There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
agc016 B
"""

from collections import Counter

n = int(input())
acnt = Counter(map(int, input().split()))

if len(acnt) > 2:
    print('No')
    exit()

if len(acnt) == 1:
    [(a, nn)] = acnt.most_common(1)
    if a in range(1, n//2+1) or a == n-1:
        print('Yes')
    else:
        print('No')
    exit()

if len(acnt) == 2:
    [(a1, n1), (a2, n2)] = sorted(acnt.most_common(2), key=lambda x: x[0])
    if a2-a1 != 1:
        print('No')
    else:
        if 1 <= a2 - n1 <= (n-n1)//2:
            print('Yes')
        else:
            print('No')

