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;

int main() {
  int n;
  cin >> n;
  vector<tuple<bool, int, int, int>> v(n);
  for (auto &e : v) {
    string s;
    cin >> s;
    int l = 0, r = 0;
    for (auto c : s) {
      if (c == '(') {
        l++;
      } else if (l > 0) {
        l--;
      } else {
        r++;
      }
    }
    e = {l <= r, l <= r ? -l : r, l, r};
  }
  sort(v.begin(), v.end());

  bool valid = true;
  int h = 0;
  for (auto [a, b, l, r] : v) {
    // cerr << a << ' ' << b << ' ' << r << ' ' << l << endl;
    if (h < r) {
      valid = false;
      break;
    }
    h -= r;
    h += l;
  }
  if (h != 0) valid = false;
  cout << (valid ? "Yes" : "No") << endl;
}
