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B. Paranoid String

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet's call a binary string $$$T$$$ of length $$$m$$$ indexed from $$$1$$$ to $$$m$$$ paranoid if we can obtain a string of length $$$1$$$ by performing the following two kinds of operations $$$m-1$$$ times in any order :

- Select any substring of $$$T$$$ that is equal to 01, and then replace it with 1.
- Select any substring of $$$T$$$ that is equal to 10, and then replace it with 0.
For example, if $$$T = $$$ 001, we can select the substring $$$[T_2T_3]$$$ and perform the first operation. So we obtain $$$T = $$$ 01.

You are given a binary string $$$S$$$ of length $$$n$$$ indexed from $$$1$$$ to $$$n$$$. Find the number of pairs of integers $$$(l, r)$$$ $$$1 \le l \le r \le n$$$ such that $$$S[l \ldots r]$$$ (the substring of $$$S$$$ from $$$l$$$ to $$$r$$$) is a paranoid string.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of $$$S$$$.

The second line of each test case contains a binary string $$$S$$$ of $$$n$$$ characters $$$S_1S_2 \ldots S_n$$$. ($$$S_i = $$$ 0 or $$$S_i = $$$ 1 for each $$$1 \le i \le n$$$)

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

Output

For each test case, output the number of pairs of integers $$$(l, r)$$$ $$$1 \le l \le r \le n$$$ such that $$$S[l \ldots r]$$$ (the substring of $$$S$$$ from $$$l$$$ to $$$r$$$) is a paranoid string.

Example

Input

511201310041001511111

Output

1 3 4 8 5

Note

In the first sample, $$$S$$$ already has length $$$1$$$ and doesn't need any operations.

In the second sample, all substrings of $$$S$$$ are paranoid. For the entire string, it's enough to perform the first operation.

In the third sample, all substrings of $$$S$$$ are paranoid except $$$[S_2S_3]$$$, because we can't perform any operations on it, and $$$[S_1S_2S_3]$$$ (the entire string).

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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