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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main {
  public static void main(String[] args) throws Exception {
    String line = null;
    long total = 0;
    int diff = 0;
    long count = 0;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    line = br.readLine();
    int size = Integer.parseInt(line);
    line = br.readLine();
    String data[] = line.split(" ");
    int[] array = new int[size];
    for (int i = 0; i < size; i ++) {
      int num = Integer.parseInt(data[i]);
      total = total + num;
      array[i] = num;
    }
    int val1 = size * (size + 1) / 2;
    long val2 = total % val1;
    if (val2 != 0) {
      System.out.println("NO");
      return;
    }
    long kk = total / val1;
    for (int i = 0; i < size; i++) {
      if (i == (size - 1)) {
        diff = array[0] - array[i];
      } else {
        diff = array[i + 1] - array[i];
      }
      if (diff < kk) {
        long k = (kk - diff)%size;
        if (k != 0) {
          System.out.println("NO");
          return;
        }
        count = count + (kk - diff)/size;
      }
    }
    if (kk != count) {
      System.out.println("NO");
    } else {
      System.out.println("YES");
    }
  }
}