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.io.*; 
import java.math.*;
import java.util.*;
import java.awt.Point;
 
public class Main {
	//static final long MOD = 998244353;
	static final long MOD = 1000000007;
	static final int INF = 1000000007;
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int N = sc.ni();
		String s = sc.next();
		int[] pref = new int[N+1];
		for (int i = 1; i <= N; i++) {
			if (s.charAt(i-1)=='(')
				pref[i] = pref[i-1]+1;
			else
				pref[i] = pref[i-1]-1;
		}
		
		if (pref[N] == 2) {
			for (int i = 1; i <= N; i++) {
				if (pref[i] < 0) {
					System.out.println(0);
					return;
				}
			}
			int ans = 0;
			for (int i = N; i > 0; i--) {
				if (pref[i] < 2) break;
				if (s.charAt(i-1)=='(') ans++;
			}
			System.out.println(ans);
		} else if (pref[N] == -2) {
			int firstNegIndex = -1;
			for (int i = 1; i <= N; i++) {
				if (pref[i] < -2) {
					System.out.println(0);
					return;
				}
				if (pref[i] < 0 && firstNegIndex == -1)
					firstNegIndex = i;
			}
			int ans = 0;
			for (int i = 1; i <= firstNegIndex; i++) {
				if (s.charAt(i-1)==')') {
					ans++;
				}
			}
			System.out.println(ans);
		} else {
			System.out.println(0);
		}
 	}
	
	static class DisjointSetUnion {
		  public int[] parent;
		  public int[] rank;
		  public int count;

		  public DisjointSetUnion(int nodes) {
			  count = nodes;
			  parent = new int[nodes];
			  rank = new int[nodes];
			  for (int i = 0; i < nodes; i++) {
				  parent[i] = i;
				  rank[i] = 0;
			  }
		  }
		  //"find"
		  public int root(int p) {
			  if (parent[p] != p)
				  parent[p] = root(parent[p]);
			  return parent[p];
		  }

		  //"union"
		  public void connect(int p, int q) {
			  int rootP = root(p);
			  int rootQ = root(q);
			  if (rootP == rootQ) return;
			  if (rank[rootP] < rank[rootQ]) {
				  parent[rootP] = rootQ;
			  } else if (rank[rootP] > rank[rootQ]) {
				  parent[rootQ] = rootP;
			  } else {
				  parent[rootP] = rootQ;
				  rank[rootQ] += 1;
			  }
			  count--;
		  }

		  public boolean connected(int p, int q) {
		    return root(p) == root(q);
		  }
	}
    
    public static long power(long x, long y, long p) { 
        // Initialize result
        long res = 1;
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
      
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
    
    public static long dist(int[] point, int[] point2) {
    	return (long)(Math.pow((point2[1]-point[1]),2)+Math.pow((point2[0]-point[0]),2));
    }
    
    public static long gcd(long a, long b) {
    	if (b == 0)
    		return a;
    	else
    		return gcd(b,a%b);
    }
    
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] arr1, int[] arr2) {
				  return arr1[1]-arr2[1]; //ascending order
	          }
		});
		return array;
	}
    
    public static long[][] sort(long[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    long[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<long[]>() {
			  @Override
        	  public int compare(long[] arr1, long[] arr2) {
				  if (arr1[0] < arr2[0])
					  return -1;
				  if (arr1[0] > arr2[0])
					  return 1;
				  return 0;
	          }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int ni() { 
            return Integer.parseInt(next()); 
        } 
  
        long nl() { 
            return Long.parseLong(next()); 
        } 
  
        double nd() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        }
    }
}