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.util.*;
import java.text.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.regex.*;
public class Main {
           public static ArrayList a[]=new ArrayList[300001];
           
			public static void main(String[] args) 
	        {
	            InputReader in = new InputReader(System.in);
	            PrintWriter pw = new PrintWriter(System.out);
	            int n=in.nextInt();
	            char s[]=in.nextLine().toCharArray();
	            if(n%2==1) {
	            	pw.println(0);
	            	pw.flush();
	            	pw.close();
	            	System.exit(0);
	            }
	            int suf[]=new int[n];
	            int pre[]=new int[n];
	            boolean suf1[]=new boolean [n];
	            boolean pre1[]=new boolean [n];
	            if(s[0]=='(')
	            {
	            	pre1[0]=true;
	            	pre[0]=1;
	            }
	            else
	            	pre[0]=-1;
	            for(int i=1;i<n;i++) {
	            	pre1[i]|=pre1[i-1];
	            	if(s[i]=='(')
	            		pre[i]=pre[i-1]+1;
	            	else
	            		pre[i]=pre[i-1]-1;
	            	if(pre[i]<0)
	            		pre1[i]=false;
	            }
	            if(s[n-1]==')')
	            {
	            	suf1[n-1]=true;
	            	suf[n-1]=-1;
	            }
	            else
	            	suf[n-1]=1;
	            for(int i=n-2;i>=0;i--) {
	            	suf1[i]|=suf1[i+1];
	            	if(s[i]=='(')
	            		suf[i]=suf[i+1]+1;
	            	else
	            		suf[i]=suf[i+1]-1;
	            	if(suf[i]>0)
	            		suf1[i]=false;
	            }
	            int ans=0;
	            if(suf1[1] && suf[1]==-1 && s[0]==')')
	            	ans++;
	            for(int i=1;i<n-1;i++) {
	            	if(suf1[i+1] && pre1[i-1]) {
	            		if(s[i]=='(')
	            		{
	            			if(pre[i-1]+suf[i+1]-1==0)
	            				ans++;
	            		}
	            		else
	            		{
	            			if(pre[i-1]+suf[i+1]+1==0)
	            				ans++;
	            		}
	            	}
	            }
	            if(pre1[n-2] && pre[n-2]==1 && s[n-1]=='(')
	            	ans++;
	            pw.println(ans);
	            pw.flush();
	            pw.close();
	        
	        }
		private static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		static class trie{
			
			Integer cnt;
			trie a[];
			trie(){
				cnt=0;
			    a=new trie[2];
			}
			
		}
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static long d;
        public static long p;
        public static long q;
        
        public static int[] suffle(int[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                int temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static int primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            int ans=Integer.MIN_VALUE;
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    ans=Math.max(ans, i);
                    n/=i;
                }
            }
            if(n!=1)
            	ans=Math.max(ans, n);
            return ans;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static int GCD(int a,int b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        
        public static long GCD(long a,long b)
        {
            if(b==0)
                return a;
            else
                return GCD(b,a%b);
        }
        
        public static void extendedEuclid(long d1,long d2)
        {
            if(d2==0)
            {
                d = d1;
                p = 1 ;
                q = 0;
            }
            else
            {
                extendedEuclid(d2, d1%d2);
                long temp = p;
                p = q;
                q = temp - (d1/d2)*q;
            }
        }
        
        public static long LCM(long a,long b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int LCM(int a,int b)
        {
            return (a*b)/GCD(a,b);
        }
        
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static boolean isPrime(int n)
        {
            
            if (n <= 1)  return false;
            if (n <= 3)  return true;
            
            if (n%2 == 0 || n%3 == 0) 
                return false;
         
            for (int i=5; i*i<=n; i=i+6)
            {
                if (n%i == 0 || n%(i+2) == 0)
                   return false;
            }
            
            return true;
        }
        
         public static pair[] shuffle(pair[] t, Random gen){ 
                for(int i = 0, n = t.length;i < n;i++){ 
                    int ind = gen.nextInt(n-i)+i; 
                    pair d = t[i]; 
                    t[i] = t[ind]; 
                    t[ind] = d; 
                } 
                return t; 
            }
        static class pair implements Comparable<pair>
        {
            Long x;
            Integer y;
            pair(long a,int w)
            {
                this.x=a;
                this.y=w;
            }
 

 
 
 
 
 
        public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            
            public int hashCode()
            {
                return new Long(x).hashCode()*31 + new Long(y).hashCode();
            }
        }
        
}