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 java.util.Stack

fun main(args: Array<String>) {
  val m = readLine()!!.toInt()
  val s = mutableListOf<String>()
  repeat(m) {
    val t = readLine()!!
    if (!t.isCompleteBracketSequence()) s.add(t.extractIncompleteBracketSequence())
  }
  val map = mutableMapOf<Int, Stack<Int>>()
  for (str in s) {
    val ket = str.replace("(", "").length
    val bra = str.length-ket
    if (!map.containsKey(ket)) map.put(ket, Stack<Int>())
    map[ket]!!.push(bra)
  }
  var level = 0
  while (map.isNotEmpty()) {
    if (!map.containsKey(level)) {
      println("No")
      return
    }
    val tmp = map[level]!!.pop()!!
    if (map[level]!!.isEmpty()) map.remove(level)
    level = tmp
  }
  println(if (level == 0) "Yes" else "No")
}
fun String.isCompleteBracketSequence(): Boolean {
  var level = 0
  for (char in this) {
    level += if (char == '(') 1 else -1
    if (level < 0) return false
  }
  return level == 0
}
fun String.extractIncompleteBracketSequence(): String {
  val stack = Stack<Char>()
  for (char in this) {
    if (char == ')' && stack.isNotEmpty() && stack.peek() == '(') {
      stack.pop()
    } else {
      stack.push(char)
    }
  }
  var res = ""
  while (stack.isNotEmpty()) res = stack.pop()!! + res
  return res
}