A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence (or, shortly, an RBS) is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example:

  * bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"); 
  * bracket sequences ")(", "(" and ")" are not. 



Let's denote the concatenation of two strings x and y as x+y. For example, "()()" + ")(" = "()())(".

You are given n bracket sequences s_1, s_2, ..., s_n. You can rearrange them in any order (you can rearrange only the strings themselves, but not the characters in them).

Your task is to rearrange the strings in such a way that the string s_1 + s_2 + ... + s_n has as many non-empty prefixes that are RBS as possible.

Input

The first line contains a single integer n (1 ≤ n ≤ 20).

Then n lines follow, the i-th of them contains s_i — a bracket sequence (a string consisting of characters "(" and/or ")". All sequences s_i are non-empty, their total length does not exceed 4 ⋅ 10^5.

Output

Print one integer — the maximum number of non-empty prefixes that are RBS for the string s_1 + s_2 + ... + s_n, if the strings s_1, s_2, ..., s_n can be rearranged arbitrarily.

Examples

Input


2
(
)


Output


1


Input


4
()()())
(
(
)


Output


4


Input


1
(())


Output


1


Input


1
)(()


Output


0

Note

In the first example, you can concatenate the strings as follows: "(" + ")" = "()", the resulting string will have one prefix, that is an RBS: "()".

In the second example, you can concatenate the strings as follows: "(" + ")" + "()()())" + "(" = "()()()())(", the resulting string will have four prefixes that are RBS: "()", "()()", "()()()", "()()()()".

The third and the fourth examples contain only one string each, so the order is fixed.
1
)(((((()((())(((((((
 1
)()())((()))((()((()
 10
((((((((((((((((()))))))))))))))))
(((((((((((((((())))))))))))))))
((((((((((((((((((((()))))))))))))))))))))
(((((((((((((((((((((())))))))))))))))))))))
()()()()()()()()()()()()()()()()()()()()
()()()()()()()()()()()()()()()()()()()()()()()()()()
(((((((((((((((((())))))))))))))))))
()()()()()()()()()()()()()()()()()()()
()()()()()()()()()()()()()()()()()()
()()()()()()()()()()()()()()()()()()()()()()()
 20
)
(
)
)
)
)
)
(
(
)
)
)
)
(
)
)
)
)
(
)
 6
()()()()()
()()()()
()
((((()))))
((()))
()()
 1
((((((((((((((((((((
 10
((((((((((((((((((((((((()))))))))))))))))))))))))
()()()()()()()()()()()()()()()()()()()
(((((((((((((((((())))))))))))))))))
()()()()()()()()()()()()()()()()()()()()()()
((((((((((((((((((()))))))))))))))))))
((((((((((((((((((((((()))))))))))))))))))))))
()()()()()()()()()()()()()()()()()()()
((((((((((((((()))))))))))))))
()()()()()()()()()()()()()()()()()()()()()()()()
()()()()()()()()()()()()()()()()
 2
))())))((()
()((((((()))))))(()
 20
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
 20
(
(
)
(
(
)
(
(
(
(
(
(
)
)
(
(
(
(
(
)
 10
()()
(())
()()
()()
(())
(((())))
()
(())
()()
()
 1
))))))))))))))))))))
 6
(((())))
(((())))
()()()
(())
()()()()()
()()
 10
)
)
))
))
))
))
))
))
)))
)))
 10
)()
()
)
)
)
)(
)))
)(
(((
))
 20
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
(
 10
))
()(
(
()
()
((((
(
(
(((
(
 10
()
()()()()
(())
((()))
(())
()()
(())
()()
()
()
 10
())
()
)
)))
))
()
)
))
)))
)
 1
))))))()))())(()))))
 10
((
(((
(
(((
((((
((
(
(
(
((
 20
)
(
(
)
)
(
)
(
(
(
)
)
)
)
(
)
(
(
)
(

0
 0
 111
 5
 14
 0
 105
 3
 0
 5
 14
 0
 13
 0
 5
 0
 4
 15
 3
 0
 0
 10

#include <bits/stdc++.h>
using namespace std;
namespace Ruri {
const int infi = 1e9;
const long long infl = 4e18;
inline long long ceil_div(long long a, long long b) { return (a + b - 1) / b; }
inline long long pos_mod(long long a, long long b) { return (a % b + b) % b; }
}  // namespace Ruri
using namespace Ruri;
namespace Read {
inline int ri() {
  int x;
  scanf("%d", &x);
  return x;
}
inline long long rl() {
  long long x;
  scanf("%lld", &x);
  return x;
}
inline double rd() {
  double x;
  scanf("%lf", &x);
  return x;
}
}  // namespace Read
namespace DeBug {}
using namespace Read;
using namespace DeBug;
int main() {
  ios::sync_with_stdio(false);
  int n = ri();
  vector<string> s(n);
  vector<int> len(n), delta(n), mn_delta(n, 0);
  vector<vector<vector<int> > > pos(n);
  for (int i = 0, bbb = n - 1; i <= bbb; ++i) {
    cin >> s[i];
    len[i] = s[i].length();
    pos[i].resize(2 * len[i] + 1);
    int now = len[i];
    for (int j = 0, bbb = len[i] - 1; j <= bbb; ++j) {
      now += (s[i][j] == '(' ? 1 : -1);
      pos[i][now].push_back(j + 1),
          mn_delta[i] = min(mn_delta[i], now - len[i]);
    }
    delta[i] = now - len[i];
  }
  int ans = 0;
  vector<int> dp(1 << n, -1);
  dp[0] = 0;
  for (int mask = 0, bbb = (1 << n) - 1; mask <= bbb; ++mask)
    if (~dp[mask]) {
      int psum = 0;
      for (int bit = 0, bbb = n - 1; bit <= bbb; ++bit)
        if ((mask >> bit) & 1) psum += delta[bit];
      for (int bit = 0, bbb = (n - 1); bit <= bbb; ++bit)
        if (!((mask >> bit) & 1)) {
          int balance_pos = len[bit] - psum;
          if (psum + mn_delta[bit] < 0) {
            int bound = pos[bit][balance_pos - 1][0];
            int res = (int)(lower_bound(pos[bit][balance_pos].begin(),
                                        pos[bit][balance_pos].end(), bound) -
                            pos[bit][balance_pos].begin());
            ans = max(ans, dp[mask] + res);
            continue;
          }
          int add = 0;
          if (0 <= balance_pos && balance_pos <= 2 * len[bit])
            add = (int)pos[bit][balance_pos].size();
          dp[mask | (1 << bit)] = max(dp[mask | (1 << bit)], dp[mask] + add);
        }
    }
  printf("%d\n", max(ans, dp.back()));
  return 0;
}
