#include <bits/stdc++.h>
using namespace std;
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long double pii = 3.14159265359;
const int MOD = 1000000007;
const char nl = '\n';
const int MX = 200001;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int N;
  cin >> N;
  map<int, int> m;
  m[0] = 1;
  long long ans = 0;
  for (int x = 0; x < (N); x++) {
    string str;
    cin >> str;
    int cnt = 0, mn = INT_MAX;
    for (int y = 0; y < ((int)(str).size()); y++) {
      if (str[y] == '(')
        cnt++;
      else
        cnt--;
      ckmin(mn, cnt);
    }
    if (mn < 0) {
      if (cnt == mn) {
        ans += m[-cnt];
        m[cnt]++;
      }
    } else if (cnt > 0) {
      ans += m[-cnt];
      m[cnt]++;
    } else if (cnt == 0) {
      ans += 2 * m[0] - 1;
      m[0]++;
    }
  }
  cout << ans << nl;
  return 0;
}
