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.
#!/usr/bin/env python
from sys import stdin as std
from collections import Counter

#Basic idea:
#If the number of repeats is so much
#that they cannot be inserted one digit apart
#print NO
#ex. 7 8 3 3 3 YES because we can have 3 7 3 8 3
#ex2. 7 8 3 3 3 3 NO because we will always have 3's side by side
std.readline()
line = Counter(std.readline().split())
k = sum(line.values())
for n in line.values():
    if n > -~(k-n):
        print "NO"
        exit(0)
print "YES"