Given the strings s1 and s2 of size n, and the string evil. Return the number of good strings.
A good string has size n, it is alphabetically greater than or equal to s1, it is alphabetically smaller than or equal to s2, and it does not contain the string evil as a substring. Since the answer can be a huge number, return this modulo 10^9 + 7.
 
Example 1:
Input: n = 2, s1 = "aa", s2 = "da", evil = "b"
Output: 51 
Explanation: There are 25 good strings starting with 'a': "aa","ac","ad",...,"az". Then there are 25 good strings starting with 'c': "ca","cc","cd",...,"cz" and finally there is one good string starting with 'd': "da". 

Example 2:
Input: n = 8, s1 = "leetcode", s2 = "leetgoes", evil = "leet"
Output: 0 
Explanation: All strings greater than or equal to s1 and smaller than or equal to s2 start with the prefix "leet", therefore, there is not any good string.

Example 3:
Input: n = 2, s1 = "gx", s2 = "gz", evil = "x"
Output: 2

 
Constraints:

s1.length == n
s2.length == n
s1 <= s2
1 <= n <= 500
1 <= evil.length <= 50
All strings consist of lowercase English letters.

```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 functools import lru_cache\nfrom itertools import takewhile\n\n\nclass Solution:\n    def findGoodStrings(self, n: int, A: str, B: str, evil: str) -> int:\n        MOD = 10 ** 9 + 7\n\n        evil_checker = KMPTable(evil)\n\n        @lru_cache(None)\n        def DP(i=0, startswith_A=True, startswith_B=True, match_evil=0):\n            # # <= s and not startwsith evil[e:]\n            if match_evil == len(evil):\n                return 0\n            if i == n:\n                return 1\n\n            start = A[i] if startswith_A else 'a'\n            end = B[i] if startswith_B else 'z'\n\n            return sum(\n                DP(\n                    i + 1,\n                    startswith_A and c == A[i],\n                    startswith_B and c == B[i],\n                    match_evil=evil_checker.match(c, idx=match_evil),\n                )\n                for c in map(chr, list(range(ord(start), ord(end) + 1)))\n            ) % MOD\n\n        return DP()\n\n\nclass KMPTable:\n    \n    def __init__(self, s):\n        self.s = s\n        self._init_table()\n        \n    def _init_table(self):\n        self.table = [0, 0]\n        for i in range(1, len(self.s)):\n            self.table.append(\n                self.match(self.s[i], idx=self.table[-1]),\n            )\n\n    def match(self, c, idx):\n        if c == self.s[idx]:\n            return idx + 1\n        return self.match(c, self.table[idx]) if idx > 0 else 0\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'findGoodStrings'
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: 13346