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>
template <class C>
C& mini(C& a, C b) {
  if (b < a) a = b;
  return a;
}
template <class C>
C& maxi(C& a, C b) {
  if (a < b) a = b;
  return a;
}
template <typename T>
void read(std::vector<T>& A) {
  for (T& x : A) std::cin >> x;
}
template <typename T>
void readv(std::vector<T>& A) {
  int N;
  std::cin >> N;
  A.resize(N);
  read(A);
}
using namespace std;
struct Bracket {
  string S;
  int tot;
  map<int, int> cnt;
  void init() {
    int c = 0;
    int low = 0;
    for (char x : S) {
      if (x == '(') {
        c++;
      } else {
        c--;
        if (c <= low) {
          cnt[c]++;
          if (c < low) low = c;
        }
      }
    }
    tot = c;
  }
  int solve(int base) { return cnt[-base]; }
};
vector<Bracket> brackets;
vector<int> sumtot;
int dp[1 << 20];
int solve(int mask) {
  int& ret = dp[mask];
  if (ret >= 0) return ret;
  int lvl = sumtot[(sumtot.size() - 1) ^ mask];
  if (lvl < 0) return ret = 0;
  ret = 0;
  for (int i = 0; i < brackets.size(); i++)
    if (mask & (1 << i)) {
      int r = solve(mask ^ (1 << i)) + brackets[i].solve(lvl);
      maxi(ret, r);
    }
  return ret;
}
int main(int argc, const char* argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.precision(20);
  cout.setf(ios::fixed);
  int N;
  cin >> N;
  brackets.resize(N);
  for (auto& b : brackets) {
    cin >> b.S;
    b.init();
  }
  sumtot.resize(1 << N);
  for (int m = 1; m < sumtot.size(); m++) {
    int lb = __builtin_ctz(m);
    sumtot[m] = sumtot[m ^ (1 << lb)] + brackets[lb].tot;
  }
  memset(dp, -1, sizeof(dp[0]) << N);
  cout << solve((1 << N) - 1) << endl;
  return 0;
}
