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;
int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  return x * f;
}
const int maxn = 4e5 + 2;
const int N = 1e6 + 1e5;
int n, dp[N], sum[22][maxn], minpos[22][maxn];
vector<int> se[21][maxn * 2];
string s[22];
int main() {
  n = read();
  memset(dp, -1, sizeof(dp));
  dp[0] = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> s[i];
    for (int j = 0; j < s[i].length(); ++j) {
      if (s[i][j] == '(')
        sum[i][j + 1] = sum[i][j] + 1;
      else
        sum[i][j + 1] = sum[i][j] - 1;
      if (minpos[i][maxn + sum[i][j + 1]] == 0)
        minpos[i][maxn + sum[i][j + 1]] = j + 1;
      se[i][maxn + sum[i][j + 1]].push_back(j + 1);
    }
  }
  for (int i = 1; i < (1 << n); ++i) {
    for (int j = 0; j < n; ++j) {
      if ((i & (1 << j)) != 0) {
        int las = i ^ (1 << j);
        int tnum = 0;
        for (int k = 0; k < n; ++k) {
          if (las & (1 << k)) {
            tnum += sum[k + 1][s[k + 1].length()];
          }
        }
        if (tnum < 0 || dp[las] == -1) {
          dp[i] = max(dp[i], dp[las]);
          continue;
        }
        int sup = minpos[j + 1][maxn - tnum - 1];
        int temp = 0;
        if (sup == 0)
          temp = se[j + 1][maxn - tnum].size();
        else {
          int real = maxn - tnum;
          int l = 0, r = se[j + 1][real].size() - 1;
          if (r < l) continue;
          if (se[j + 1][real][r] < sup)
            temp = se[j + 1][real].size();
          else if (se[j + 1][real][l] >= sup)
            temp = 0;
          else {
            while (l + 1 < r) {
              int mid = (l + r) / 2;
              if (se[j + 1][real][mid] < sup)
                l = mid;
              else
                r = mid;
            }
            temp = l + 1;
          }
        }
        dp[i] = max(dp[i], dp[las] + temp);
      }
    }
  }
  cout << dp[(1 << n) - 1];
}
