Given an equation, represented by words on left side and the result on right side.
You need to check if the equation is solvable under the following rules:

Each character is decoded as one digit (0 - 9).
Every pair of different characters they must map to different digits.
Each words[i] and result are decoded as one number without leading zeros.
Sum of numbers on left side (words) will equal to the number on right side (result). 

Return True if the equation is solvable otherwise return False.
 
Example 1:
Input: words = ["SEND","MORE"], result = "MONEY"
Output: true
Explanation: Map 'S'-> 9, 'E'->5, 'N'->6, 'D'->7, 'M'->1, 'O'->0, 'R'->8, 'Y'->'2'
Such that: "SEND" + "MORE" = "MONEY" ,  9567 + 1085 = 10652
Example 2:
Input: words = ["SIX","SEVEN","SEVEN"], result = "TWENTY"
Output: true
Explanation: Map 'S'-> 6, 'I'->5, 'X'->0, 'E'->8, 'V'->7, 'N'->2, 'T'->1, 'W'->'3', 'Y'->4
Such that: "SIX" + "SEVEN" + "SEVEN" = "TWENTY" ,  650 + 68782 + 68782 = 138214
Example 3:
Input: words = ["THIS","IS","TOO"], result = "FUNNY"
Output: true

Example 4:
Input: words = ["LEET","CODE"], result = "POINT"
Output: false

 
Constraints:

2 <= words.length <= 5
1 <= words[i].length, result.length <= 7
words[i], result contains only upper case English letters.
Number of different characters used on the expression is at most 10.

```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 itertools import permutations, zip_longest\nfrom collections import OrderedDict\nclass Solution:\n    def isSolvable(self, words: List[str], result: str) -> bool:\n        \n        self.matched_chars = list(zip_longest(*[result[::-1]]+[w[::-1] for w in words]))        \n        self.first_chars = set([result[0]]+[w[0] for w in words])\n        self.chars = []            \n        self.free_vars = []\n        self.idx = {}\n        observed = set()\n        for chars in self.matched_chars:\n            free_vars = []\n            for c in chars:\n                if c is None:\n                    continue\n                if c not in observed:\n                    self.chars.append(c)\n                    free_vars.append(c)\n                    observed.add(c)\n                    self.idx[c]=len(self.idx)\n            self.free_vars.append(free_vars)\n        #print(self.free_vars)\n        #print(self.chars)    \n\n        return self.dfs(0,(),0)\n        \n    @lru_cache(maxsize=None)\n    def dfs(self, i, used_digits, carry):\n        #pemutations\n        if i >= len(self.matched_chars):\n            #print('R:',used_digits)\n            return not max(used_digits[self.idx[f]]==0 for f in self.first_chars)\n        free_vars = self.free_vars[i]\n        perms = permutations(set(range(10))-set(list(used_digits)),len(free_vars))\n        for p in perms:\n            values = tuple(list(used_digits)+list(p))\n            #check for contradiction\n            nxt_carry = self.contradict(values,i,carry)\n            if nxt_carry<0:\n                continue\n            if self.dfs(i+1,values,nxt_carry):\n                return True\n        return False\n    \n    def contradict(self, values, i, carry):\n        r, *i = self.matched_chars[i]\n        s = sum(values[self.idx[d]] for d in i if d)+carry\n        if (s-values[self.idx[r]])%10:\n            return -1\n        return s//10\n        \n    \n        \n        \n    \n        \n    \n                            \n                    \n        \n        \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isSolvable'
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: 113464