A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /



Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.

Input

Input is given from Standard Input in the following format:


N
S_1
:
S_N


Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

4
((()))
((((((
))))))
()()()


Output

Yes


Input

3
(((
)
)


Output

No
#include <bits/stdc++.h>
using namespace std;
using P = pair<int, int>;

int main() {
  int N, total = 0;
  cin >> N;
  string S;
  vector<P> p, m;
  for (int i = 0; i < N; i++) {
    cin >> S;
    int d = 0, b = 0;
    for (char c: S) {
      if (c == '(')
        d++;
      else
        d--;
      b = min(b, d);
    }
    if (d>=0)
      p.push_back({b, d});
    else
      m.push_back({b-d, d});
    total += d;
  }
  sort(p.rbegin(), p.rend());
  sort(m.begin(), m.end());
  bool check = (total == 0);
  int h = 0;
  for (P e: p) {
    if (h+e.first<0)
      check = false;
    h += e.second;
  }
  for (P e: m) {
    if (h+e.first+e.second<0)
      check = false;
    h += e.second;
  }
  if (check)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}