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 = "def findall(p, s):\n    '''Yields all the positions of\n    the pattern p in the string s.'''\n    i = s.find(p)\n    while i != -1:\n        yield i\n        i = s.find(p, i+1)\n\ndef choose(n, k):\n    c = 1\n    if k > n // 2:\n        k = n - k\n    for i in range(1, k + 1):\n        c = c * (n - i + 1) // i\n    return c\n\ndef modulo(n):\n    return n % (10 ** 9 + 7)\n\nclass Solution:\n    \n    def numWays(self, s: str) -> int:\n        n = len(s)\n        c = s.count('1')\n        if c % 3 != 0:\n            return 0\n        cp = c // 3 # count in each part\n        if cp == 0:\n            #special case, no 1, chosse 2 separators in the (n-1) possible spaces\n            return modulo(choose(n - 1, 2))\n        # find the size n1 of the substring between (cp+1)-th and cp-th occurrances of 1,\n        # and the size n2 of the subsring betwwen (cp*2+1)-th and (cp*2)-th occurrances of 1\n        indices = list(findall('1', s))\n        n1 = indices[cp] - indices[cp - 1] - 1\n        n2 = indices[cp*2] - indices[cp*2 - 1] - 1\n        # find one separater in (n1 + 1) possible spaces, \n        # and one separater in (n2 + 1) possible spaces \n        result = 0\n        if n1 == 0:\n            result = n2 + 1\n        elif n2 == 0:\n            result = n1 + 1\n        else:\n            result = (n1 + 1) * (n2 + 1)\n        return(modulo(result))\n"
_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: 5894