A bracketed sequence is called correct (regular) if by inserting "+" and "1" you can get a well-formed mathematical expression from it. For example, sequences "(())()", "()" and "(()(()))" are correct, while ")(", "(()" and "(()))(" are not.

The teacher gave Dmitry's class a very strange task — she asked every student to come up with a sequence of arbitrary length, consisting only of opening and closing brackets. After that all the students took turns naming the sequences they had invented. When Dima's turn came, he suddenly realized that all his classmates got the correct bracketed sequence, and whether he got the correct bracketed sequence, he did not know.

Dima suspects now that he simply missed the word "correct" in the task statement, so now he wants to save the situation by modifying his sequence slightly. More precisely, he can the arbitrary number of times (possibly zero) perform the reorder operation.

The reorder operation consists of choosing an arbitrary consecutive subsegment (substring) of the sequence and then reordering all the characters in it in an arbitrary way. Such operation takes l nanoseconds, where l is the length of the subsegment being reordered. It's easy to see that reorder operation doesn't change the number of opening and closing brackets. For example for "))((" he can choose the substring ")(" and do reorder ")()(" (this operation will take 2 nanoseconds).

Since Dima will soon have to answer, he wants to make his sequence correct as fast as possible. Help him to do this, or determine that it's impossible.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of Dima's sequence.

The second line contains string of length n, consisting of characters "(" and ")" only.

Output

Print a single integer — the minimum number of nanoseconds to make the sequence correct or "-1" if it is impossible to do so.

Examples

Input


8
))((())(


Output


6


Input


3
(()


Output


-1

Note

In the first example we can firstly reorder the segment from first to the fourth character, replacing it with "()()", the whole sequence will be "()()())(". And then reorder the segment from the seventh to eighth character, replacing it with "()". In the end the sequence will be "()()()()", while the total time spent is 4 + 2 = 6 nanoseconds.
import java.io.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.math.*;
 
public class Main{
    static ArrayList[] a = new ArrayList[200001];
    static long f(long x , long y , long a , long b) {
    	long x1 = a - x + 1;
    	long y1 = b - y + 1;
    	if(x1 >= 0 && y1 >= 0 )
    		return x1 * y1;
    	else
    		return 0L;
    }
	public void solve () throws IOException  {
       
    	InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        
        int n = in.nextInt();
        char s[] = in.nextLine().toCharArray();
        int cnt = 0;
        for(int i = 0 ; i < n ; i++)
        {
        	if(s[i] == '(') cnt ++;
        }
        if(cnt != n - cnt) {
        	pw.println(-1);
        }
        else {
        	int val = 0;
        	int idx = -1;
        	int ans = 0;
        	for(int i = 0 ; i < n ; i++) {
        		if(s[i] == '(') val ++;
        		if(s[i] == ')') val --;
        		if(val < 0 && idx == -1) {
        			idx = i;
        		}
        		if(idx > -1 && val >= 0) {
        			ans += (i - idx + 1);
        			idx = -1;
        		}
        	}
        	pw.println(ans);
        }
        pw.flush(); 
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                    try {
                        new Main().solve();
                    } catch (FileNotFoundException e) {
                        e.printStackTrace();
                    } catch (IOException e) {
						e.printStackTrace();
					}
            }  
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        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;
        }
 
        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 int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        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 long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long 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 HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        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 long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
            Integer y ;
            Long x ;
            
            pair(long  l, int w )
            {
                this.x=l;
                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()*3 + new Long(y).hashCode();
                
            }
        }
        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 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);
        }
        static class Segment{ 
    		int seg[]; 
    		int a[];
    		int lazy[];
    	    Segment (int n,int b[]){
    			seg=new int[4*n];
    			lazy=new int[4*n];
    			a=new int[b.length];
    			a=b.clone();
    		}
    	    public void build(int node,int start,int end) {
    	    	if(start==end) {
    	    		seg[node]=a[start];
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	build(2*node+1,start,mid);
    	    	build(2*node+2,mid+1,end);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public void update(int node,int start,int end,int id,int val) {
    	    	if(start==end) {
    	    		seg[node]=a[start]=val;
    	    		return;
    	    	}
    	    	int mid=(start+end)/2;
    	    	if(id>=start && id<=mid) {
    	    		update(2*node+1,start,mid,id,val);
    	    	}
    	    	else
    	    		update(2*node+2,mid+1,end,id,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int query(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    	    }
    	    public void updateRange(int node,int start,int end,int l,int r,int val) {
    	    	if(lazy[node]!=0) {
	    			seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(l>end || r<start)
    	    		return ;
    	    	if(start>=l && end<=r) {
    	    		seg[node] += val;
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=val;
    	    			lazy[2*node+2]+=val;
    	    		}
    	    		lazy[node]=0;
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	updateRange(2*node+1,start,mid,l,r,val);
    	    	updateRange(2*node+2,mid+1,end,l,r,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int queryRange(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(lazy[node]!=0) {
    	    		seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (queryRange(2*node+1,start,mid,l,r)+queryRange(2*node+2,mid+1,end,l,r));
    	    }
    	    
    	}
       
        
                    
         
}