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>

#define fr(i, a, b) for(int i = (a); i <= (b); i++)
#define rf(i, a, b) for(int i = (a); i >= (b); i--)
#define fe(x, y) for(auto& x : y)

#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple

#define pw(x) (1LL << (x))
#define sqr(x) (1LL * (x) * (x))
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()

using namespace std;

using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template<typename T>
using ve = vector<T>;

#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<typename T>
using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define fbo find_by_order
#define ook order_of_key

mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());

template<typename T>
bool umn(T& a, T b) { return a > b ? a = b, 1 : 0; }
template<typename T>
bool umx(T& a, T b) { return a < b ? a = b, 1 : 0; }

const int N = 8e5 + 5;

int n;
int cnt_[20][N];
int pos_[20][N];
int last[20];
int mn[20];
string s[20];

int dp[pw(20)];

int& cnt(int i, int bal) {
    return cnt_[i][bal + 400001];
}

int& pos(int i, int bal) {
    return pos_[i][bal + 400001];
}

int main() {
#ifndef LOCAL
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    ios::sync_with_stdio(0);
    cin.tie(0);
#else
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
#endif

    cin >> n;

    fr(i, 0, n - 1) {
        cin >> s[i];
        int bal = 0;
        mn[i] = 1;
        fr(j, 0, sz(s[i]) - 1) {
            if(s[i][j] == '(') bal++;
            else bal--;
            
            if(cnt(i, bal) == 0) {
                pos(i, bal) = cnt(i, bal + 1);
            }
            cnt(i, bal)++;
            umn(mn[i], bal);
        }
        last[i] = bal;
    }

    int best = 0;
    fr(mask, 0, pw(n) - 1) {
        int bal = 0;
        fr(i, 0, n - 1) {
            if(mask & pw(i)) {
                bal += last[i];
            }
        }

        fr(i, 0, n - 1) {
            if(!(mask & pw(i))) {
                if(mn[i] + bal >= 0) {
                    umx(dp[mask | pw(i)], dp[mask] + cnt(i, -bal));
                } else {
                    umx(best, dp[mask] + pos(i, -bal - 1));
                }
            }
        }
    }

    fr(mask, 0, pw(n) - 1) {
        umx(best, dp[mask]);
    }

    cout << best << "\n";

    return 0;
}