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 int INF = int(1e9);
const int N = 20;
const int M = (1 << N);
struct BracketSeqn {
  int balance;
  int lowestBalance;
  vector<int> queryAns;
  pair<int, bool> go(int x, bool f) {
    if (f)
      return make_pair(0, true);
    else
      return make_pair(x < queryAns.size() ? queryAns[x] : 0,
                       x + lowestBalance < 0);
  }
  BracketSeqn(){};
  BracketSeqn(string s) {
    vector<int> bal;
    int cur = 0;
    int n = s.size();
    for (auto x : s) {
      if (x == '(')
        cur++;
      else
        cur--;
      bal.push_back(cur);
    }
    balance = bal.back();
    lowestBalance = min(0, *min_element(bal.begin(), bal.end()));
    vector<vector<int>> negPos(-lowestBalance + 1);
    for (int i = 0; i < n; i++) {
      if (bal[i] > 0) continue;
      negPos[-bal[i]].push_back(i);
    }
    queryAns.resize(-lowestBalance + 1);
    for (int i = 0; i < queryAns.size(); i++) {
      int lastPos = int(1e9);
      if (i != -lowestBalance) lastPos = negPos[i + 1][0];
      queryAns[i] = lower_bound(negPos[i].begin(), negPos[i].end(), lastPos) -
                    negPos[i].begin();
    }
  };
};
int dp[M][2];
char buf[M];
int total_bal[M];
int main() {
  int n;
  scanf("%d", &n);
  vector<BracketSeqn> bs;
  for (int i = 0; i < n; i++) {
    scanf("%s", buf);
    string s = buf;
    bs.push_back(BracketSeqn(s));
  }
  for (int i = 0; i < (1 << n); i++)
    for (int j = 0; j < n; j++)
      if (i & (1 << j)) total_bal[i] += bs[j].balance;
  for (int i = 0; i < (1 << n); i++)
    for (int j = 0; j < 2; j++) dp[i][j] = -int(1e9);
  dp[0][0] = 0;
  for (int i = 0; i < (1 << n); i++)
    for (int f = 0; f < 2; f++) {
      if (dp[i][f] < 0) continue;
      for (int k = 0; k < n; k++) {
        if (i & (1 << k)) continue;
        pair<int, bool> res = bs[k].go(total_bal[i], f);
        dp[i ^ (1 << k)][res.second] =
            max(dp[i ^ (1 << k)][res.second], dp[i][f] + res.first);
      }
    }
  printf("%d\n", max(dp[(1 << n) - 1][0], dp[(1 << n) - 1][1]));
}
