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.*;



public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static int MOD = 998244353;
	static int M = 5005;
	static long INF = (long)1e15;
	
	public static void main(String[] args) throws IOException {

		int n = in.nextInt();
		char[] ca = in.readString().toCharArray();
		char[] a = new char[n+2];
		for(int i=0; i < n; ++i)
			a[i+1] = ca[i];
		
		int[] l = new int[n+2];
		int[] r = new int[n+2];
		
		int x = 0;
		for(int i=1; i <= n; ++i) {
			if(x == -1) {
				l[i] = -1;
				continue;
			}
			if(a[i] == '(')
				x++;
			else
				x--;
			l[i] = x;
		}
		int y = 0;
		for(int i = n; i >= 1; --i) {
			if(y == -1) {
				r[i] = -1;
				continue;
			}
			if(a[i] == ')')
				y++;
			else
				y--;
			r[i] = y;
		}
		
		int cnt = 0;
		for(int i=1; i <= n; ++i) {
			if(l[i-1] == -1 || r[i+1] == -1)
				continue;
			if(a[i] == '(') {
				if(l[i-1] - 1 == r[i+1])
					cnt++;
			}
			else {
				if(l[i-1] + 1 == r[i+1])
					cnt++;
			}
		}
		System.out.println(cnt);
		
		out.close();
	}
	
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int x, y, idx;

		public Pair(int first, int second, int idx) {
			super();
			this.x = first;
			this.y = second;
			this.idx = idx;
		}

		@Override
		public int compareTo(Pair o) {
			return this.x != o.x ? this.x - o.x : this.y - o.y;
		}

		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}

		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (x != other.x)
				return false;
			if (y != other.y)
				return false;
			return true;
		}
	}
	
	
}



class InputReader {

	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;

	public InputReader(InputStream st) {
		this.stream = st;
	}

	public int read() {
		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 = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} 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 = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	public String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	public boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

}