akhauriyash/Code-Regression huggingface dataset:
You are given three non-negative integers $X$, $Y$ and $N$. Find the number of integers $Z$ such that $0 \le Z \le N$ and $(X \oplus Z) < (Y \oplus Z)$, where $\oplus$ denotes the bitwise XOR operation.

-----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 three space-separated integers $X$, $Y$ and $N$.

-----Output-----
For each test case, print a single line containing one integer ― the number of integers $Z$ which satisfy all conditions.

-----Constraints-----
- $1 \le T \le 1,000$
- $0 \le X, Y, N \le 2^{30} - 1$

-----Subtasks-----
Subtask #1 (5 points): $X, Y, N \le 2^6 - 1$
Subtask #2 (95 points): original constraints

-----Example Input-----
3
1 2 10
2 1 10
0 0 7

-----Example Output-----
6
5
0

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'for t in range(int(input())):\n x,y,n=map(int,input().split())\n n+=1\n count=0\n flag=0\n for i in range(28,-1,-1):\n  if flag==0:\n   if(x & (1<<i)) != (y & (1<<i)):\n    for k in range(28,-1,-1):\n     if (n & (1<<k)):\n      if k>i:\n       count+=(1<<(k-1))\n      elif k==i:\n       if (x & (1<<i))==0:\n        count+=(1<<k)\n      else:\n       if (x & (1<<i)) == (n & (1<<i)):\n        count+=(1<<k)\n    flag=1\n print(count)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13191
Chef has an array of N natural numbers. Cheffina challenges the chef to choose the two numbers from the array and following the condition as the area of the rectangle formed from the two numbers is maximum. Cheffina also asks the chef to choose two numbers different from the previous two to form the rectangle with a minimum area.

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

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

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

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

-----Sample Output:-----
20 2

```python

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

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

```

Measured memory_bytes: 13067
Dustin, is the head of an Intelligence agency. He wants to send a secret message S$S$ to his colleague.The message is a single word consisting of only lowercase english letters but he decides to encrypt the message for security reasons. He makes a string M$M$ of length N$N$, such that after deleting a substring of non-zero length from M$M$, the remaining string is S$S$.
Calculate the number of all such possible strings he can form.

-----Input:-----
- First line will contain T$T$, number of testcases. Then the testcases follow.
- For each testcase the there is a single line which contains an integer, N$N$ and then a string S$S$.

-----Output:-----
For each testcase, output the number of possible strings modulo 109+7$10^9+7$.

-----Constraints-----
- 1≤T≤50$1 \leq T \leq 50$
- 1≤N≤1018$1 \leq N \leq 10^{18}$
- 1≤|S|≤105$1 \leq |S| \leq 10^5$
- S$S$ can contain only lowercase English letters.

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

3 a

3 ab     

-----Sample Output:-----
1326

76

```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, s = map(str, input().split())\n    n = int(n)\n    if n <= len(s):\n     print("0")\n    else:\n     m = pow(26, n - len(s) - 1, 1000000007)\n     m = m * (26 + 25 * len(s))\n     print(m % 1000000007)\n    t = t - 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13089
The chef is trying to solve 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:-----
2
2
4

-----Sample Output:-----
2
21
210
21
2
4
43
432
4321
43210
4321
432
43
4

-----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 = 't=int(input())\r\nfor i in range(t):\r\n    n=int(input())\r\n    ans=[]\r\n    meow=\'\'\r\n    tot = n+1\r\n    for i in range(n,-1,-1):\r\n        meow+=str(i)\r\n        an=" "*(tot-len(str(meow)))+str(meow)\r\n        ans.append(an)\r\n    for j in ans:\r\n        print(j)\r\n    ans=list(reversed(ans))\r\n    ans.pop(0)\r\n    for j in ans:\r\n        print(j)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13193
There are N towns on a line running east-west.
The towns are numbered 1 through N, in order from west to east.
Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value.
The coordinate of town i is X_i.
You are now at town 1, and you want to visit all the other towns.
You have two ways to travel:
 - Walk on the line.
Your fatigue level increases by A each time you travel a distance of 1, regardless of direction.
 - Teleport to any location of your choice.
Your fatigue level increases by B, regardless of the distance covered.
Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways.

-----Constraints-----
 - All input values are integers.
 - 2≤N≤10^5
 - 1≤X_i≤10^9
 - For all i(1≤i≤N-1), X_i<X_{i+1}.
 - 1≤A≤10^9
 - 1≤B≤10^9

-----Input-----
The input is given from Standard Input in the following format:
N A B
X_1 X_2 ... X_N

-----Output-----
Print the minimum possible total increase of your fatigue level when you visit all the towns.

-----Sample Input-----
4 2 5
1 2 5 7

-----Sample Output-----
11

From town 1, walk a distance of 1 to town 2, then teleport to town 3, then walk a distance of 2 to town 4.
The total increase of your fatigue level in this case is 2×1+5+2×2=11, which is the minimum possible value.

```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, a, b = list(map(int, input().split()))\nx = list(map(int, input().split()))\n\ncnt = 0\n\nfor i in range(1, n):\n    cnt += min(a*(x[i]-x[i-1]), b)\n\nprint(cnt)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13071
John Doe started thinking about graphs. After some thought he decided that he wants to paint an undirected graph, containing exactly k cycles of length 3. 

A cycle of length 3 is an unordered group of three distinct graph vertices a, b and c, such that each pair of them is connected by a graph edge. 

John has been painting for long, but he has not been a success. Help him find such graph. Note that the number of vertices there shouldn't exceed 100, or else John will have problems painting it.


-----Input-----

A single line contains an integer k (1 ≤ k ≤ 10^5) — the number of cycles of length 3 in the required graph.


-----Output-----

In the first line print integer n (3 ≤ n ≤ 100) — the number of vertices in the found graph. In each of next n lines print n characters "0" and "1": the i-th character of the j-th line should equal "0", if vertices i and j do not have an edge between them, otherwise it should equal "1". Note that as the required graph is undirected, the i-th character of the j-th line must equal the j-th character of the i-th line. The graph shouldn't contain self-loops, so the i-th character of the i-th line must equal "0" for all i.


-----Examples-----
Input
1

Output
3
011
101
110

Input
10

Output
5
01111
10111
11011
11101
11110

```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 = 0 , int(input())\np=[['0']*100 for i in range(100)]\nwhile k:\n for i in range(n):\n  if i>k:\n   break\n  p[n][i]=p[i][n]='1'\n  k=k-i\n n+=1\nprint(n)\nfor i in range(n): print(''.join(p[i][:n]))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 92107
Write a method that takes one argument as name and then greets that name, capitalized and ends with an exclamation point.

Example:

```
"riley" --> "Hello Riley!"
"JACK"  --> "Hello Jack!"
```

```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 greet(name): \n    name=name[0].upper()+name[1:].lower()\n    name="Hello "+name+"!"\n    return name'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'greet'
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: 5453
You are given a set of n pens, each of them can be red, blue, green, orange, and violet in color. Count a minimum number of pens that should be taken out from the set so that any two neighboring pens have different colors. Pens are considered to be neighboring if there are no other pens between them.

-----Input:-----
- 
The first line contains t denoting the number of test cases.
- 
The first line of each test case will contain a single integer n.
- 
The second line of each test case will contain a string s.
(s contains only 'R', 'B', 'G', 'O', and 'V' characters denoting red, blue, green, orange, and violet respectively)

-----Output:-----
For each test case, print single line containing one integer - The minimum number of pens that need to be taken out.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq n \leq 1000$

-----Sample Input:-----
2
5
RBBRG
5
RBGOV

-----Sample Output:-----
1
0

-----EXPLANATION:-----
In first test case, two blue pens are neighboring each other, if we take out any one of them then the string will be RBRG in which each pen has different neighbors.
In second test case, no pen needs to be taken out as each pen has different neighbors.

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# cook your dish here\nfor t in range(int(input())):\n    n=int(input())\n    a=list(input())\n    count=0\n    j=1\n    for i in range(0,n-1):\n        if a[i]==a[j]:\n            j+=1 \n            count+=1\n            pass\n        else:\n            j+=1\n    print(count)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12995
Chef is now a corporate person. He has to attend office regularly. But chef does not want to go to office, rather he wants to stay home and discover different recipes and cook them. 
In the office where chef works, has two guards who count how many times a person enters into the office building. Though the duty of a guard is 24 hour in a day, but sometimes they fall asleep during their duty and could not track the entry of a person in the office building. But one better thing is that they never fall asleep at the same time. At least one of them remains awake and counts who enters into the office.
Now boss of Chef wants to calculate how many times Chef has entered into the building. He asked to the guard and they give him two integers A and B, count of first guard and second guard respectively.
Help the boss to count the minimum and maximum number of times Chef could have entered into the office building.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of the T test cases follows. 
Each test case consists of a line containing two space separated integers A and B.

-----Output-----
For each test case, output a single line containing two space separated integers, the minimum and maximum number of times Chef could have entered into the office building.

-----Constraints-----
- 1 ≤ T ≤ 100
- 0 ≤ A, B ≤ 1000000

-----Example-----
Input:
1
19 17

Output:
19 36

```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\nv=int(input())\nfor i in range (0,v):\n    s=list(map(int,input().split()))\n    print(max(s),sum(s))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12961
The chef is having one array of N natural numbers(numbers may be repeated). i.e. All natural numbers must be less than N. Chef wants to rearrange the array and try to place a natural number on its index of the array, i.e array[i]=i. If multiple natural numbers are found for given index place one natural number to its index and ignore others.i.e. arr[i]=i and multiple i found in array ignore all remaining i's If any index in the array is empty place 0 at that place. i.e. if for arr[i], i is not present do arr[i]=0.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains two lines of input.
- First-line has $N$ denoting the size of an array.
- Second-line has $N$ space-separated natural numbers.

-----Output:-----
For each test case, output in a single line with the new rearranged array.

-----Constraints-----
- $1 \leq T \leq 10^3$
- $2 \leq N \leq 10^3$
- $arr[i] \leq N-1$

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

-----Sample Output:-----
0 1
0 1 2 0

-----EXPLANATION:-----
For 1) $1$ occurs twice in the array hence print 0 at 0th index and 1 at 1st index
For 2) $1$ occurs thrice and 2 once in the array hence print 0 at 0th index and 1 at 1st index, 2 at 2nd index and 0 at 3rd index.

```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    l1=[0]*n\n    for i in range(n):\n        if(i in l):\n            l1[i]=i\n        else:\n            l1[i]=0\n    print(*l1)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13017
There are N towns on a line running east-west.
The towns are numbered 1 through N, in order from west to east.
Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value.
The coordinate of town i is X_i.
You are now at town 1, and you want to visit all the other towns.
You have two ways to travel:
 - Walk on the line.
Your fatigue level increases by A each time you travel a distance of 1, regardless of direction.
 - Teleport to any location of your choice.
Your fatigue level increases by B, regardless of the distance covered.
Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways.

-----Constraints-----
 - All input values are integers.
 - 2≤N≤10^5
 - 1≤X_i≤10^9
 - For all i(1≤i≤N-1), X_i<X_{i+1}.
 - 1≤A≤10^9
 - 1≤B≤10^9

-----Input-----
The input is given from Standard Input in the following format:
N A B
X_1 X_2 ... X_N

-----Output-----
Print the minimum possible total increase of your fatigue level when you visit all the towns.

-----Sample Input-----
4 2 5
1 2 5 7

-----Sample Output-----
11

From town 1, walk a distance of 1 to town 2, then teleport to town 3, then walk a distance of 2 to town 4.
The total increase of your fatigue level in this case is 2×1+5+2×2=11, which is the minimum possible value.

```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,A,B=map(int,input().split())\n*X,=map(int,input().split())\ni=1\nans=0\nwhile i<N:\n    ans+=min(B,A*(X[i]-X[i-1]))\n    i+=1\nprint(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13045
Divya's watch of worth Rs10 cr is abducted by N thieves(1,2....i...N). The fight over the watch leads to a final decision that it should belong to the thief who wins a simple game. The rules of the game state that every thief  registers a time in the format HH:MM:SS . Accordingly the average A of three clockwise angles  between the hours , minutes and seconds hands is calculated . Thus the ith thief  with the maximum A wins the game and gets to keep the watch.

The thieves are poor in mathematics and will need your help . Given the number of thieves and their registered time resolves the conflict and help them in choosing the winner 

-----Input-----
First line of input contains T which denotes the number of test cases.

The first line of each test case consists of an integer which denotes the number of thieves thereby N line follow which give the time choosen by each thieve in the format HH:MM:SS.

-----Output:-----
Output single integer i which denotes the ith thief.

-----Constraints:-----

1<=T<=100

1<=N<=50

01<=HH<=12

00<=MM<=60

00<=SS<=60

-----Example:-----
Input:
2
3
12:28:26
07:26:04
11:23:17
2
07:43:25
06:23:34

Output:
3
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 = 'for t in range(int(input())):\n n = int(input())\n mx = -1\n for i in range(n):\n  h, m, s = list(map(int,input().split(":")))\n  h %= 12\n  m %= 60\n  s %= 60\n  ha = h*30 + m*0.5 + s*0.5/60\n  ma = m*6 + s*0.1\n  sa = s*6\n  \n  hm1 = abs(ha - ma)\n  hm2 = 360 - hm1\n  hm3 = abs(hm1 - hm2)\n  hm = min(hm1, hm2, hm3)\n  \n  ms1 = abs(ma - sa)\n  ms2 = 360 - ms1\n  ms3 = abs(ms1 - ms2)\n  ms = min(ms1, ms2, ms3)\n  \n  sh1 = abs(sa - ha)\n  sh2 = 360 - sh1\n  sh3 = abs(sh1 - sh2)\n  sh = min(sh1, sh2, sh3)\n  \n  avg = (hm + ms + sh) / 3\n  if (mx < avg):\n   ans = i+1\n   mx = avg\n print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13447
Chef is playing a game which contains a binary string. 
He can perform one operation only:
- Toggle the i_th bit of the string (0 to 1 or 1 to 0)
By performing operations on the string (can be zero times), you have to convert the string with no adjacent bit being the same.
Can you help chef ?

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- First line of each test case, contains the size of the  string $N$
- Seond line contains a single line of input, the binary string. 

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

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq |S| \leq 10^3$

-----Sample Input:-----
1
4
1011

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

```python

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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def min_changes(a, n): \n \n # To store the inversions required \n # to make the array {1, 0, 1, 0, 1, 0, 1, ...} \n # and {0, 1, 0, 1, 0, 1, 0, ...} respectively \n ans_a = 0; \n ans_b = 0; \n \n # Find all the changes required \n for i in range(n): \n  if (i % 2 == 0): \n   if (a[i] == 0): \n    ans_a += 1; \n   else: \n    ans_b += 1; \n \n  else: \n   if (a[i] == 0): \n    ans_b += 1; \n   else: \n    ans_a += 1; \n \n # Return the required answer \n return min(ans_a, ans_b); \nfor _ in range(int(input())):\n n=int(input())\n s=input()\n s=list(s)\n s=[int(x) for x in s]\n print(min_changes(s,len(s)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13131
Chef is playing a game which contains a binary string. 
He can perform one operation only:
- Toggle the i_th bit of the string (0 to 1 or 1 to 0)
By performing operations on the string (can be zero times), you have to convert the string with no adjacent bit being the same.
Can you help chef ?

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- First line of each test case, contains the size of the  string $N$
- Seond line contains a single line of input, the binary string. 

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

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq |S| \leq 10^3$

-----Sample Input:-----
1
4
1011

-----Sample Output:-----
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 = "for i in range(int(input())):\n n=int(input())\n l=input()\n k=n//2\n p='10'*k\n q='01'*k\n x=y=0\n if n%2==0:\n  for i in range(n):\n   if l[i]!=p[i]:\n    x=x+1\n   if l[i]!=q[i]:\n    y=y+1\n  print(min(x,y))\n else:\n  p=p+'1'\n  q=q+'0'\n  for i in range(n):\n   if l[i]!=p[i]:\n    x=x+1\n   if l[i]!=q[i]:\n    y=y+1\n  print(min(x,y))\n \n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13253
Little Praneet loves experimenting with algorithms and has devised a new algorithm. The algorithm is performed on an integer as follows:
- if the rearmost digit is $0$, he will erase it.
- else, he will replace the rearmost digit $d$ with $d-1$.
If a point comes when the integer becomes $0$, the algorithm stops.
You are given an integer $n$. Praneet will perform the algorithm on it $a$ times. You have to print the result after $a$ operations.

-----Input:-----
- The first and only line of input contains two integers $n$ — initial number, and $a$ —the number of operations.

-----Output:-----
- Print one integer — the result of performing the algorithm on $n$ $a$ times.

-----Constraints-----
- $2 \leq n \leq 10^9$
- $1 \leq a \leq 50$

-----Sample Input 1-----
1001 2

-----Sample Input 2-----
5 2

-----Sample Output 1-----
100

-----Sample Output 2-----
3

-----Explanation-----
- In the first example, the transformation is as follows: $1001->1000->100$.
- In the second example, the transformation is as follows: $5->4->3$.

```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 = 'n,a=map(int,input().split())\nwhile a>0:\n if n%10==0:\n  n=n//10\n else:\n  n=n-1\n a=a-1\nprint(n)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12893
John Doe started thinking about graphs. After some thought he decided that he wants to paint an undirected graph, containing exactly k cycles of length 3. 

A cycle of length 3 is an unordered group of three distinct graph vertices a, b and c, such that each pair of them is connected by a graph edge. 

John has been painting for long, but he has not been a success. Help him find such graph. Note that the number of vertices there shouldn't exceed 100, or else John will have problems painting it.


-----Input-----

A single line contains an integer k (1 ≤ k ≤ 10^5) — the number of cycles of length 3 in the required graph.


-----Output-----

In the first line print integer n (3 ≤ n ≤ 100) — the number of vertices in the found graph. In each of next n lines print n characters "0" and "1": the i-th character of the j-th line should equal "0", if vertices i and j do not have an edge between them, otherwise it should equal "1". Note that as the required graph is undirected, the i-th character of the j-th line must equal the j-th character of the i-th line. The graph shouldn't contain self-loops, so the i-th character of the i-th line must equal "0" for all i.


-----Examples-----
Input
1

Output
3
011
101
110

Input
10

Output
5
01111
10111
11011
11101
11110

```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 = 0, int(input())\n\np = [['0'] * 100 for i in range(100)]\n\nwhile k:\n\n    for i in range(n):\n\n        if i > k: break\n\n        p[n][i] = p[i][n] = '1'\n\n        k -= i\n\n    n += 1\n\nprint(n)\n\nfor i in range(n): print(''.join(p[i][:n]))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 92107
per nextum in unam tum XI conscribementis fac sic

    vestibulo perlegementum da varo.

    morde varo.

    seqis cumula varum.

cis



per nextum in unam tum XI conscribementis fac sic

    seqis decumulamenta da varo.

    varum privamentum fodementum da aresulto.

    varum tum III elevamentum tum V multiplicamentum da bresulto.

    aresultum tum bresultum addementum da resulto.



    si CD tum resultum non praestantiam fac sic

        dictum sic f(%d) = %.2f cis tum varum tum resultum egresso describe.

        novumversum egresso scribe.

    cis

    si CD tum resultum praestantiam fac sic

        dictum sic f(%d) = MAGNA NIMIS! cis tum varum egresso describe.

        novumversum egresso scribe.        

    cis

cis




-----Input-----

The input consists of several integers, one per line. Each integer is between -50 and 50, inclusive.


-----Output-----

As described in the problem statement.


-----Example-----
Input
0
1
-2
-3
-4
-5
-6
-7
-8
-9
10

Output
f(10) = MAGNA NIMIS!
f(-9) = -3642.00
f(-8) = -2557.17
f(-7) = -1712.35
f(-6) = -1077.55
f(-5) = -622.76
f(-4) = -318.00
f(-3) = -133.27
f(-2) = -38.59
f(1) = 6.00
f(0) = 0.00

```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 = '\nfrom collections import deque\nimport math\n\nnumbers = deque()\n\nfor _ in range(11):\n    numbers.append(int(input()))\n\n\nfor _ in range(11):\n    num = numbers.pop()\n    a = math.sqrt(abs(num))\n    b = num**3 * 5\n    res = a + b\n\n    if res < 400:\n        print("f(%d) = %.2f" % (num, res))\n    else:\n        print("f(%d) = MAGNA NIMIS!" % num)\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14435