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 IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        StringTokenizer st=new StringTokenizer(br.readLine());
        long[] a=new long[n];
        long sum=0;
        long count=0;
        for(int i=0;i<n;i++){ a[i]=Long.parseLong(st.nextToken()); sum+=a[i]; }
        if(sum%((n*(n+1))/2)!=0){
            System.out.println("NO");
            System.exit(0);
        }
        long times=sum/((n*(n+1))/2);
        for(int i=0;i<n;i++){
            count=(a[(i+1)%n]-a[i]);
            if((count>times)||count%n!=0){
                System.out.println("NO");
                System.exit(0);
            }else if(count<0 && Math.abs(count)>times){
                    System.out.println("NO");
                    System.exit(0);
            }
        }System.out.println("YES");
    }
}