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
 /*                       In_The_Name_Of_Allah_The_Merciful                        */
import java.util.*;
import java.io.*;  
public class Main 
{
    PrintWriter out;
    FastReader sc;
    long[] m1= {(long)(1e9+7),998244353};
    long mod=m1[0];
    long maxlong=Long.MAX_VALUE;
    long minlong=Long.MIN_VALUE;
    StringBuilder sb;
    int[] st, A,lazy;
    int n;
    int left (int p) { return p << 1; }
    int right(int p) { return (p << 1) + 1; }
    void build(int p, int L, int R) {
        if (L == R)
            st[p] = A[L];
        else {
            build(left(p) , L , (L + R) / 2);
            build(right(p), (L + R) / 2 + 1, R );
            int p1 = left(p), p2 = right(p);
            st[p] = min(st[p1],st[p2]);
        }
    }
    int rsq(int node, int start, int endd, int l, int r){
        if(start > endd || start > r || endd < l) return 10000000;
        if(lazy[node] != 0){
            st[node] += lazy[node];
            if(start != endd){
                lazy[node*2] += lazy[node];
                lazy[node*2+1] += lazy[node];
            }
            lazy[node] = 0;
        }
        if(start >= l && endd <= r)
            return st[node];
        int mid = (start + endd) / 2;
        int p1 = rsq(node*2, start, mid, l, r);
        int p2 = rsq(node*2 + 1, mid + 1, endd, l, r);
        return min(p1,p2);}
    void updateRange(int node, int start, int endd, int l, int r, int val){
        if(lazy[node] != 0){
            st[node] += lazy[node];
            if(start != endd){
                lazy[node*2] += lazy[node];
                lazy[node*2+1] += lazy[node];}
            lazy[node] = 0;}
        if(start > endd || start > r || endd < l) return;
        if(start >= l && endd <= r){
            st[node] += val;
            if(start != endd){
                lazy[node*2] += val;
                lazy[node*2+1] += val;}
            return;}
        int mid = (start + endd) / 2;
        updateRange(node*2, start, mid, l, r, val);
        updateRange(node*2 + 1, mid + 1, endd, l, r, val);
        st[node] = min(st[node*2],st[node*2+1]);}
        void segmentTree(int[] _A) {
            A = _A; n = (int)A.length;
            st=new int[4*n];
            lazy=new int[4*n];
            build(1, 0, n - 1);}
        int rsq(int i, int j){return rsq(1, 0, n - 1, i, j);}
        void updateRange(int i,int j, int v){updateRange(1,0,n-1,i,j,v);}

    /******************************************************************************************
     *****************************************************************************************/
   
	public void sol() {
		int n1=ni();
		char[] s=rl();
		int[] sum=new int[n1];
		if(s[0]=='(')sum[0]=1;
		else sum[0]=-1;
		for(int i=1;i<n1;i++) {
			if(s[i]=='(')sum[i]=1+sum[i-1];
			else sum[i]=sum[i-1]-1;
		}segmentTree(sum);
		int ans=0;
		 for(int i=0; i<n; i++){
		        if(s[i]=='('){
		            updateRange(i,n-1,-2);
		            if(rsq(0,n-1)==0&&rsq(n-1,n-1)==0) ans++;
		            updateRange(i,n-1,2);
		        }
		        else{
		            updateRange(i,n-1,2);
		            if(rsq(0,n-1)==0&&rsq(n-1,n-1)==0) ans++;
		            updateRange(i,n-1,-2);
		        }
		    }
		pl(ans);
	}
    public static void main(String[] args) 
	{ 
	    Main g=new Main();
		g.out=new PrintWriter(System.out);
		g.sc=new FastReader();
		int t=1;
// 		t=g.ni();
		while(t-->0)
		g.sol();
		g.out.flush();
	}
	
	/****************************************************************************************
     *****************************************************************************************/
	static class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
 
		public FastReader() 
		{ 
			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 nextInt() 
		{ 
			return Integer.parseInt(next()); 
		} 
 
		long nextLong() 
		{ 
			return Long.parseLong(next()); 
		} 
 
		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 
 
		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	} public int ni(){
	      return sc.nextInt();
	}public long nl(){
	      return sc.nextLong();
	}public double nd(){
	      return sc.nextDouble();
	}public char[] rl(){
	      return sc.nextLine().toCharArray();
	}public String rl1(){
	      return sc.nextLine();
	}
	public void pl(Object s){
	      out.println(s);
	}
	public void pr(Object s){
	      out.print(s);
	}public String next(){
	      return sc.next();
	}public long abs(long x){
	      return Math.abs(x);
	}
	public int abs(int x){
	      return Math.abs(x);
	}
	public double abs(double x){
	      return Math.abs(x);
	}public long min(long x,long y){
            return (long)Math.min(x,y);
      }
      public int min(int x,int y){
            return (int)Math.min(x,y);
      }
      public double min(double x,double y){
            return Math.min(x,y);
      }public long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}public long lcm(long a, long b) {
            return (a / gcd(a, b)) * b;
      }
       void sort1(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a) {
			l.add(i);
		}
		Collections.sort(l,Collections.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}
	 void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort(char[] a) {
		ArrayList<Character> l = new ArrayList<>();
		for (char i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort1(char[] a) {
		ArrayList<Character> l = new ArrayList<>();
		for (char i : a) {
			l.add(i);
		}
		Collections.sort(l,Collections.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}
	 void sort(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort1(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a) {
			l.add(i);
		}
		Collections.sort(l,Collections.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}
	void sort(double[] a) {
		ArrayList<Double> l = new ArrayList<>();
		for (double i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}long pow(long a,long b){
          if(b==0){
                return 1;
          }long p=pow(a,b/2);
          if(b%2==0) return mMultiplication(p,p)%mod;
          else return (mMultiplication(mMultiplication(p,p),a))%mod;
    }
	
	int  swap(int a,int b){
	      return a;
	}long  swap(long a,long b){
	      return a;
	}double  swap(double a,double b){
	      return a;
	}
	boolean isPowerOfTwo (int x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }boolean isPowerOfTwo (long x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }public long max(long x,long y){
            return (long)Math.max(x,y);
      }
      public int max(int x,int y){
            return (int)Math.max(x,y);
      }
      public double max(double x,double y){
            return Math.max(x,y);
      }long sqrt(long x){
            return (long)Math.sqrt(x);
      }int sqrt(int x){
            return (int)Math.sqrt(x);
      }void input(int[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=ni();
      }void input(long[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=nl();
      }void fill(int[] ar,int k){
            Arrays.fill(ar,k);
      }void yes(){
            pl("YES");
      }void no(){
            pl("NO");
      }
      long c2(long n) {
    	  return (n*(n-1))/2;
      }
    long[] sieve(int n) 
    {
          long[] k=new long[n+1];
          boolean[] pr=new boolean[n+1];
          for(int i=1;i<=n;i++){
                k[i]=i;
                pr[i]=true;
          }for(int i=2;i<=n;i++){
                if(pr[i]){
                      for(int j=i+i;j<=n;j+=i){
                            pr[j]=false;
                            if(k[j]==j){
                                  k[j]=i;
                            }
                      }
                }
          }return k;
    }
    int strSmall(int[] arr, int target)  
    {  
        int start = 0, end = arr.length-1;  
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;   
            if (arr[mid] >= target) {  
                end = mid - 1;  
            }   
            else {  
                ans = mid;  
                start = mid + 1;  
            }  
        }  
        return ans;  
    } int strSmall(ArrayList<Integer> arr, int target)  
    {  
        int start = 0, end = arr.size()-1;  
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;   
            if (arr.get(mid) > target) {  
                start = mid + 1; 
                ans=start;
            }   
            else {
                end = mid - 1;  
            }  
        }  
        return ans;  
    }long mMultiplication(long a,long b) 
    { 
        long res = 0;    
        a %= mod; 
  
        while (b > 0)  
        {  
            if ((b & 1) > 0)  
            { 
                res = (res + a) % mod; 
            }  
            a = (2 * a) % mod; 
  
            b >>= 1;  
        } 
        return res; 
    }long nCr(int n, int r ,long p)
    {
 
          if (n<r) 
              return 0;
        if (r == 0)
            return 1;
            long[] fac = new long[n + 1];
        fac[0] = 1;
 
        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i %p;
        return (fac[n] * modInverse(fac[r], p)
                % p * modInverse(fac[n - r], p)
                % p)
            % p;
    }long power(long x, long y, long p)
    {
        long res = 1;
        x = x % p;
 
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; 
            x = (x * x) % p;
        }
 
        return res;
    }long modInverse(long n, long p)
    {
        return power(n, p - 2, p);
    }
    
    int[][] floydWarshall(int graph[][],int INF,int V)
    {
        int dist[][] = new int[V][V];
        int i, j, k;
        for (i = 0; i < V; i++)
            for (j = 0; j < V; j++)
                dist[i][j] = graph[i][j];
        for (k = 0; k < V; k++)
        {
            for (i = 0; i < V; i++)
            {
                for (j = 0; j < V; j++)
                {
                    if (dist[i][k] + dist[k][j] < dist[i][j])
                        dist[i][j] = dist[i][k] + dist[k][j];
                }
            }
        }return dist;
    }
    class minque {
		Deque<Long> q;
		minque(){
			q=new ArrayDeque<Long>();
		}public void add(long p){
			while(!q.isEmpty()&&q.peekLast()>p)q.pollLast();
			q.addLast(p);
		}public void remove(long p) {
			if(!q.isEmpty()&&q.getFirst()==p)q.removeFirst();
		}public long min() {
			return q.getFirst();
		}
	}
      int find(subset[] subsets, int i)
      {
          if (subsets[i].parent != i)
              subsets[i].parent
                  = find(subsets, subsets[i].parent);
          return subsets[i].parent;
      }void Union(subset[] subsets, int x, int y)
      {
          int xroot = find(subsets, x);
          int yroot = find(subsets, y);
   
          if (subsets[xroot].rank < subsets[yroot].rank) {
          	subsets[xroot].parent = yroot;
          }
          else if (subsets[yroot].rank < subsets[xroot].rank) {
          	subsets[yroot].parent = xroot;
          }
          else {
              subsets[xroot].parent = yroot;
              subsets[yroot].rank++;
          }
      }class subset
      {
          int parent;
          int rank;
      }
	 
} 