BinaryStringForces

2000ms

262144K

Description:

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.

Sample Input:

Sample Output:

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.

Informação

Provedor Codeforces

Código CF1750H