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() {
    val builder = StringBuilder()

    val n = readInputLine().toInt()

    val tmpBuilder = StringBuilder()

    repeat(n) {
        val input = readInputLine()
        var lbCnt = 0
        var rbCnt = 0

        for (c in input) {
            when(c) {
                ')' -> lbCnt++
                else -> rbCnt++
            }
            if (lbCnt > rbCnt) {
                break
            }
        }
        if (lbCnt > rbCnt) {
            tmpBuilder.append(input)
        } else {
            tmpBuilder.insert(0, input)
        }
    }

    var lbCnt = 0
    var rbCnt = 0

    for (c in tmpBuilder.toString()) {
        when(c) {
            ')' -> lbCnt++
            else -> rbCnt++
        }
        if (lbCnt > rbCnt) {
            println("No")
            return
        }
    }

    if (lbCnt != rbCnt) {
        println("No")
    } else {
        println("Yes")
    }

    /*
    var allParenCol = true
    var existsLopen = false
    var existsRopen = false

    for (i in 0 until n) {
        val input = readInputLine().toCharArray()
        var lbCntLocal = 0
        var rbCntLocal = 0

        var isLopen = false
        var isRopen = false
        for (c in input) {
            when(c) {
                ')' -> {
                    lbCntLocal++
                    if (lbCntLocal > rbCntLocal) {
                        isLopen = true
                    }
                }
                '(' -> {
                    rbCntLocal++
                }
            }
        }

        var lbCntLocal2 = 0
        var rbCntLocal2 = 0
        for (c in input.reversed()) {
            when(c) {
                ')' -> {
                    lbCntLocal2++
                }
                '(' -> {
                    rbCntLocal2++
                    if (rbCntLocal2 > lbCntLocal2) {
                        isRopen = true
                    }
                }
            }
            if (isRopen) {
                break
            }
        }

        if (isLopen || isRopen) {
            allParenCol = false
        }
        if (isLopen && !isRopen) {
            existsLopen = true
        }
        if (isRopen && !isLopen) {
            existsRopen = true
        }

        lbCnt += lbCntLocal
        rbCnt += rbCntLocal
    }

    if (lbCnt != rbCnt) {
        builder.appendln("No")
    } else if (allParenCol || (existsLopen && existsRopen)) {
        builder.appendln("Yes")
    } else {
        builder.appendln("No")
    }

    print(builder.toString())
     */
}

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