A12958 | The Number Of Good Substrings

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.

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

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