[Solution] Dense Bracket Sequence CodeChef Solution | CodeChef Problem Solution 2022

[Solution] Dense Bracket Sequence CodeChef Solution | CodeChef Problem Solution 2022

A bracket sequence S$S$ is called dense if one of the following is true:

• S$S$ is empty.
• S=(X)$S=(X)$ where X$X$ is dense.

You are given a bracket sequence S$S$. What is the minimum number of brackets you must remove to make it dense?

Input Format

• The first line of input will contain a single integer T$T$, the number of test cases. The description of the T$T$ test cases follows.
• The first line of each test case contains one integer N$N$, denoting the length of the bracket sequence.

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• The second line of each test case contains the bracket sequence S$S$ of length N$N$.

Output Format

For each test case, output on a new line the minimum number of brackets you must remove from S$S$ to make it dense.

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Constraints

• 1≤T≤2⋅104$1\le T\le 2\cdot {10}^4$
• 2≤N≤3⋅105$2\le N\le 3\cdot {10}^5$