Yaroslav has an array that consists of n integers. In one second Yaroslav can swap two neighboring array elements. Now Yaroslav is wondering if he can obtain an array where any two neighboring elements would be distinct in a finite time.

Help Yaroslav.

Input

The first line contains integer n (1 ≤ n ≤ 100) — the number of elements in the array. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the array elements.

Output

In the single line print "YES" (without the quotes) if Yaroslav can obtain the array he needs, and "NO" (without the quotes) otherwise.

Examples

Input

1
1


Output

YES


Input

3
1 1 2


Output

YES


Input

4
7 7 7 7


Output

NO

Note

In the first sample the initial array fits well.

In the second sample Yaroslav can get array: 1, 2, 1. He can swap the last and the second last elements to obtain it.

In the third sample Yarosav can't get the array he needs.
import java.util.*;

public class Yaroslav {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t, n = sc.nextInt(), m;
        int[] arr = new int[1001];
        for (t = 0; t < n; t++)
            arr[sc.nextInt()]++;
        Arrays.sort(arr);
        m = arr[1000];
        if (n % 2 == 0 && m > n / 2)
            m = -1;
        else if (n % 2 != 0 && m > n / 2 + 1)
            m = -1;
        System.out.print(m == -1 ? "NO" : "YES");
    }
}