All strings in Chefland are beautiful because they are binary strings (a binary string contains only characters '0' and '1'). The beauty of a binary string $S$ is defined as the number of pairs $(i, j)$ ($1 \le i \le j \le |S|$) such that the substring $S_i, S_{i+1}, \ldots, S_j$ is special.
For a binary string $U$, let's denote the number of occurrences of the characters '1' and '0' in $U$ by $cnt_1$ and $cnt_0$ respectively; then, $U$ is special if $cnt_0 = cnt_1 \cdot cnt_1$.
Today, Chef's friend Araspa is celebrating her birthday. Chef wants to give Araspa the most beautiful binary string he can find. Currently, he is checking out binary strings in a shop, but he needs your help to calculate their beauties. Tell Chef the beauty of each binary string he gives you.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single string $S$.

-----Output-----
For each test case, print a single line containing one integer — the beauty of the string $S$.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le |S| \le 10^5$
- each character of $S$ is '0' or '1'

-----Example Input-----
2
010001
10

-----Example Output-----
4
1

-----Explanation-----
Example case 1: The special substrings correspond to $(i, j) = (1, 2), (1, 6), (2, 3), (5, 6)$.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "\nt = int(input())\nfor k in range(t):\n s = input().strip()\n n = len(s)\n dp = [0]\n for i in s:\n  if i == '1':\n   dp.append(dp[-1]+1)\n  else:\n   dp.append(dp[-1])\n d = 1\n ans = 0\n l = d * d + d\n while l <= n:\n  i = 0\n  while i <= n - l:  # for i in range(0, n - l + 1):\n   j = i + l\n   cnt1 = dp[j] - dp[i]\n   if cnt1 == d:\n    ans += 1\n    i += 1\n   else:\n    i += abs(d - cnt1)\n    # print(i, j)\n  d += 1\n  l = d * d + d\n print(ans)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13259