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()
	N=parse(Int,readline())
	pos=Pair{Int,Int}[]
	neg=Pair{Int,Int}[]
	for _=1:N
		s=readline()
		cnt=0
		mc=0
		for c=s
			if c=='('
				cnt+=1
			else
				cnt-=1
			end
			mc=min(mc,cnt)
		end
		if cnt>=0
			push!(pos,-mc=>cnt)
		else
			push!(neg,mc-cnt=>cnt)
		end
	end
	now=0
	flag=true
	for (a,b)=pos
		if now-a<0
			flag=false
		end
		now+=b
	end
	for (a,b)=neg
		if now+a+b<0
			flag=false
		end
		now+=b
	end
	println(flag&&now==0 ? "Yes" : "No")
end
main()