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E. Almost Regular Bracket Sequence

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a bracket sequence $$$s$$$ consisting of $$$n$$$ opening '(' and closing ')' brackets.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You can change the type of some bracket $$$s_i$$$. It means that if $$$s_i = $$$ ')' then you can change it to '(' and vice versa.

Your task is to calculate the number of positions $$$i$$$ such that if you change the type of the $$$i$$$-th bracket, then the resulting bracket sequence becomes regular.

Input

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the length of the bracket sequence.

The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ opening '(' and closing ')' brackets.

Output

Print one integer — the number of positions $$$i$$$ such that if you change the type of the $$$i$$$-th bracket, then the resulting bracket sequence becomes regular.

Examples

Input

6 (((())

Output

3

Input

6 ()()()

Output

0

Input

1 )

Output

0

Input

8 )))(((((

Output

0

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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