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;
const int64_t mod = 1e9 + 7;
void solve() {
  int64_t n;
  cin >> n;
  vector<string> s(n);
  for (int64_t i = 0; i < n; i++) cin >> s[i];
  vector<vector<int64_t>> mp(n), mp_cnt(n);
  vector<int64_t> str_bal(n);
  for (int64_t i = 0; i < n; i++) {
    mp[i].resize(s[i].size());
    mp_cnt[i].resize(s[i].size());
    int64_t bal = 0, Min = 1;
    for (int64_t j = 0; j < s[i].size(); j++) {
      if (s[i][j] == '(')
        bal++;
      else
        bal--;
      Min = min(Min, bal);
      mp[i][j] = Min;
      if (j > 0 && mp[i][j - 1] == Min) {
        if (bal == Min)
          mp_cnt[i][j] = mp_cnt[i][j - 1] + 1;
        else
          mp_cnt[i][j] = mp_cnt[i][j - 1];
      } else
        mp_cnt[i][j] = 1;
    }
    str_bal[i] = bal;
  }
  int64_t msk = 1 << n;
  vector<int64_t> dp(msk, -1), msk_bal(msk);
  dp[0] = 0;
  int64_t ans = 0;
  for (int64_t i = 1; i < msk; i++) {
    for (int64_t j = 0; j < n; j++) {
      int64_t to = i ^ (1 << j);
      if (to == i || dp[to] == -1) continue;
      msk_bal[i] = msk_bal[to] + str_bal[j];
      int64_t l = 0, r = s[j].size();
      while (l < r) {
        int64_t mid = (l + r) / 2;
        if (mp[j][mid] >= -msk_bal[to])
          l = mid + 1;
        else
          r = mid;
      }
      if (l == s[j].size()) {
        if (mp[j].back() == -msk_bal[to])
          dp[i] = max(dp[i], dp[to] + mp_cnt[j].back());
        else
          dp[i] = max(dp[i], dp[to]);
      } else
        ans = max(ans, dp[to] + (l > 0 ? mp_cnt[j][l - 1] : 0));
    }
  }
  ans = max(ans, dp.back());
  cout << ans << "\n";
  return;
}
signed main() {
  int64_t t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
