Given a string s1, we may represent it as a binary tree by partitioning it to two non-empty substrings recursively.

Below is one possible representation of s1 = "great":


    great
   /    \
  gr    eat
 / \    /  \
g   r  e   at
           / \
          a   t


To scramble the string, we may choose any non-leaf node and swap its two children.

For example, if we choose the node "gr" and swap its two children, it produces a scrambled string "rgeat".


    rgeat
   /    \
  rg    eat
 / \    /  \
r   g  e   at
           / \
          a   t


We say that "rgeat" is a scrambled string of "great".

Similarly, if we continue to swap the children of nodes "eat" and "at", it produces a scrambled string "rgtae".


    rgtae
   /    \
  rg    tae
 / \    /  \
r   g  ta  e
       / \
      t   a


We say that "rgtae" is a scrambled string of "great".

Given two strings s1 and s2 of the same length, determine if s2 is a scrambled string of s1.

Example 1:


Input: s1 = "great", s2 = "rgeat"
Output: true


Example 2:


Input: s1 = "abcde", s2 = "caebd"
Output: false

```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 isScramble(self, s1, s2):\n         """\n         :type s1: str\n         :type s2: str\n         :rtype: bool\n         """\n         \n         """\n         CHECKING TWO STRINGS ARE ANAGRAMS IS FASTER BY SORTING THAN BY COUNTE (AT WHAT LEN DOES THIS FLIP)\n         RETURNING WHEN SORTED(S1) != SORTED(S2[LEFT:RIGHT+1]) GOT MY CODE FROM 1800 MS TO 150MS.\n         """\n         \n         def getfromdictt(strr, left, right):\n             args = (strr, s2[left:right+1])\n             if args in dictt:\n                 return dictt[args]\n             res = scramble(strr, left, right)\n             dictt[args] = res\n             return res\n         \n         def putindictt(strr, left, right, val):\n             dictt[(strr, s2[left:right+1])] = val\n             return val\n         \n         def scramble(s1, left, right):\n             \n             if sorted(s1) != sorted(s2[left:right+1]):\n                 return putindictt(s1, left, right, False)\n             # if collections.Counter(s1) != collections.Counter(s2[left:right+1]): return False\n             \n             \n             if s2[left:right+1] == s1:\n                 return putindictt(s1, left, right, True)\n             \n             for i in range(len(s1)-1):\n                 leftstr, rightstr = s1[:i+1], s1[i+1:]\n                 leftmatch = getfromdictt(leftstr, left, left+i)\n                 rightmatch = getfromdictt(rightstr, left+i+1,right)\n                 \n                 if leftmatch and rightmatch:\n                     return putindictt(s1, left, right, True)\n                 \n                 flipleftmatch = getfromdictt(rightstr, left, left + len(rightstr)-1)\n                 fliprightmatch = getfromdictt(leftstr, left + len(rightstr), right)\n \n                 if flipleftmatch and fliprightmatch:\n                     return putindictt(s1, left, right, True)\n             \n             return putindictt(s1, left, right, False)\n         \n         dictt = {}\n         return scramble(s1, 0, len(s1)-1)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isScramble'
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: 10281