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;
#pragma GCC optimize(2)
#pragma GCC optimize(3)
inline int read() {
  int x = 0, f = 0;
  char ch = getchar();
  while (!isdigit(ch)) f |= ch == '-', ch = getchar();
  while (isdigit(ch)) x = 10 * x + ch - '0', ch = getchar();
  return f ? -x : x;
}
inline long long llread() {
  long long x = 0, f = 0;
  char ch = getchar();
  while (!isdigit(ch)) f |= ch == '-', ch = getchar();
  while (isdigit(ch)) x = 10 * x + ch - '0', ch = getchar();
  return f ? -x : x;
}
long long n;
char s[25][400010], l[25], rest[25];
vector<long long> v[25][400010];
long long dp[(1 << 20) + 10][2], g[(1 << 20) + 10];
signed main() {
  n = llread();
  for (long long i = (1); i <= (n); i++) cin >> s[i];
  for (long long i = (1); i <= (n); i++) l[i] = strlen(s[i]);
  for (long long i = (1); i <= (n); i++) {
    long long top = 0;
    for (long long j = (1); j <= (l[i]); j++) {
      if (s[i][j - 1] == ')')
        top++;
      else
        top--;
      if (top >= 0) v[i][top].push_back(j);
    }
    rest[i] = top;
  }
  for (long long i = (1); i <= ((1 << n) - 1); i++) dp[i][0] = dp[i][1] = -1e18;
  dp[0][0] = dp[0][1] = g[0] = 0;
  for (long long mask = (1); mask <= ((1 << n) - 1); mask++) {
    for (long long i = (1); i <= (n); i++) {
      if (mask & (1 << (i - 1))) {
        long long S = mask ^ (1 << (i - 1));
        if (g[S] >= 0) {
          long long x;
          if (v[i][g[S] + 1].size() == 0)
            x = l[i] + 1;
          else
            x = v[i][g[S] + 1][0];
          long long y = lower_bound(v[i][g[S]].begin(), v[i][g[S]].end(), x) -
                        v[i][g[S]].begin();
          if (x == l[i] + 1) {
            if ((dp[mask][1]) < (dp[S][1] + y)) {
              (dp[mask][1]) = (dp[S][1] + y);
            };
          }
          if ((dp[mask][0]) < (dp[S][1] + y)) {
            (dp[mask][0]) = (dp[S][1] + y);
          };
          if ((dp[mask][0]) < (dp[S][0])) {
            (dp[mask][0]) = (dp[S][0]);
          };
        } else {
          if ((dp[mask][0]) < (dp[S][0])) {
            (dp[mask][0]) = (dp[S][0]);
          };
        }
        g[mask] = g[S] - rest[i];
      }
    }
  }
  printf("%lld\n", max(dp[(1 << n) - 1][0], dp[(1 << n) - 1][1]));
  return 0;
}
