Strings A and B are K-similar (for some non-negative integer K) if we can swap the positions of two letters in A exactly K times so that the resulting string equals B.
Given two anagrams A and B, return the smallest K for which A and B are K-similar.
Example 1:
Input: A = "ab", B = "ba"
Output: 1


Example 2:
Input: A = "abc", B = "bca"
Output: 2


Example 3:
Input: A = "abac", B = "baca"
Output: 2


Example 4:
Input: A = "aabc", B = "abca"
Output: 2



Note:

1 <= A.length == B.length <= 20
A and B contain only lowercase letters from the set {'a', 'b', 'c', 'd', 'e', 'f'}

```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 = 'class Solution:\n    def kSimilarity(self, A: str, B: str) -> int:\n\n        def dist(a, b):\n            # count number of differing characters\n            return sum( (1 if c!=d else 0 for (c,d) in zip(a,b) ) )\n\n        def estimate_remaining(string):\n            # count number of wrong letters\n            # assume a perfect scenario:\n            #    each swap corrects two letters\n            count = dist(string, A)\n            return count/2 if count % 2 == 0 else count//2 + 1\n\n        def find_wrong_letters(working):\n            # given a working string, return two dicts that track work to be done:\n            #   (wants, wrongs)\n            # `wants[target]` maps to set of positions that need `target` letter\n            # `wrongs[letter]` maps to set positions that have a wrong `letter`\n            #     if i in wants{target] and j in wrongs[letter]\n            #       we can swap ith and jth letters to improve working\n\n            wants = defaultdict(set)\n            wrongs = defaultdict(set)\n            for i, c in enumerate(working):\n                target = A[i]\n                if c != target:\n                    wants[target].add(i)\n                    wrongs[c].add(i)\n            return wants, wrongs\n\n        def swap(s, i, j):\n            # swap ith and jth chars of string s\n            # assert i != j\n            if i > j:\n                i, j = j, i\n            return s[:i] + s[j] + s[i+1:j] + s[i] + s[j+1:]\n\n        def extend(working):\n            wrongs, needs = find_wrong_letters(working)\n            for letter, wrong_set in list(wrongs.items()):\n                return ( swap(working, i, j) for i in wrong_set for j in needs[letter] )\n\n        # BFS\n        # q is a heap that holds triples:\n        #   (estimate, swap_count_so_far, the_working_string)\n        # q = deque()\n        q = [ (0, 0, B) ]\n        seen = dict()\n        best = len(A)\n        while q:\n            estimate, k, working = heapq.heappop(q)\n            if estimate >= best or -k >= best:\n                return best\n            if working == A:\n                best = min( best, -k)\n                continue\n            for extension in extend(working):\n                if extension not in seen or seen[extension] > -k+1:\n                    seen[extension] = k+1\n                    new_estimate = estimate_remaining(extension) -k + 1\n                    heapq.heappush( q, (new_estimate, k-1, extension) )\n        return best\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'kSimilarity'
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: 10661