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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main() = abc167f()

@OptIn(ExperimentalStdlibApi::class)
fun abc167f() {
    val n = readLine()!!.toInt()
    val remains = (1..n).map {
        val s = readLine()!!
        var leftRem = 0L
        var rightRem = 0L
        for (c in s) {
            when (c) {
                '(' -> leftRem++
                else -> if (leftRem > 0) leftRem-- else rightRem++
            }
        }
        leftRem to rightRem
    }

    var leftRemSum = 0L
    for ((leftRem, rightRem) in remains.sortedByDescending { it.first - it.second }) {
        leftRemSum -= rightRem
        if (leftRemSum < 0) return println("No")
        leftRemSum += leftRem
    }

    val answer = if (leftRemSum == 0L) "Yes" else "No"

    println(answer)
}