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 <algorithm>
#include <cstdio>
#include <string>
#define MAXN 1000001
#define a first
#define b second

char buf[MAXN];
std::pair<int, int> s[MAXN];

int main() {
  using namespace std;

  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%s", buf);
    s[i].a = s[i].b = 0;
    for (int j = 0; buf[j]; ++j) {
      if (buf[j] == '(')
        ++s[i].a;
      else {
        if (s[i].a)
          --s[i].a;
        else
          ++s[i].b;
      }
    }
  }

  auto cmp = [](const pair<int, int> &l, const pair<int, int> &r) {
    if (l.a <= l.b && r.a > r.b)
      return true;
    else if (l.a > l.b && r.a <= r.b)
      return false;
    else if (l.a > l.b && r.a > r.b)
      return l.b > r.b;
    else
      return l.a < r.a;
  };

  std::sort(s, s + n, cmp);

  int t = 0;
  for (int i = 0; i < n; i++) {
    if (t < s[i].a) {
      printf("No\n");
      return 0;
    }
    t += s[i].b - s[i].a;
  }
  if (t)
    printf("No\n");
  else
    printf("Yes\n");

  return 0;
}
