Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in Julia (1.4.0) (judge verdict: Wrong Answer)

function main()
    function calc_low_total()
        total = low = 0
        for c in readline()
            if c == '('
                total += 1
            else
                total -= 1
                low = min(low,total)
            end
        end
        (ifelse(0<=total,1,-1),low,total)
    end
    flag = true
    res = 0
    for (p_or_n,low,total)  in sort([calc_low_total() for i in 1:parse(Int,readline())],rev=true)
        if res+low < 0
            flag = false
            break
        end
        res+=total
    end
    println(ifelse(flag && res == 0,"Yes","No"))
end
main()