----

In the single line print a single number — the maximum possible beauty of the resulting array.


-----Examples-----
Input
6 1
3 6 10 12 13 16

Output
3

Input
5 3
8 21 52 15 77

Output
7



-----Note-----

In the first sample we can obtain the array:

3 6 9 12 12 15

In the second sample we can obtain the next array:

7 21 49 14 77

```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, k = list(map(int, input().split()))\n\nt = set(map(int, input().split()))\n\ny = x = min(t)\n\nt = list(t)\n\nwhile True:\n\n    for i in t:\n\n        if i % x > k: x = i // (i // x + 1)\n\n    if y == x: break\n\n    y = x\n\nprint(y)\n\n\n\n# Made By Mostafa_Khaled\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13067
The code provided is supposed replace all the dots `.` in the specified String `str` with dashes `-`

But it's not working properly.

# Task

Fix the bug so we can all go home early.

# Notes

String `str` will never be null.

```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 = 'import re\ndef replace_dots(s):\n  if \'.\' in s: \n    \n    return s.replace(".", "-")\n  else:\n    return s'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'replace_dots'
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: 5318
You're given an array $a$ of $n$ integers, such that $a_1 + a_2 + \cdots + a_n = 0$.

In one operation, you can choose two different indices $i$ and $j$ ($1 \le i, j \le n$), decrement $a_i$ by one and increment $a_j$ by one. If $i < j$ this operation is free, otherwise it costs one coin.

How many coins do you have to spend in order to make all elements equal to $0$?


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 5000$). Description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 10^5$)  — the number of elements.

The next line contains $n$ integers $a_1, \ldots, a_n$ ($-10^9 \le a_i \le 10^9$). It is given that $\sum_{i=1}^n a_i = 0$.

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


-----Output-----

For each test case, print the minimum number of coins we have to spend in order to make all elements equal to $0$.


-----Example-----
Input
7
4
-3 5 -3 1
2
1 -1
4
-3 2 -3 4
4
-1 1 1 -1
7
-5 7 -6 -4 17 -13 4
6
-1000000000 -1000000000 -1000000000 1000000000 1000000000 1000000000
1
0

Output
3
0
4
1
8
3000000000
0



-----Note-----

Possible strategy for the first test case:   Do $(i=2, j=3)$ three times (free), $a = [-3, 2, 0, 1]$.  Do $(i=2, j=1)$ two times (pay two coins), $a = [-1, 0, 0, 1]$.  Do $(i=4, j=1)$ one time (pay one coin), $a = [0, 0, 0, 0]$.

```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    a = list(map(int,input().split()))\n    cnt = 0\n    av = 0\n    for i in range(n):\n        if a[i]<0:\n            cr = min(-1*a[i],av)\n            a[i]+=cr\n            av-=cr\n            cnt+=a[i]\n            a[i]=0\n        else:\n            av+=a[i]\n    print(-1*cnt)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13161
You are given several queries. Each query consists of three integers $p$, $q$ and $b$. You need to answer whether the result of $p/q$ in notation with base $b$ is a finite fraction.

A fraction in notation with base $b$ is finite if it contains finite number of numerals after the decimal point. It is also possible that a fraction has zero numerals after the decimal point.


-----Input-----

The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the number of queries.

Next $n$ lines contain queries, one per line. Each line contains three integers $p$, $q$, and $b$ ($0 \le p \le 10^{18}$, $1 \le q \le 10^{18}$, $2 \le b \le 10^{18}$). All numbers are given in notation with base $10$.


-----Output-----

For each question, in a separate line, print Finite if the fraction is finite and Infinite otherwise.


-----Examples-----
Input
2
6 12 10
4 3 10

Output
Finite
Infinite

Input
4
1 1 2
9 36 2
4 12 3
3 5 4

Output
Finite
Finite
Finite
Infinite



-----Note-----

$\frac{6}{12} = \frac{1}{2} = 0,5_{10}$

$\frac{4}{3} = 1,(3)_{10}$

$\frac{9}{36} = \frac{1}{4} = 0,01_2$

$\frac{4}{12} = \frac{1}{3} = 0,1_3$

```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 = "n=int(input())  \ns=''  \nfor i in range(n):  \n    p,q,b=map(int,input().split())  \n    for i in range(6):  \n        b=(b*b)%q  \n          \n    if((p*b)%q):  \n        s+='Infinite\\n'  \n    else:  \n        s+='Finite\\n'  \nprint(s) "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12981
Write a function to split a string and convert it into an array of words. For example:

```python
"Robin Singh" ==> ["Robin", "Singh"]

"I love arrays they are my favorite" ==> ["I", "love", "arrays", "they", "are", "my", "favorite"]
```

```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 string_to_array(s):\n    return [''] if not(len(s)) else s.split()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'string_to_array'
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: 5598
Devu loves to play with his dear mouse Jerry.  One day they play a game on 2 dimensional grid of dimensions n * n (n ≥ 2). Jerry is currently at coordinates (sx, sy) and wants to move to location (ex, ey) where cheese is placed by Devu. Also Devu is very cunning and has placed a bomb at location (bx, by). All these three locations are distinct. 

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

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

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

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

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

Output:
2
4

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

Example case 2. ...

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your code here\nT = int(input())\nfor i in range(T):\n (n,sx,sy,ex,ey,bx,by) = list(map(int,input().split()))\n if sx!=ex and sy!=ey:\n  a = abs(sx-ex)+abs(sy-ey)\n  print(a)\n else:\n  if sx==ex:\n   if ex==bx and (by-sy)*(ey-by)>0:\n    print(abs(sy-ey)+2)\n   else:\n    print(abs(sy-ey))\n  else:\n   if ey==by and (bx-sx)*(ex-bx)>0:\n    print(abs(sx-ex)+2)\n   else:\n    print(abs(sx-ex))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13323
The chef is trying to decode some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, one integer $K$. 

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

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$

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

-----Sample Output:-----
2
23
34
234
345
456
2345
3456
4567
5678

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

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "# cook your dish here\nfor _ in range(int(input())):\n    k = int(input())\n    x = 2\n    for i in range(k):\n        for j in range(k):\n            print(x+j, end = '')\n        x = x + 1\n        print()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12953
Raj loves to listen to songs in his free time. It’s his birthday tomorrow and his friend Neelansh wants his gift to be the most unique. Being great at making music, he decides to produce a song for him. However, Raj likes songs according to their beauty. He determines the beauty of the song as the number of times all the octave musical tones are completed in ascending order.

He begins with a jumbled tone of length N and numbers each octave tone as 1,2,3….8.

Neelansh wants to maximize the beauty of the song but since he uses the trial version of the software,
- He cannot change the size of N.
- He cannot introduce any new tone, but can choose any two tones and swap their positions

However, Neelansh just received a mail that he needs to submit all his pending assignments by tomorrow. He has tons of assignments left to do, but he doesn’t want to spoil the idea of his gift. Can you help him? 

-----INPUT-----
- The first line contains a single integer T- the number of test cases  
- The first line of each test case contains a single integer N- the length of the song  
- The second line contains N- space separated integers ai,  ai+1,.....aN 

-----OUTPUT-----
For each test case, print a single line containing one integer- the maximum possible beauty of the song  

-----CONSTRAINTS-----
1<=T<=102
1<=N<=105
1<=a<=8

-----EXAMPLE INPUT-----
2

8

1 2 3 4 5 6 7 8

16

1 2 1 2 3 3 4 4 5 5 6 6 7 8 7 8

-----EXAMPLE OUTPUT-----
1

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())):\r\n\tn = int(input())\r\n\tarr = [int(x) for x in input().split()]\r\n\tres = [0]*8\r\n\tfor i in range(8):\r\n\t\tres[i] = arr.count(i+1)\r\n\tprint(min(res))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13033
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 = 'def main():\n    from math import factorial as f\n    n, res = 0, 1\n    for _ in range(int(input())):\n        m = int(input())\n        res = res * f(n + m - 1) // f(n) // f(m - 1) % 1000000007\n        n += m\n    print(res)\n\n\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13745
Given an array of integers as strings and numbers, return the sum of the array values as if all were numbers.

Return your answer as a number.

```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 sum_mix(arr):\n    b = []\n    for i in arr:\n         b.append(int(i))\n    return sum(b)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sum_mix'
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: 5374
When provided with a number between 0-9, return it in words.

Input :: 1

Output :: "One".

If your language supports it, try using a switch statement.

```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 switch_it_up(number):\n    return 'Zero One Two Three Four Five Six Seven Eight Nine'.split()[number]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'switch_it_up'
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: 5396
The Gray code (see wikipedia for more details) is a well-known concept.
One of its important properties is that every two adjacent numbers have exactly one different digit in their binary representation.

In this problem, we will give you n non-negative integers in a sequence A[1..n] (0<=A[i]<2^64), such that every two adjacent integers have exactly one different digit in their binary representation, similar to the Gray code.

Your task is to check whether there exist 4 numbers A[i1], A[i2], A[i3], A[i4] (1 <= i1 < i2 < i3 < i4 <= n) out of the given n numbers such that A[i1] xor A[i2] xor A[i3] xor A[i4] = 0. Here xor is a bitwise operation which is same as ^ in C, C++, Java and xor in Pascal.

-----Input-----
First line contains one integer n (4<=n<=100000).
Second line contains n space seperated non-negative integers denoting the sequence A.

-----Output-----
Output “Yes” (quotes exclusive) if there exist four distinct indices i1, i2, i3, i4 such that A[i1] xor A[i2] xor A[i3] xor A[i4] = 0. Otherwise, output "No" (quotes exclusive) please.

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

5
1 0 2 3 7

Output:

Yes

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'n = int(input())\ns = input()\ns = s.split()\nd = {}\nflag = "No"\n\ntwo,four = 0,0\nfor i in s:\n if i in d:\n  d[i] += 1;\n  if d[i] == 2:\n   two += 1\n  elif d[i] == 4:\n   four += 1\n else:\n  d[i] = 1;\nd = {}\nif two>1 or four>0:\n flag = "Yes"\nelse:\n \n for i in range(n-1):\n  ex = int(s[i]) ^ int(s[i+1])\n  if ex in d:\n   d[ex].append(i)\n   if d[ex][-1] - d[ex][0] > 1:\n    flag = "Yes"\n    break;  \n  else:\n   d[ex] = [i]\nprint(flag)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13295
The code provided is supposed replace all the dots `.` in the specified String `str` with dashes `-`

But it's not working properly.

# Task

Fix the bug so we can all go home early.

# Notes

String `str` will never be null.

```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 = 'import re\ndef replace_dots(e):\n    return e.replace(".", "-")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'replace_dots'
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: 5306
Leha like all kinds of strange things. Recently he liked the function F(n, k). Consider all possible k-element subsets of the set [1, 2, ..., n]. For subset find minimal element in it. F(n, k) — mathematical expectation of the minimal element among all k-element subsets.

But only function does not interest him. He wants to do interesting things with it. Mom brought him two arrays A and B, each consists of m integers. For all i, j such that 1 ≤ i, j ≤ m the condition A_{i} ≥ B_{j} holds. Help Leha rearrange the numbers in the array A so that the sum $\sum_{i = 1}^{m} F(A_{i}^{\prime}, B_{i})$ is maximally possible, where A' is already rearranged array.


-----Input-----

First line of input data contains single integer m (1 ≤ m ≤ 2·10^5) — length of arrays A and B.

Next line contains m integers a_1, a_2, ..., a_{m} (1 ≤ a_{i} ≤ 10^9) — array A.

Next line contains m integers b_1, b_2, ..., b_{m} (1 ≤ b_{i} ≤ 10^9) — array B.


-----Output-----

Output m integers a'_1, a'_2, ..., a'_{m} — array A' which is permutation of the array A.


-----Examples-----
Input
5
7 3 5 3 4
2 1 3 2 3

Output
4 7 3 5 3

Input
7
4 6 5 8 8 2 6
2 1 2 2 1 1 2

Output
2 6 4 5 8 8 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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'n = int(input())\na = list(map(int,input().split()))\nb = list(map(int,input().split()))\np =[]\nfor i in range(n):\n    p.append((b[i],i+1));\n#print(p)\np.sort()\n#print(p)\na.sort()\n#print(a)\na.reverse()\n#print(a)\nc = [0]*(n+1)\nfor i in range(n):\n    #print(p[i][1],a[i])\n    c[p[i][1]]=a[i]\nfor i in range(n):\n    print(c[i+1],end=" ")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13337
Your task is to remove all duplicate words from a string, leaving only single (first) words entries.

Example:

Input:

'alpha beta beta gamma gamma gamma delta alpha beta beta gamma gamma gamma delta'

Output:

'alpha beta gamma delta'

```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 remove_duplicate_words(s):\n    return ' '.join(dict.fromkeys(s.split()))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'remove_duplicate_words'
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: 6020