You 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 ≤ n ≤ 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
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		String s=in.next();
		int[] pre=new int[n];
		int[] suf=new int[n];
		boolean[] precan=new boolean[n];
		boolean[] sufcan=new boolean[n];
		precan[0]=sufcan[n-1]=true;
		for (int i=0;i<n;++i) {
			if (s.charAt(i)=='(') ++pre[i];
			else --pre[i];
			if (i>0) pre[i]+=pre[i-1];
			if (i>0) precan[i]=precan[i-1]&(pre[i-1]>=0);
		}
		for (int i=n-1;i>=0;--i) {
			if (s.charAt(i)==')') ++suf[i];
			else --suf[i];
			if (i<n-1) suf[i]+=suf[i+1];
			if (i<n-1) sufcan[i]=sufcan[i+1]&(suf[i+1]>=0);
		}
		int res=0;
		for (int i=0;i<n;++i) {
			if (!precan[i]||!sufcan[i]) continue;
			if (s.charAt(i)=='(') {
				if (pre[i]>1&&pre[i]-suf[i]==3) ++res;
			} else {
				if (suf[i]>1&&suf[i]-pre[i]==3) ++res;
			}
		}
		System.out.println(res);
	}
}