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: Accepted)

import java.util.*
import kotlin.math.min

data class ParenParts(val min: Int, val sum: Int)

fun main() {
//    val builder = StringBuilder()

    val n = readInputLine().toInt()

    val up = PriorityQueue<ParenParts> { x, y -> y.min.compareTo(x.min) }
    val down = PriorityQueue<ParenParts> { x, y -> (y.sum - y.min).compareTo(x.sum - x.min) }

    repeat(n) {
        val s = readInputLine()

        var minTmp = 0
        var sumTmp = 0

        for (c in s) {
            when(c) {
                '(' -> {
                    sumTmp++
                }
                else -> {
                    sumTmp--
                    minTmp = min(minTmp, sumTmp)
                }
            }
        }

        if (sumTmp >= 0) {
            up.add(ParenParts(minTmp, sumTmp))
        } else {
            down.add(ParenParts(minTmp, sumTmp))
        }
    }

    var current = 0

    while (up.isNotEmpty()) {
        val (min, sum) = up.poll()
        if (current + min < 0) {
            println("No")
            return
        }
        current += sum
    }

    while (down.isNotEmpty()) {
        val (min, sum) = down.poll()
        if (current + min < 0) {
            println("No")
            return
        }
        current += sum
    }

    if (current == 0) {
        println("Yes")
    } else {
        println("No")
    }

//    builder.appendln(ans)

//    print(builder.toString())
}

fun readInputLine(): String {
    return readLine()!!
}