H. BinaryStringForces
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a binary string $s$ of length $n$. We define a maximal substring as a substring that cannot be extended while keeping all elements equal. For example, in the string $11000111$ there are three maximal substrings: $11$, $000$ and $111$.

In one operation, you can select two maximal adjacent substrings. Since they are maximal and adjacent, it's easy to see their elements must have different values. Let $a$ be the length of the sequence of ones and $b$ be the length of the sequence of zeros. Then do the following:

• If $a \ge b$, then replace $b$ selected zeros with $b$ ones.
• If $a < b$, then replace $a$ selected ones with $a$ zeros.

As an example, for $1110000$ we make it $0000000$, for $0011$ we make it $1111$. We call a string being good if it can be turned into $1111...1111$ using the aforementioned operation any number of times (possibly, zero). Find the number of good substrings among all $\frac{n(n+1)}{2}$ non-empty substrings of $s$.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^5$) — the number of test cases. The description of test cases follows.

The first line of each test case contains $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the string $s$.

The second line of each test case contains the binary string $s$ of length $n$.

It is guaranteed that sum of $n$ across all test cases doesn't exceed $2 \cdot 10^5$.

Output

For each test case, print a single integer — the number of good substrings.

Example
Input
4610001131015111116010101
Output
8
5
15
18

Note

Let's define a substring from index $l$ to index $r$ as $[l, r]$.

For the first test case, the good substrings are:

• $[1,1]$,
• $[1,2]$,
• $[3,6]$,
• $[4,5]$,
• $[4,6]$,
• $[5,5]$,
• $[5,6]$,
• $[6,6]$.

In the second test case, all substrings are good except $[2,2]$.

In the third test case, all substrings are good.