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 t = 1, n, m, k, q, l, r, ans, a[29], mn[29], cnt[29][800009], b, c, u, v, x,
    y, z, qwq[1 << 20], sum[1 << 20], f[1 << 20][21], vis[1 << 20][21],
    mod = 1e9 + 7;
string s[29];
struct st {
  int x, y;
};
bool cmp(const st &a, const st &b) { return a.x < b.x; }
inline int read() {
  int s = 0, w = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (ch <= '9' && ch >= '0')
    s = (s << 1) + (s << 3) + (ch ^ 48), ch = getchar();
  return s * w;
}
int qp(int x, int y) {
  int a = 1, b = x;
  while (y) {
    if (y & 1) a = a * b % mod;
    b = b * b % mod, y >>= 1;
  }
  return a;
}
int main() {
  while (t--) {
    n = read();
    for (int i = 1; i <= n; i += 1) {
      cin >> s[i];
      for (int j = 0; j < s[i].length(); j += 1) {
        a[i] += s[i][j] == '(' ? 1 : -1, mn[i] = min(mn[i], a[i]);
        if (mn[i] == a[i]) cnt[i][a[i] + 400001] += 1;
      }
    }
    for (int i = 0; i < (1 << n); i += 1)
      for (int j = 1; j <= n; j += 1)
        if (i & (1 << j - 1)) sum[i] += a[j], qwq[i] += 1;
    for (int i = 1; i < (1 << n); i += 1)
      if (qwq[i] == 1) {
        for (int j = 1; j <= n; j += 1)
          if (i & (1 << j - 1)) {
            if (mn[j] < 0)
              vis[i][j] = 1, ans = max(ans, cnt[i][400001]);
            else
              f[i][j] = cnt[i][400001], ans = max(ans, f[i][j]);
          }
      }
    for (int i = 2; i < (1 << n); i += 1)
      if (qwq[i] > 1) {
        for (int j = 1; j <= n; j += 1)
          if (i & (1 << j - 1)) {
            int sts = (i ^ (1 << j - 1));
            bool wtf = 0;
            for (int k = 1; k <= n; k += 1)
              if (!vis[sts][k] && (sts & (1 << k - 1))) {
                if (sum[sts] + mn[j] < 0)
                  ans = max(ans, f[sts][k] + cnt[j][-sum[sts] + 400001]);
                else
                  wtf = 1,
                  f[i][j] =
                      max(f[i][j], f[sts][k] + cnt[j][-sum[sts] + 400001]),
                  ans = max(ans, f[i][j]);
              }
            if (!wtf) vis[i][j] = 1;
          }
      }
    printf("%lld", ans);
  }
  return 0;
}
