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;

template <class T> inline bool chmax(T &a, T b) { /* {{{ */
  if (a < b) {
    a = b;
    return true;
  }
  return false;
} /* }}} */

bool check(vector<pair<int, int>> v) {
  int now = 0;
  for (auto p : v) {
    if (now - p.first < 0) return false;
    now += p.second;
  }
  return true;
}

int main() {
  int N;
  cin >> N;
  vector<pair<int, int>> v1, v2;
  int total = 0;
  for (int i = 0; i < N; i++) {
    string s;
    cin >> s;
    int cnt = 0;
    int m = 0;
    for (auto c : s) {
      if (c == '(') {
        cnt++;
      } else {
        cnt--;
      }
      chmax(m, -cnt);
    }
    if (cnt >= 0) {
      v1.push_back({m, cnt});
    } else {
      v2.push_back({cnt + m, -cnt});
    }
    total += cnt;
  }
  if (total != 0) {
    cout << "No" << endl;
    return 0;
  }

  sort(v1.begin(), v1.end());
  sort(v2.begin(), v2.end());

  if (check(v1) && check(v2)) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }

  return 0;
}
/* vim:set fdm=marker: */
