Problem:
Score : 300 points

Problem Statement

There are N integers written on a blackboard. The i-th integer is A_i.

Takahashi will repeatedly perform the following operation on these numbers:

Select a pair of integers, A_i and A_j, that have the same parity (that is, both are even or both are odd) and erase them.

Then, write a new integer on the blackboard that is equal to the sum of those integers, A_i+A_j.

Determine whether it is possible to have only one integer on the blackboard.

Constraints

2 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N

Output

If it is possible to have only one integer on the blackboard, print YES. Otherwise, print NO.

Sample Input 1

3
1 2 3

Sample Output 1

YES

It is possible to have only one integer on the blackboard, as follows:

Erase 1 and 3 from the blackboard, then write 4. Now, there are two integers on the blackboard: 2 and 4.

Erase 2 and 4 from the blackboard, then write 6. Now, there is only one integer on the blackboard: 6.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

NO

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val DEBUG = false
    val scanner = Scanner(System.`in`)
    val N = scanner.nextLong()
    val AN: LongArray = (0..N.toInt() - 1).map { scanner.nextLong() }.toLongArray()
    val sum: Long = AN.sum()
    val once = (N * (N + 1)) / 2
    if (sum % once != 0L || sum % N != 0L) {
        println("NO")
        return
    }
    val k: Long = sum / once
    val d = (0..N.toInt() - 1).map { index -> AN[(index % N).toInt()] - AN[index - 1] - k }.toLongArray()
    var count: Long = 0
    (0..N - 1).forEach { i ->
        while (d[i.toInt()] < 0) {
            d[i.toInt()] += N
            count += 1
        }
        if (d[i.toInt()] != 0L) {
            if (DEBUG) println("d[$i]=${d[i.toInt()]}")
            println("NO")
            return
        }

    }
    if (k == count) println("YES")
    else {
        if (DEBUG) println("k=$k ,count=$count")

        println("NO")
    }
}