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)

import kotlin.math.min

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val t = (1..n).map {
        val s = readLine()!!
        var minMinus = 0
        var add = 0
        s.forEach {
            when (it) {
                '(' -> add++
                else -> add--
            }
            minMinus = min(minMinus, add)
        }
        Pair(add, minMinus)
    }

    var depth = t.filter { it.first >= 0 && it.second >= 0 }.sumBy { it.first }
    val med = t.filter { it.first >= 0 && it.second < 0 }.sortedByDescending { it.second }
    for (x in med) {
        if (depth + x.second < 0) {
            println("No")
            return
        }
        depth += x.first
    }

    val last = t.filter { it.first < 0 }.sortedBy { it.second }
    for (x in last) {
        if (depth + x.second < 0 || depth + x.first < 0) {
            println("No")
            return
        }
        depth += x.first
    }

    println(if (depth == 0) "Yes" else "No")
}