# Task
 Define crossover operation over two equal-length strings A and B as follows:

 the result of that operation is a string of the same length as the input strings result[i] is chosen at random between A[i] and B[i]. 
 
 Given array of strings `arr` and a string result, find for how many pairs of strings from `arr` the result of the crossover operation over them may be equal to result.

 Note that (A, B) and (B, A) are the same pair. Also note that the pair cannot include the same element of the array twice (however, if there are two equal elements in the array, they can form a pair).

# Example

 For `arr = ["abc", "aaa", "aba", "bab"]` and `result = "bbb"`, the output should be `2`.

 ```
"abc" and "bab" can crossover to "bbb"
"aba" and "bab" can crossover to "bbb"
```
# Input/Output


 - `[input]` string array `arr`

   A non-empty array of equal-length strings.

   Constraints: `2 ≤ arr.length ≤ 10, 1 ≤ arr[i].length ≤ 10.`


 - `[input]` string `result`

   A string of the same length as each of the arr elements.

   Constraints: `result.length = arr[i].length.`


 - `[output]` an integer

```python

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

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

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from collections import Counter\n\ndef strings_crossover(arr, result):\n    lstBit = [ int(''.join(['01'[x==y] for x,y in zip(result, w)]), 2) for w in arr ]\n    target = 2**len(result) - 1\n    c      = Counter(lstBit)\n    \n    v1 = sum( v*w for k,v in list(c.items()) for l,w in list(c.items()) if k|l == target and k!=target and l!=target) // 2\n    v2 = 0 if target not in c else (sum(c.values())-c[target]) * c[target]\n    v3 = 0 if c[target] < 2 else c[target] * (c[target]-1) // 2\n    \n    return v1+v2+v3\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'strings_crossover'
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: 10956