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 sys

def main():
    all_input = iter(sys.stdin.read().strip().replace('\n', ' ').split(' '))
    n = int(all_input.next())

    somas = {}
    max = 0
    for i in xrange(n):
        num = int(all_input.next())
        try:
            somas[num] += 1
        except KeyError:
            somas[num] = 1
        if max < somas[num]:
            max = somas[num]

    # print somas
    # print n - 2 * (n-max), n/2, max


    if n - 2 * (n-max) > 1:
        print "NO"
    else:
        print "YES"

if __name__ == '__main__':
    main()