You are given an array a_1, a_2, …, a_n.

In one operation you can choose two elements a_i and a_j (i ≠ j) and decrease each of them by one.

You need to check whether it is possible to make all the elements equal to zero or not.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5) — the size of the array.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the array.

Output

Print "YES" if it is possible to make all elements zero, otherwise print "NO".

Examples

Input


4
1 1 2 2


Output


YES

Input


6
1 2 3 4 5 6


Output


NO

Note

In the first example, you can make all elements equal to zero in 3 operations: 

  * Decrease a_1 and a_2, 
  * Decrease a_3 and a_4, 
  * Decrease a_3 and a_4 



In the second example, one can show that it is impossible to make all elements equal to zero.
//package com.company;

import java.util.Arrays;
import java.util.Scanner;

public class CF_1201_B {
    public static void main(String args[]) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        long sum=0;
        int max=0;
        for(int i=0;i<n;++i) {
            a[i] = sc.nextInt();
            sum+=a[i];
            max=Math.max(max,a[i]);
        }
//        Arrays.sort(a);
//        for(int i=0;i<a.length-1;++i) {
//            a[i+1]-=a[i];
//        }
        if(sum%2==0&&sum-max>=max) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
    }
}
