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

import io,os
import bisect
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline



def getnext(state,pre,infor,dic,dp):


    if state in dp:  return dp[state]

#    print(state,pre[state])
    output = 0
    for i in range(len(infor)):
        if state & (1<<i) > 0:  continue 
        if pre[state] + infor[i][1] < 0:
           
            firstappear = dic[i][-pre[state]-1][0]

            temp = 0
            if -pre[state] in dic[i]:
                temp = bisect.bisect_left( dic[i][-pre[state]], firstappear )
            output = max(output,temp)
            continue 

        base = 0
        if -pre[state] in dic[i]:  base = len( dic[i][-pre[state]] )

        temp = base + getnext(state+(1<<i), pre,infor,dic,dp)
        output = max(output,temp)

    dp[state] = output 
    return output 
 

            
            
        



   


    
    




    



def main(t):


    n = int(input())
    grid = []
    infor = []
    dic = [{} for _ in range(n)]

    pre = [0 for _ in range(1<<n)]


    for k in range(n): 
        curr = 0
        minimum = 1
        s = input()
        for i in range(len(s)):
            if s[i]==ord('('):  curr += 1
            elif s[i]==ord(')'):  curr -= 1
            else: break
            if curr < minimum:  minimum = curr
            if curr not in dic[k]:  dic[k][curr] = []
            dic[k][curr].append(i)
        infor.append([curr, minimum, len(dic[k][minimum])]  )  


    for state in range(1<<n):
        s = bin(state)[2:][::-1]
        s += '0'*(n-len(s))

        for i in range(n):
            if s[i]=='1':   pre[state] += infor[i][0]


             

    dp = {}
    ans = getnext(0,pre,infor,dic,dp)
#    print(dp)
#    print(pre)
#    print(infor)


    print(ans)

        
            



        
























T = 1 #int(input())
t = 1
while t<=T:
    main(t)
    t += 1
