Given a binary string s (a string consisting only of '0's and '1's), we can split s into 3 non-empty strings s1, s2, s3 (s1+ s2+ s3 = s).
Return the number of ways s can be split such that the number of characters '1' is the same in s1, s2, and s3.
Since the answer may be too large, return it modulo 10^9 + 7.
 
Example 1:
Input: s = "10101"
Output: 4
Explanation: There are four ways to split s in 3 parts where each part contain the same number of letters '1'.
"1|010|1"
"1|01|01"
"10|10|1"
"10|1|01"

Example 2:
Input: s = "1001"
Output: 0

Example 3:
Input: s = "0000"
Output: 3
Explanation: There are three ways to split s in 3 parts.
"0|0|00"
"0|00|0"
"00|0|0"

Example 4:
Input: s = "100100010100110"
Output: 12

 
Constraints:

3 <= s.length <= 10^5
s[i] is '0' or '1'.

```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 math import factorial\n\nclass Solution:\n    def numWays(self, s: str) -> int:\n        ans = 0\n        n = len(s)\n        xd = s.count('1')\n        if s.count('0') == 0:\n            if xd % 3 != 0:\n                return 0\n            return 1\n        if xd == 0:\n            if n == 3:\n                return 1\n            n = n - 1\n            ans = factorial(n) / factorial(n-2) / factorial(2)\n        else:\n            if xd % 3 != 0:\n                return 0\n            x = xd // 3\n            ti = [x, x]\n            j = 0\n            while ti[0] > 0:\n                if s[j] == '1':\n                    ti[0] -= 1\n                j += 1 \n            ti[0] = j\n            while ti[1] > 0:\n                if s[j] == '1':\n                    ti[1] -= 1\n                j += 1 \n            ti[1] = j\n\n            zc = [0, 0]\n            j = ti[0]\n            while s[j] == '0':\n                zc[0] += 1\n                j += 1\n            j = ti[1]\n            while s[j] == '0':\n                zc[1] += 1\n                j += 1\n                \n            # print(zc)\n            \n            lv = 0\n            rv = 0\n            if zc[0] > 0:\n                zc[0] += 1\n                lv = factorial(zc[0]) / factorial(zc[0]-1)\n            if zc[1] > 0:\n                zc[1] += 1\n                rv = factorial(zc[1]) / factorial(zc[1]-1)\n            \n            if max([lv, rv]) == 0:\n                return 1\n            \n            if lv > 0 and rv > 0:\n                ans = lv * rv\n            else:\n                ans = lv + rv\n        # print(1)\n        ans = int(ans)\n        return ans % (10**9 + 7)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numWays'
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: 6688