akhauriyash/Code-Regression huggingface dataset:
You are given an array $A$ of $N$ positive and pairwise distinct integers. 
You can permute the elements in any way you want. 
The cost of an ordering $(A_1, A_2, \ldots, A_N)$ is defined as $ (((A_1 \bmod A_2) \bmod A_3)......) \bmod A_N$ where $X \bmod Y$ means the remainder when $X$ is divided by $Y$. 
You need to find the maximum cost which can be attained through any possible ordering of the elements.

-----Input:-----
- The first line contains $T$ denoting the number of test cases.
- The first line of each testcase contains a single integer $N$. 
- The second line of each testcase contains $N$ space-separated integers, the elements of $A$. 

-----Output:-----
- For each testcase, output the maximum possible cost in a new line. 

-----Constraints-----
- $1 \leq T \leq 5*10^5$
- $2 \leq N \leq 5*10^5$
- $1 \leq A_i  \leq 10^9$
- Sum of $N$ over all testcases is less than or equal to $10^6$
- All elements in a single testcase are distinct.

-----Subtasks-----
- 100 points : Original constraints.

-----Sample Input:-----
1
2
7 12

-----Sample Output:-----
7

-----Explanation:-----
The two possible ways to order the elements are [7, 12] and [12, 7]. In the first case, the cost is $7 \bmod 12 = 7$ and in the second case the cost is $12 \bmod 7 = 5$. Clearly the answer is 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 = 'for i in range(int(input())):\n n=int(input())\n a=list(map(int,input().split()))\n a.sort()\n print(max(a[0]%a[n-1],a[n-1]%a[0]))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13095
There is an integer sequence of length 2^N: A_0, A_1, ..., A_{2^N-1}. (Note that the sequence is 0-indexed.)
For every integer K satisfying 1 \leq K \leq 2^N-1, solve the following problem:
 - Let i and j be integers. Find the maximum value of A_i + A_j where 0 \leq i < j \leq 2^N-1 and (i or j) \leq K.
Here, or denotes the bitwise OR.

-----Constraints-----
 - 1 \leq N \leq 18
 - 1 \leq A_i \leq 10^9
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_0 A_1 ... A_{2^N-1}

-----Output-----
Print 2^N-1 lines.
In the i-th line, print the answer of the problem above for K=i.

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

-----Sample Output-----
3
4
5

For K=1, the only possible pair of i and j is (i,j)=(0,1), so the answer is A_0+A_1=1+2=3.
For K=2, the possible pairs of i and j are (i,j)=(0,1),(0,2).
When (i,j)=(0,2), A_i+A_j=1+3=4. This is the maximum value, so the answer is 4.
For K=3, the possible pairs of i and j are (i,j)=(0,1),(0,2),(0,3),(1,2),(1,3),(2,3) .
When (i,j)=(1,2), A_i+A_j=2+3=5. This is the maximum value, so the answer is 5.

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\n\nn = int(input())\nalst = list(map(int, input().split()))\nmax_ = 0\ndp = [[a, 0] for a in alst]\n\nfor i in range(n):\n    for s in range(1 << n):\n        if (s >> i) & 1:\n            lst = dp[s] + dp[s - (1 << i)]\n            lst.sort(reverse = True)\n            dp[s] = lst[:2].copy()\n\nfor a, b in dp[1:]:\n    max_ = max(max_, a + b)\n    print(max_)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13309
Chef is interested to solve series problems. Chef wants to solve a series problem but he can't 
solve it till now.Can you help Chef to solve the series problem?
- In series problem, the series goes as follows 1,9,31,73,141 . . . . . . . . 
Your task is to find the Nth term of series. For larger value of $N$ answer becomes very large, So your output should be performed $N$th term modulo 1000000007 ($10^9+7$ ).

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

-----Output:-----
For each testcase,  output in a single line answer i.e. The $N$th term of series modulo 1000000007.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^9$

-----Sample Input:-----
2

8

10

-----Sample Output:-----
561

1081

```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\ntry:\n for _ in range(int(input())):\n  n=int(input())\n  r=n**3+(n-1)**2\n  print(r%1000000007)\nexcept:pass \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12897
Our chef has been assigned a task to make a necklace of length N, from gold, diamond and platinum.There is single kind of gold, two types of diamond and three types of platinum available.
A necklace can be represented as strings of the form (G)∗(D1|D2)∗(P1|P2|P3)∗$ (G)*(D1|D2)*(P1|P2|P3)* $ where (x|y) means we can use x or y and ∗$ * $ means we can repeat the previous parenthesized expression 0 or more times.
Instead of making necklace he choose to count all such distinct necklaces possible for a given length N.

-----Input:-----
-The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
-Only line of every test case contains an integer N$N$ denoting the length of the necklace required.

-----Output:-----
For each test case, print the number of all such distinct necklaces, with given length. As the number can be really large, print it modulo  109+7$10^{9}+7$.

-----Constraints-----
- 1≤T≤10000$1 \leq T \leq 10000$
- 2≤N≤1000000000$2 \leq N \leq 1000000000$
- String S$S$ consists of only upper case english alphabets.

-----Subtasks-----
- 20 points : 1≤N≤5$1 \leq N \leq 5$
- 70 points : Original$Original$ Constraints$Constraints$

-----Sample Input:-----
2
1
2

-----Sample Output:-----
6
25

```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 = 'MOD = int(1e9 + 7)\r\nfor _ in range(int(input())):\r\n    n = int(input()) + 1\r\n    res = (((3*pow(3, n, MOD) - 3) % MOD) * 500000004)% MOD\r\n    res = (res - (2*(pow(2, n, MOD) - 1)) % MOD) % MOD\r\n    print(res)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13033
You get an array of numbers, return the sum of all of the positives ones.

Example `[1,-4,7,12]` => `1 + 7 + 12 = 20`

Note: if there is nothing to sum, the sum is default to `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

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 = 'from functools import reduce\ndef positive_sum(arr):\n    return reduce(lambda x,y: x+max(0,y), arr, 0)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'positive_sum'
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: 5458
# Grasshopper - Function syntax debugging

A student was working on a function and made some syntax mistakes while coding. Help them find their mistakes and fix them.

```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 = 'main=lambda v,b:v+b'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'main'
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: 5330
=====Problem Statement=====
Given the participants' score sheet for your University Sports Day, you are required to find the runner-up score. You are given n scores. Store them in a list and find the score of the runner-up.

=====Input Format=====
The first line contains n. The second line contains an array A[] of n integers each separated by a space.

=====Constraints=====
2≤n≤10
-100≤A[i]≤ 100

=====Output Format=====
Print the runner-up score.

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def __starting_point():\n    n = int(input())\n    arr = list(map(int, input().split()))\n    first = max(arr)\n    \n    print((max(list([a for a in arr if a != first]))))\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13459
"QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth.

Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu 

Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact.


-----Input-----

The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.


-----Output-----

Print a single integer — the number of subsequences "QAQ" in the string.


-----Examples-----
Input
QAQAQYSYIOIWIN

Output
4

Input
QAQQQZZYNOIWIN

Output
3



-----Note-----

In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN".

```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 = "# IAWT\ns = input()\nans = 0\nfor i in range(len(s)):\n    for j in range(i+1, len(s)):\n        for k in range(j+1, len(s)):\n            if s[i] == 'Q' and s[j] == 'A' and s[k] == 'Q':\n                ans += 1\n\nprint(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13021
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 = '# python3\ndef solve():\n    for __ in range(int(input())):\n        p, q, b = tuple(map(int, input().split()))\n        yield "Infinite" if p * pow(b, 63, q) % q else "Finite"\n\n\nprint("\\n".join(solve()))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13935
The chef is having one string of English lower case alphabets only. The chef wants to remove all "abc" special pairs where a,b,c are occurring consecutively. After removing the pair, create a new string and again remove "abc" special pair from a newly formed string. Repeate the process until no such pair remains in a string.

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

-----Output:-----
For each testcase, output in a single line answer, new String with no "abc" special pair.

-----Constraints:-----
$T \leq 2 $
$1 \leq String length \leq 1000 $

-----Sample Input:-----
2
aabcc
bababccc

-----Sample Output:-----
ac
bc

-----EXPLANATION:-----
For 1) after removing "abc" at middle we get a new string as ac.
For 2) string = bababccc
newString1 = babcc  // After removing middle "abc"
newString2 = bc   //After removing "abc"

```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    string=str(input())\n    target="abc"\n    while(target in string):\n        start=string.find(target)\n        string=string[:start]+string[start+3:]\n\n    print(string)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12955
"I don't have any fancy quotes." - vijju123
Chef was reading some quotes by great people. Now, he is interested in classifying all the fancy quotes he knows. He thinks that all fancy quotes which contain the word "not" are Real Fancy; quotes that do not contain it are regularly fancy.
You are given some quotes. For each quote, you need to tell Chef if it is Real Fancy or just regularly fancy.

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

-----Output-----
For each test case, print a single line containing the string "Real Fancy" or "regularly fancy" (without quotes).

-----Constraints-----
- $1 \le T \le 50$
- $1 \le |S| \le 100$
- each character of $S$ is either a lowercase English letter or a space

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

-----Example Input-----
2
i do not have any fancy quotes
when nothing goes right go left

-----Example Output-----
Real Fancy
regularly fancy

-----Explanation-----
Example case 1: "i do not have any fancy quotes"
Example case 2: The word "not" does not appear in the given quote.

```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())\nwhile n>0:\n s1=list(input().split())\n flag=0\n for i in range(0,len(s1)):\n  if str(s1[i])=="not":\n   #print(s1[i])\n   flag=1\n if flag==1:\n  print("Real Fancy")\n else:\n  print("regularly fancy")\n n=n-1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13029
Chang's new maths teacher is very enthusiastic about making sure that students understand the concept rather than remembering it. On her first day at teaching, she gives an assignment to all the students to test their potential. Chang wants to demonstrate that he understands the concept rather than rote learning. Help Chang in doing this by solving the hardest problem in the assignment. The problem is written as follows. 

A perfect function is defined in the following manner.

- F(x, y) = x2 + y for 1 ≤ x ≤ A, 1 ≤ y ≤ B
- F(x, y) = 2 otherwise

Find the number of integral pairs (x, y) such that F(x, y) is a perfect square.

-----Input-----
First and the only line of the input contains two single space separated integers A and B.

-----Output-----
Output a single integer indicating the output to the only test case.

-----Constraints-----
- 1 ≤ A, B ≤ 106

-----Example-----
Input:
4 4

Output:
1

-----Explanation-----
Example case 1.
(1, 3) is the only pair such that x = 1, y = 3 satisfying x <= 4 and y <= 4. 1^2 + 3 = 4 which is a perfect square.

```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\n\np=[int(i) for i in input().split()]\n\ncount=0\nfor i in range(1,p[0]+1):\n for j in range(1,p[1]+1):\n  k=i*i+j\n  k1=int(math.sqrt(k))\n  if k1*k1==k:\n   count+=1\nprint(count)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13183
You are given two positive integers N and K. How many multisets of rational numbers satisfy all of the following conditions?
 - The multiset has exactly N elements and the sum of them is equal to K.
 - Each element of the multiset is one of 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots. In other words, each element can be represented as \frac{1}{2^i}\ (i = 0,1,\dots).
The answer may be large, so print it modulo 998244353.

-----Constraints-----
 - 1 \leq K \leq N \leq 3000
 - All values in input are integers.

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

-----Output-----
Print the number of multisets of rational numbers that satisfy all of the given conditions modulo 998244353.

-----Sample Input-----
4 2

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

The following two multisets satisfy all of the given conditions:
 - {1, \frac{1}{2}, \frac{1}{4}, \frac{1}{4}}
 - {\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{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 = 'import sys\n\nsys.setrecursionlimit(10**7)\ndef I(): return int(sys.stdin.readline().rstrip())\ndef MI(): return list(map(int,sys.stdin.readline().rstrip().split()))\ndef LI(): return list(map(int,sys.stdin.readline().rstrip().split()))\ndef LI2(): return list(map(int,sys.stdin.readline().rstrip()))\ndef S(): return sys.stdin.readline().rstrip()\ndef LS(): return list(sys.stdin.readline().rstrip().split())\ndef LS2(): return list(sys.stdin.readline().rstrip())\n\n\nN,K = MI()\nmod = 998244353\n\ndp = [[0]*(N+1) for _ in range(N+1)]\ndp[0][0] = 1\nfor i in range(1,N+1):\n    for j in range(N,0,-1):\n        dp[i][j] = dp[i-1][j-1]\n        if 2*j <= N:\n            dp[i][j] += dp[i][2*j]\n            dp[i][j] %= mod\nprint((dp[-1][K]))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14755
Chef and his friends are playing the game AMONG US. They all have chosen their names as numbers. There are N people in Chef’s group including him, and each swears that he is not the imposter. However, it turns out there were N+1 people in the game. Now all that Chef needs to know is the name of the imposter, which is a number. Also remember that numbers can be duplicate. Can you help out Chef in finding the imposter?
Input : 
First line contains the value of N. Second line contains the N numbers that Chef’s friends used as their names. Third line contains the N+1 numbers that people in the game have used as their names.
Output : 
Print the extra number in new line.
Constraints : 
1 ≤ Numbers used as names ≤ 1,000
1 ≤ N ≤ 1,000,000
Sample Input : 
3
4 2 5
4 2 3 5
Sample Output : 
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 = '# cook your dish here\ndef gcd(x, y):\n    while y:\n        x, y = y, x % y\n    return x\n\ndef lcm(x, y):\n    return (x*y)//(gcd(x,y))\n\ndef isPrime(n) : \n    if (n <= 1) : \n        return False\n    if (n <= 3) : \n        return True\n    if (n % 2 == 0 or n % 3 == 0) : \n        return False\n    i = 5\n    while(i * i <= n) : \n        if (n % i == 0 or n % (i + 2) == 0) : \n            return False\n        i = i + 6\n    return True\n\nabc="abcdefghijklmnopqrstuvwxyz"\n\npi=3.141592653589793238\n\n\n\n\n\nn = int(input())\narr1 = list(map(int,input().split()))\narr2 = list(map(int,input().split()))\n\narr1.sort()\narr2.sort()\nx = False\nfor i in range(n):\n    if(arr1[i]!=arr2[i]):\n        print(arr2[i])\n        x = True\n        break\n\n\n\nif(not x):\n    print(arr2[-1])\n\n\n\n\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13671
In this problem the input will consist of a number of lines of English text consisting of the letters of the English alphabet, the punctuation marks ' (apostrophe), . (full stop), , (comma), ; (semicolon), :(colon) and white space characters (blank, newline).
Your task is print the words in the text in lexicographic order (that is, dictionary order). Each word should appear exactly once in your list. You can ignore the case (for instance, "The" and "the" are to be treated as the same word). There should be no uppercase letters in the output.
For example, consider the following candidate for the input text: 
This is a sample piece of text to illustrate this 
problem.

The corresponding output would read as:
a
illustrate
is
of
piece
problem
sample
text
this
to

-----Input format-----
- The first line of input contains a single integer $N$, indicating the number of lines in the input.
- This is followed by $N$ lines of input text.

-----Output format-----
- The first line of output contains a single integer $M$ indicating the number of distinct words in the given text. 
- The next $M$ lines list out these words in lexicographic order.

-----Constraints-----
- $1 \leq N \leq 10000$
- There are at most 80 characters in each line.
- There are at the most 1000 distinct words in the given text.

-----Sample Input-----
2
This is a sample piece of text to illustrate this 
problem. 

-----Sample Output-----
10
a
illustrate
is
of
piece
problem
sample
text
this
to

```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())\ns1=\'\'\nfor _ in range(n):\n    s=input()\n    s1=s1+s\ns1=s1.lower()\ns1=s1.replace(\'.\',\'\').replace(\',\',\'\').replace("\'","").replace(\':\',\'\').replace(\';\',\'\')\na=set(s1.split())\nb=list(a)\nb.sort()\nprint(len(b))\nfor i in b:\n    print(i)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13251
Lots of geeky customers visit our chef's restaurant everyday. So, when asked to fill the feedback form, these customers represent the feedback using a binary string (i.e a string that contains only characters '0' and '1'. 

Now since chef is not that great in deciphering binary strings, he has decided the following criteria to classify the feedback as Good or Bad : 

If the string contains the substring "010" or "101", then the feedback is Good, else it is Bad. Note that, to be Good it is not necessary to have both of them as substring.

So given some binary strings, you need to output whether according to the chef, the strings are Good or Bad. 

-----Input-----
The first line contains an integer T denoting the number of feedbacks. Each of the next T lines contains a string composed of only '0'  and '1'.

-----Output-----
For every test case, print in a single line Good or Bad as per the Chef's method of classification.

-----Constraints-----
-  1 ≤  T ≤   100 
-  1  ≤  |S|   ≤  105 

Sum of length of all strings in one test file will not exceed 6*106.

-----Example-----
Input:
2
11111110
10101010101010

Output:
Bad
Good

-----Explanation-----
Example case 1.

The string doesn't contain 010 or 101 as substrings.

Example case 2.

The string contains both 010 and 101 as substrings.

```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 input_1 = str(input())\n str1 = "010"\n str2 = "101"\n \n if input_1.find(str1) == -1 and input_1.find(str2)== -1:\n  print("Bad")\n else: \n  print("Good")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12977
Chef has some numbers. His girlfriend Chefina feels good when chef gives her a particular pattern number also called as Armstrong number.
Armstrong number is a number whose sum of its all individual digit raise to the power of the number of digit in that number is equal to that number itself
eg.. 153 = 1^3 + 5^3 + 3^3 (153 is an Armstrong number)
1634 = 1^4 + 6^4 + 3^4 + 4^4 (1634 is an Armstrong number)
As a love guru of chef you have to help chef to find Armstrong numbers Among the numbers which chef has initially so that Chefina feels good

-----Input:-----
First line will contain a positive Integer $T$ which is the number of testcases
Next $T$ lines follows an Integer $N$.

-----Output:-----
For Every n You have to print "FEELS GOOD" without qoutes if it is an armstrong number otherwise Print "FEELS BAD" without quotes

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq N \leq 10^6$

-----Sample Input:-----
3
153
11
1634

-----Sample Output:-----
FEELS GOOD
FEELS BAD
FEELS GOOD

-----EXPLANATION:-----
For test case 1 --> 153 = 1^3 + 5^3 + 3^3 (153 is an armstrong 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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish her\nfor _ in range(int(input())):\n    num = int(input())\n    s = 0\n    temp = num\n    while temp > 0:\n       digit = temp % 10\n       s += digit ** len(str(num))\n       temp //= 10\n    \n    if num == s:\n       print("FEELS GOOD")\n    else:\n       print("FEELS BAD")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13001