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Tuesday 6 September 2022

[Solution] Jatayu's Balanced Bracket Sequence Codeforces Solution



C. Jatayu's Balanced Bracket Sequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Last summer, Feluda gifted Lalmohan-Babu a balanced bracket sequence s of length 2n.

Topshe was bored during his summer vacations, and hence he decided to draw an undirected graph of 2n vertices using the balanced bracket sequence s. For any two distinct vertices i and j (1i<j2n), Topshe draws an edge (undirected and unweighted) between these two nodes if and only if the subsegment s[ij] forms a balanced bracket sequence.

Determine the number of connected components in Topshe's graph.

See the Notes section for definitions of the underlined terms.

Input

Each test contains multiple test cases. The first line contains a single integer t (1t105) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer n (1n105) — the number of opening brackets in string s.

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The second line of each test case contains a string s of length 2n — a balanced bracket sequence consisting of n opening brackets "(", and n closing brackets ")".

It is guaranteed that the sum of n over all test cases does not exceed 105.

Output

For each test case, output a single integer — the number of connected components in Topshe's graph.


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