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 MOD = 1000000007;
const int inf = 0x3f3f3f3f;
const int N = 410000;
const int M = 20;
template <typename T>
inline bool scan_d(T& ret) {
  char c;
  int sgn;
  if (c = getchar(), c == EOF) return 0;
  while (c != '-' && (c < '0' || c > '9')) {
    if ((c = getchar()) == EOF) return 0;
  }
  sgn = (c == '-') ? -1 : 1;
  ret = (c == '-') ? 0 : (c - '0');
  while (c = getchar(), c >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  ret *= sgn;
  return 1;
}
template <typename T>
void print(T x) {
  static char s[33], *s1;
  s1 = s;
  if (!x) *s1++ = '0';
  if (x < 0) putchar('-'), x = -x;
  while (x) *s1++ = (x % 10 + '0'), x /= 10;
  while (s1-- != s) putchar(*s1);
}
template <typename T>
void println(T x) {
  print(x);
  putchar('\n');
}
struct TPoint {
  string s;
  int x, y;
  map<int, int> v;
  void solve() {
    x = y;
    v.clear();
    int n = s.length();
    vector<int> a(n + 2, -1);
    vector<int> b(n + 2, -1);
    a[0] = b[0] = 0;
    a[n + 1] = b[n + 1] = 0;
    stack<char> s1, s2, s3;
    for (int i = (0); i < (n); ++i) {
      if (!s1.empty() && s1.top() == '(' && s[i] == ')')
        s1.pop();
      else
        s1.push(s[i]);
      if (s1.empty() || s1.top() == ')') a[i + 1] = s1.size();
      if (s1.empty() || s1.top() == ')') v[s1.size()]++;
    }
    for (int i = (n)-1; i >= (0); --i) {
      if (!s2.empty() && s2.top() == ')' && s[i] == '(')
        s2.pop();
      else
        s2.push(s[i]);
      if (s2.empty() || s2.top() == '(') b[i + 1] = s2.size();
    }
    for (int i = (0); i < (n + 1); ++i) {
      if (a[i] != -1 && b[i + 1] != -1) {
        x = a[i], y = b[i + 1];
        break;
      }
    }
  }
};
TPoint a[M];
int n, dp[(1ll << (M))], b[(1ll << (M))];
char sread[N];
void fmain() {
  scan_d(n);
  for (int i = (0); i < (n); ++i) {
    scanf("%s", sread);
    a[i].s.assign(sread);
    a[i].solve();
  }
  int res = 0;
  for (int cur = (1); cur < ((1ll << (n))); ++cur) {
    dp[cur] = -1;
    for (int i = (0); i < (n); ++i)
      if (cur & (1ll << (i))) {
        int las = cur ^ (1ll << (i));
        if (dp[las] == -1) continue;
        if (a[i].x > b[las]) {
          res = max(res, dp[las] + a[i].v[b[las]]);
          continue;
        }
        int val = dp[las];
        int leave = b[las] - a[i].x;
        if (leave == 0) val += a[i].v[b[las]];
        if (dp[cur] <= val) {
          dp[cur] = val;
          b[cur] = leave + a[i].y;
        }
      }
  }
  res = max(res, dp[(1ll << (n)) - 1]);
  println(res);
}
int main() {
  char ch;
  while (scanf(" %c", &ch) != EOF) {
    ungetc(ch, stdin);
    fmain();
  }
  return 0;
}
