You are given a binary string $s$ (recall that a string is binary if each character is either $0$ or $1$).

Let $f(t)$ be the decimal representation of integer $t$ written in binary form (possibly with leading zeroes). For example $f(011) = 3, f(00101) = 5, f(00001) = 1, f(10) = 2, f(000) = 0$ and $f(000100) = 4$.

The substring $s_{l}, s_{l+1}, \dots , s_{r}$ is good if $r - l + 1 = f(s_l \dots s_r)$.

For example string $s = 1011$ has $5$ good substrings: $s_1 \dots s_1 = 1$, $s_3 \dots s_3 = 1$, $s_4 \dots s_4 = 1$, $s_1 \dots s_2 = 10$ and $s_2 \dots s_4 = 011$. 

Your task is to calculate the number of good substrings of string $s$.

You have to answer $t$ independent queries.


-----Input-----

The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of queries.

The only line of each query contains string $s$ ($1 \le |s| \le 2 \cdot 10^5$), consisting of only digits $0$ and $1$.

It is guaranteed that $\sum\limits_{i=1}^{t} |s_i| \le 2 \cdot 10^5$.


-----Output-----

For each query print one integer — the number of good substrings of string $s$.


-----Example-----
Input
4
0110
0101
00001000
0001000

Output
4
3
4
3

```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 = 'from math import log2\nfrom math import ceil\n\nfor _ in range(int(input())):\n    S = list(map(int, list(input())))\n    combs = 0\n    maxlen = ceil(log2(len(S)))\n    #print(maxlen)\n    prezeros = 0\n    next1 = [0] * len(S)\n    nxt = len(S) - 1\n    for i in range(len(S) - 1, -1, -1):\n        if S[i] == 1:\n            nxt = i\n        next1[i] = nxt\n    for l in range(len(S)):\n        if S[l] == 0:\n            nxtl = next1[l]\n            val = 0\n            lcomb = 0\n            for r in range(nxtl, min(nxtl + maxlen + 1, len(S))):\n                val = 2 * val + S[r]\n                if val == r - l + 1:\n                    # print(l, r)\n                    lcomb += 1\n            combs += lcomb\n            continue\n        val = 0\n        lcomb = 0\n        for r in range(l, min(l + maxlen + 1, len(S))):\n            val = 2 * val + S[r]\n            if val == r - l + 1:\n                #print(l, r)\n                lcomb += 1\n        combs += lcomb\n        prezeros = 0\n    print(combs)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13581