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.util.Arrays;

public class Main {

  static class SegmentTreeRMQ {
    public int M, H, N;
    public long[] st;

    public SegmentTreeRMQ(int n) {
      N = n;
      M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
      H = M >>> 1;
      st = new long[M];
      Arrays.fill(st, 0, M, Long.MAX_VALUE);
    }

    public SegmentTreeRMQ(int[] a) {
      N = a.length;
      M = Integer.highestOneBit(Math.max(N - 1, 1)) << 2;
      H = M >>> 1;
      st = new long[M];
      for (int i = 0; i < N; i++) {
        st[H + i] = a[i];
      }
      Arrays.fill(st, H + N, M, Integer.MAX_VALUE);
      for (int i = H - 1; i >= 1; i--)
        propagate(i);
    }

    public void update(int pos, long x) {
      st[H + pos] = x;
      for (int i = (H + pos) >>> 1; i >= 1; i >>>= 1)
        propagate(i);
    }

    private void propagate(int i) {
      st[i] = Math.min(st[2 * i], st[2 * i + 1]);
    }

    public long min(int l, int r) {
      return l >= r ? 0 : min(l, r, 0, H, 1);
    }

    private long min(int l, int r, int cl, int cr, int cur) {
      if (l <= cl && cr <= r) {
        return st[cur];
      } else {
        int mid = cl + cr >>> 1;
        long ret = Long.MAX_VALUE;
        if (cl < r && l < mid) {
          ret = Math.min(ret, min(l, r, cl, mid, 2 * cur));
        }
        if (mid < r && l < cr) {
          ret = Math.min(ret, min(l, r, mid, cr, 2 * cur + 1));
        }
        return ret;
      }
    }

  }

  private static void solve() {
    int n = ni();
    char[] s = ns();

    int[] d = new int[n + 1];
    for (int i = 0; i < n; i++) {
      d[i + 1] = d[i] + (s[i] == '(' ? 1 : -1);
    }
    SegmentTreeRMQ st = new SegmentTreeRMQ(d);

    int ret = 0;
    for (int i = 1; i <= n; i ++) {
      if (s[i - 1] == '(') {
        if (st.min(0, i) == 0 && st.min(i, n + 1) == 2 && d[n] == 2) {
          ret ++;
        }
      } else {
        if (st.min(0, i) == 0 && st.min(i, n + 1) == -2 && d[n] == -2) {
          ret ++;
        }
      }
    }
    System.out.println(ret);

  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}
