akhauriyash/Code-Regression huggingface dataset:
Chef and Roma are playing a game. Rules of the game are quite simple.
Initially there are N piles of stones on the table.
In each turn, a player can choose one pile and remove it from the table.
Each player want to maximize the total number of stones removed by him.
Chef takes the first turn. 

Please tell Chef the maximum number of stones he can remove assuming that both players play optimally.

-----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 a single integer N denoting the number of piles.
The second line contains N space separated integers A1, A2, ..., AN denoting the number of stones in each pile.

-----Output-----
For each test case, output a single line containg the maximum number of stones that Chef can remove.

-----Constraints-----
- 1 ≤ Ai ≤ 109
- Subtask 1 (35 points): T = 10, 1 ≤ N ≤ 1000
- Subtask 2 (65 points): T = 10, 1 ≤ N ≤ 105 

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

Output:
4
3

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't = int(input())\nwhile t > 0:\n n = int(input())\n li = [int(x) for x in input().split()]\n li.sort(reverse=True)\n c = 0\n for i in range(n):\n  if i % 2 == 0:\n   c += li[i]\n print(c)\n t = t - 1\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13035
You are given a sequence a consisting of n integers. Find the maximum possible value of $a_{i} \operatorname{mod} a_{j}$ (integer remainder of a_{i} divided by a_{j}), where 1 ≤ i, j ≤ n and a_{i} ≥ a_{j}.


-----Input-----

The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·10^5). 

The second line contains n space-separated integers a_{i} (1 ≤ a_{i} ≤ 10^6).


-----Output-----

Print the answer to the problem.


-----Examples-----
Input
3
3 4 5

Output
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 = 'def main():\n    input()\n    #aa = sorted(set(map(int, input().split())))\n    aa = sorted(map(int, set(input().split())))\n    x = []\n    b = res = 0\n    for a in aa:\n        if b != a:\n            for _ in range(b, a):\n                x.append(b)\n            b = a\n    x.append(b)\n    maxa = aa.pop()\n    for a in reversed(aa):\n        if a < res:\n            break\n        for b in range(2 * a - 1, maxa + 2 * a, a):\n            res = max(res, x[min(b, maxa)] % a)\n    print(res)\n\n\ndef __starting_point():\n    main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14097
Chef made $N$ pieces of cakes, numbered them $1$ through $N$ and arranged them in a row in this order. There are $K$ possible types of flavours (numbered $1$ through $K$); for each valid $i$, the $i$-th piece of cake has a flavour $A_i$.
Chef wants to select a contiguous subsegment of the pieces of cake such that there is at least one flavour which does not occur in that subsegment. Find the maximum possible length of such a subsegment of cakes.

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

-----Output-----
For each test case, print a single line containing one integer ― the maximum length of a valid subsegment.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- $2 \le K \le 10^5$
- $1 \le A_i \le K$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points):
- $N \le 10^3$
- $K = 2$
- the sum of $N$ over all test cases does not exceed $10^4$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
6 2
1 1 1 2 2 1
5 3
1 1 2 2 1

-----Example Output-----
3
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 = '#\n\nfor _ in range(int(input())):\n n,k = list(map(int,input().split()))\n arr = list(map(int,input().split()))\n m=-1\n for i in range(n):\n  flag=0\n  count=1 \n  s=set()\n  s.add(arr[i])\n  for j in range(i+1,n):\n   if arr[j] not in s:\n    if len(s)==k-1:\n     flag=1\n    else:\n     s.add(arr[j])\n     count+=1 \n   else:\n    count+=1\n   if flag==1:\n    break\n  if count>m:\n   m=count\n print(m)\n    \n    \n    \n   \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13341
Write a function which takes a number and returns the corresponding ASCII char for that value.

Example: 

~~~if-not:java,racket
```
get_char(65) # => 'A'
```
~~~
~~~if:java
~~~
~~~if:racket
~~~

For ASCII table, you can refer to http://www.asciitable.com/

```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 get_char(num_of_char):\n  return chr(num_of_char)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'get_char'
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: 5292
Implement a function, `multiples(m, n)`, which returns an array of the first `m` multiples of the real number `n`. Assume that `m` is a positive integer.

Ex.
```
multiples(3, 5.0)
```
should return
```
[5.0, 10.0, 15.0]
```

```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 = 'def multiples(m, n):\n    return [n*h for h in (range(1,m+1))]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'multiples'
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: 5440
Very simple, given a number, find its opposite.

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

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

```python

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

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

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def opposite(n):\n    e = n - (n + n)\n    return e'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

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

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

```

Measured memory_bytes: 5282
Chef was bored staying at home in the lockdown. He wanted to go out for a change. Chef and Chefu are fond of eating Cakes,so they decided to go the Cake shop where cakes of all possible price are available .
They decided to purchase cakes of equal price and each of them will pay for their cakes. Chef only has coins of denomination $N$ whereas Chefu has that of denomination $M$.
So they want your help to find out the minimum amount to be spent in order to purchase the cakes.

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

-----Output:-----
For each testcase, output in a single line answer the minimum amount to be spent in order to purchase the cake.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq N,M \leq 10^7$

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

-----Sample Output:-----
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 = 'import math\nfor _ in range(int(input())):\n    n,m=list(map(int,input().split()))\n    val1=n*m\n    val2=math.gcd(n,m)\n    print(val1//val2)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12981
Once, a genius guy Cristo visited NASA where he met many scientists. A young intern Mark at NASA asked Cristo to observe the strange behaviour of two

independent particles (say Alpha and Beta) moving in the free space.Cristo was astonished to see the movement of Alpha and Beta. However, he formulated a procedure

to evaluate the distance covered by the particles in given time.
The procedure calculates the distance covered by Alpha and Beta for a given time. Mark, however struggles

to evaluate the procedure manually and asks you to help him. 
Cristo's Procedure :- 
alpha = 0
beta = 0
Procedure CristoSutra( Ti ) :
if Ti <= 0 :
alpha = alpha + 1 
else if Ti == 1 :
	beta = beta + 1
else :
CristoSutra(Ti-1)
	         CristoSutra(Ti-2)
	         CristoSutra(Ti-3)
end procedure
Note: Print the answer by taking mod from 109+7 .

-----Constraints:-----
- 1<=T<=105
- 1<=Ti<=105

-----Input Format:-----
First line consists an integer t, number of Test cases.For each test case, there is an integer denoting time Ti.

-----Output Format:-----
For each test case, a single output line contains two space seperated numbers ,distance covered by alpha and beta in the given time.

-----Subtasks:-----
Subtask 1 (30 points)
- 1<=T<=10
- 1<=Ti<=1000
Subtask 2 (70 points)
original contraints
Sample Input:
2
1
2
Sample Output:
0 1
2 1

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'lim=100007\nz=(10**9+7)\na=[0]*lim\na[2]=1\nfor i in range(3,lim):\n a[i]=a[i-1]+a[i-2]+a[i-3]\nb=[0]*lim\nb[1]=1\nb[0]=1\nfor i in range(3,lim):\n b[i]=b[i-1]+b[i-2]+b[i-3]\n \nfor _ in range(0,int(input())):\n inp=int(input())\n print(b[inp+1]%z,a[inp+1]%z)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 1179898186
Rahul is a serial killer. Rahul has been betrayed by his lover in the past and now he want to eliminate entire Universe.He has already Eliminated majority of the population and now only a handful number of people are left. Like other Serial killers, he has an interesting pattern of killing people. 
He either kill one individual at a time or if he find two individuals of different heights,he eliminates both of them simultaneously. Now Rahul wants to eliminate them as quickly as he can.
So given $N$ as the number of people left and an array containing height of those $N$ people,tell the minimum number of kills Rahul require to eliminate the entire universe.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each test case constitutes of Two lines. 
- First line contains $N$, representing the number of people left in the universe
- The second line contains an array $a[i]$ of size $N$ containing heights of those $N$ people.

-----Output:-----
For each testcase, you have to output a Single line Containing the minimum number of kills required by Rahul to eliminate the Universe.

-----Constraints-----
- $1 \leq T \leq 50000$
- $1 \leq N \leq 50000$
- $100 \leq a[i] \leq 10^5$

-----Sample Input:-----
1
10
178 184 178 177 171 173 171 183 171 175

-----Sample Output:-----
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 = '#dt = {} for i in x: dt[i] = dt.get(i,0)+1\r\nimport sys;input = sys.stdin.readline\r\ninp,ip = lambda :int(input()),lambda :[int(w) for w in input().split()]\r\n\r\nfor _ in range(inp()):\r\n    n = inp()\r\n    x = ip()\r\n    dt = {} \r\n    for i in x: dt[i] = dt.get(i,0)+1\r\n    ans = max(max(dt.values()),(n-1)//2+1)\r\n    print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13649
You are given an array with $N$ integers: $A[1], A[2], \ldots, A[N]$ (where $N$ is even). You are allowed to permute the elements however you want. Say, after permuting the elements, you end up with the array $A'[1], A'[2], \ldots, A'[N]$. Your goal is to maximize the following sum:
|A′[1]−A′[2]| + |A′[3]−A′[4]| + ... + |A′[N−1]−A′[N]||A′[1]−A′[2]| + |A′[3]−A′[4]| + ... + |A′[N−1]−A′[N]|
|A'[1] - A'[2]| \ + \ |A'[3] - A'[4]| \ + \ ... \ + \ |A'[N - 1] - A'[N]|

Here, $|x|$ denotes the absolute value of $x$.
You have to print the maximum sum achievable.

-----Input-----
- The first line contains $T$, the number of test cases.
- Each test case starts with an integer $N$ in the first line.
- The second line of each test case contains $N$ space separated integers, denoting the values of array $A$.

-----Output-----
For each test case, output the maximum sum achievable in a new line.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le N \le 10^5$
- $N$ is even
- $|A[i]| \le 10^9$
- Sum of $N$ over all test cases $\le 2 * 10^5$

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

-----Example Output 1-----
9

-----Explanation 1-----
The original array is {$1, -3, 2, -3$}. Suppose you permute it and get the array {$2, 1, -3, -3$}. Then the corresponding sum would be $|2 - 1| \ + \ |-3 - (-3)| = 1 + 0 = 1$.
But suppose you permute it differently and get the array {$-3, 2, 1, -3$}. Then the corresponding sum would be $|-3 - 2| \ + \ |1 - (-3)| = 5 + 4 = 9$. You can check that you cannot do any better, and hence the answer is 9.

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't=int(input())\nfor i in range(t):\n n=int(input())\n a=list(map(int,input().split()))\n c=0\n a.sort()\n for i in range(0,n//2):\n  c+=abs(a[i]-a[n-1-i])\n print(c)\n \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13117
Once, a genius guy Cristo visited NASA where he met many scientists. A young intern Mark at NASA asked Cristo to observe the strange behaviour of two

independent particles (say Alpha and Beta) moving in the free space.Cristo was astonished to see the movement of Alpha and Beta. However, he formulated a procedure

to evaluate the distance covered by the particles in given time.
The procedure calculates the distance covered by Alpha and Beta for a given time. Mark, however struggles

to evaluate the procedure manually and asks you to help him. 
Cristo's Procedure :- 
alpha = 0
beta = 0
Procedure CristoSutra( Ti ) :
if Ti <= 0 :
alpha = alpha + 1 
else if Ti == 1 :
	beta = beta + 1
else :
CristoSutra(Ti-1)
	         CristoSutra(Ti-2)
	         CristoSutra(Ti-3)
end procedure
Note: Print the answer by taking mod from 109+7 .

-----Constraints:-----
- 1<=T<=105
- 1<=Ti<=105

-----Input Format:-----
First line consists an integer t, number of Test cases.For each test case, there is an integer denoting time Ti.

-----Output Format:-----
For each test case, a single output line contains two space seperated numbers ,distance covered by alpha and beta in the given time.

-----Subtasks:-----
Subtask 1 (30 points)
- 1<=T<=10
- 1<=Ti<=1000
Subtask 2 (70 points)
original contraints
Sample Input:
2
1
2
Sample Output:
0 1
2 1

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'MOD = 10**9+7\nlst = [(1,0),(0,1),(2,1),(3,2)]\nfor t in range(int(input())):\n n = int(input())\n l = len(lst)\n while (n >= l):\n  a = (lst[-1][0]+lst[-2][0]+lst[-3][0])%MOD\n  b = (lst[-1][1]+lst[-2][1]+lst[-3][1])%MOD\n  lst.append((a,b))\n  l+=1\n print(lst[n][0],lst[n][1])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13285
Return the Nth Even Number

The input will not be 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 = 'def nth_even(n):\n    a = range(0,10000000000)\n    return a[n*2-2]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

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

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

```

Measured memory_bytes: 5322
Given an array $A$ of size $N$ , count number of pairs of index $i,j$ such that $A_i$ is even, $A_j$ is odd and $i < j$

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases.   
- The first line of each test case contains integer $N$.    
- The second line of each test case contains $N$ space separated integers $A_i$. 

-----Output-----
For each test case, print a single line containing an integer denoting number of pairs.

-----Constraints-----
- $1 \le T \le 100$
- $2 \le N \le 10^5$ 
- $1 \le A_i \le 10^9$
- Sum of $N$ over all test cases doesn't exceed $10^6 $ 

-----Subtasks-----
Subtask #1 (30 points):
- $2 \le N \le 100$ 
Subtask #2 (70 points): original constraints

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

-----Example Output-----
2
3

-----Explanation-----
Example case 1:$(A_2,A_3)$ and $(A_2,A_4)$ . 
Example case 2:$(A_2,A_3)$ , $(A_2,A_5)$ and $(A_4,A_5)$  .

```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 = '# cook your dish here\nt=int(input())\nfor i in range(t):\n n=int(input())\n a=list(map(int,input().split()))\n c=0\n odd=0\n for k in range(n-2,-1,-1):\n  if a[k+1]%2!=0:\n   odd+=1\n  if a[k]%2==0:\n   c+=odd\n print(c)\n  \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13091
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:-----
0
01
10
010
101
010
0101
1010
0101
1010

-----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\n\n# cook your dish here\nt = int(input())\n\nwhile t:\n    n = int(input())\n\n\n    for i in range(1, n + 1):\n        for j in range(1, n + 1):\n            if i % 2 == 1:\n                if j % 2 == 1:\n                    print(0, end='')\n                else:\n                    print(1, end='')\n            else:\n                if j % 2 == 1:\n                    print(1, end='')\n                else:\n                    print(0, end='')\n            \n        print()\n        \n    t -= 1"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13077
Given a string consisting of only lowercase English alphabets, your task is to find the smallest palindromic substring.
In case there are multiple palindromic substrings of the same length present, print the lexicographically smallest substring. 
Formally, a substring is a contiguous sequence of characters within a string. So in a string "abcdef", "abc" is a substring whereas "adf" is not a substring.
A palindrome is a word, phrase, or sequence that reads the same backwards as forwards, e.g. madam or mom.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains of two lines of input, two integers.
- First, we have a single integer $N$ which signifies the length of the substring.
- Next, we have a string of length $N$ that only has lowercase English alphabets.

-----Output:-----
For each testcase, output in a single line the shortest palindromic substring.

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq N \leq 10^5$

-----Sample Input:-----
2
2
zy
1
cd

-----Sample Output:-----
y
c

-----EXPLANATION:-----
There are only two possibilities. "z" and "y". Since both of them have the same length. We print the lexicographically smaller substring which is y.

```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 = map(int,input().strip().split(" ")) takes two number as input in a \xa0\xa0\xa0\xa0single line\n# arr = list(map(int,input().split())) takes an array as a input in a single \xa0\xa0\xa0\xa0line\n# arr = [int(input()) for i in range(n)] takes an array as input in different \xa0\xa0\xa0\xa0lines\n\ndef solve() :\n n = int(input())\n sr = input()\n print(min(sr))\n \nt = int(input())\nwhile t>0 :\n solve()\n t -= 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12961
A beautiful sequence is defined as a sequence that do not have any repeating elements in it.
You will be given any random sequence of integers, and you have to tell whether it is a beautiful sequence or not. 

-----Input:-----
- The first line of the input contains a single integer $T$. $T$ denoting the number of test cases. The description of $T$ test cases is as follows.
- The next line of the input contains a single integer $N$. $N$ denotes the total number of elements in the sequence.
- The next line of the input contains $N$ space-separated integers $A1, A2, A3...An$ denoting the sequence.

-----Output:-----
- Print "prekrasnyy"(without quotes) if the given sequence is a beautiful sequence, else print "ne krasivo"(without quotes)
Note: each test case output must be printed on new line

-----Constraints:-----
- $1 \leq T \leq 10^2$
- $1 \leq N \leq 10^3$
- $1 \leq A1, A2, A3...An \leq 10^5$

-----Sample Input:-----
2
4
1 2 3 4
6
1 2 3 5 1 4

-----Sample Output:-----
prekrasnyy
ne krasivo

-----Explanation:-----
- 
As 1st sequence do not have any elements repeating, hence it is a beautiful sequence
- 
As in 2nd sequence the element 1 is repeated twice, hence it is not a beautiful sequence

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nt=int(input())\nfor _ in range(t):\n    n=int(input())\n    l=list(map(int,input().split()))\n    s=set(l)\n    if(len(l)==len(s)):\n        print("prekrasnyy")\n    else:\n        print("ne krasivo")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13053