import std.conv, std.functional, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


int N;
string S;

void main() {
  /*
  int opt = -1;
  int[][][] ps;
  {
    // auto p = [[3, 1], [4, 1], [5, 9], [2, 1]];
    auto p = [[3, 1], [4, 1], [5, 9], [1, 2]];
    p.sort;
    do {
      int score;
      int[] a = [0, 0];
      foreach (b; p) {
        if (a[1] <= b[0]) {
          score += a[1];
          a = [a[0] + (b[0] - a[1]), b[1]];
        } else {
          score += b[0];
          a = [a[0], (a[1] - b[0]) + b[1]];
        }
      }
      if (chmax(opt, score)) {
        ps = [];
      }
      if (opt == score) {
        ps ~= p.dup;
      }
    } while (p.nextPermutation);
  }
  writeln(opt);
  foreach (p; ps) {
    writeln(p);
  }
  return;
  //*/
  
  try {
    for (; ; ) {
      N = readInt();
      S = readToken();
      long ans;
      alias Entry = Tuple!(long, long);
      Entry[] es;
      Entry e;
      long cnt;
      foreach (c; S) {
        switch (c) {
          case '(': {
            ++e[1];
          } break;
          case ')': {
            if (e[1] > 0) {
              ++cnt;
              --e[1];
            } else {
              ++e[0];
            }
          } break;
          default: assert(false);
        }
        ans += cnt;
        es ~= e;
      }
      debug {
        writeln("es = ", es);
      }
      es.sort!((a, b){
        /*
        const sa = sgn(a[0] - a[1]);
        const sb = sgn(b[0] - b[1]);
        if (sa != sb) {
          return (sa < sb);
        } else if (sa <= 0) {
          return ((a[0] != b[0]) ? (a[0] < b[0]) : (a[1] > b[1]));
        } else {
          return ((a[1] != b[1]) ? (a[1] > b[1]) : (a[0] < b[0]));
        }
        */
        return (min(a[1], b[0]) > min(b[1], a[0]));
      });
      debug {
        writeln("es = ", es);
      }
      Entry f;
      foreach (i; 0 .. N) {
        const t = min(f[1], es[i][0]);
        ans += t;
        f = tuple(f[0] + (es[i][0] - t), (f[1] - t) + es[i][1]);
      }
      ans *= 2;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}