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.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		
		String str=s.next();
		
		int[] pre=new int[n+2];
		int[] suf=new int[n+2];
		
		boolean[] pp=new boolean[n+2];
		boolean[] sp=new boolean[n+2];
		
		pp[0]=true;
		
		sp[n+1]=true;
		
		for(int i=0;i<n;i++)
		{
			if(str.charAt(i)=='(')
			{
				pre[i+1]=pre[i]+1;
				
				if(pre[i+1]>=0&&pp[i])
				{
					pp[i+1]=true;
				}
				
			}
			else
			{
				pre[i+1]=pre[i]-1;
				
				if(pre[i+1]>=0&&pp[i])
				{
					pp[i+1]=true;
				}
				
			}
		}
		
		pp[n+1]=pp[n];
		
		for(int i=n-1;i>=0;i--)
		{
			if(str.charAt(i)==')')
			{
				suf[i+1]=suf[i+2]+1;
				
				if(suf[i+1]>=0&&sp[i+2])
				{
					sp[i+1]=true;
				}
			}
			else
			{
				suf[i+1]=suf[i+2]-1;
				
				if(suf[i+1]>=0&&sp[i+2])
				{
					sp[i+1]=true;
				}
				
			}
		}
		
		sp[0]=sp[1];
		
		int count=0;
		
		for(int i=1;i<n+1;i++)
		{
			if(str.charAt(i-1)=='(')
			{
				if(pre[i-1]-1>=0&&pp[i-1]&&sp[i+1]&&pre[i-1]-1==suf[i+1])
				{
					count++;
				}
			}
			else
			{
				if(pp[i-1]&&sp[i+1]&&suf[i+1]-1>=0&&pre[i-1]==suf[i+1]-1)
				{
					count++;
				}
			}
		}
		
		System.out.println(count);
		
	}
	
}