package contest180511;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class C {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	int simulate(int a, int b, int c, int d, int e, int f)
	{
		int o = a;
		int ret = 0;
		ret += Math.min(o, b);
		o -= Math.min(o, b);
		o += c;
		ret += Math.min(o, d);
		o -= Math.min(o, d);
		o += e;
		ret += Math.min(o, f);
		return ret;
	}
	
	void solve()
	{
		// O+(c1,o1) +(c2,o2)+C
		// min(O,c1) max(O-c1,0)+o1 
		int n = ni();
		char[] s = ns(n);
		
		int[][] as = new int[n][];
		int o = 0, c = 0;
		int g = 0;
		int hh = 0;
		long ans = 0;
		for(int i = 0;i < n;i++){
			if(s[i] == '('){
				o++;
				hh++;
			}else{
				c++;
				hh--;
				if(hh >= 0){
					g++;
				}
			}
			ans += g;
			as[i] = new int[]{-1, o-g, c-g};
		}
		Arrays.sort(as, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				for(int i = 0;i < 1000000;i+=999999){
					for(int j = 0;j < 1000000;j+=999999){
						int v = -(simulate(i, a[2], a[1], b[2], b[1], j) - simulate(i, b[2], b[1], a[2], a[1], j));
						if(v != 0)return v;
					}
				}
				return 0;
			}
		});
		long open = 0;
		for(int[] a : as){
			ans += Math.min(open, a[2]);
			open -= Math.min(open, a[2]);
			open += a[1];
		}
		out.println(ans*2);
	}
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//			@Override
//			public void run() {
//				long s = System.currentTimeMillis();
//				solve();
//				out.flush();
//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//			}
//		};
//		t.start();
//		t.join();
	}
	
	public static void main(String[] args) throws Exception { new C().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}