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
# coding:utf-8

import sys
from collections import Counter


input = sys.stdin.readline
INF = float('inf')
MOD = 10 ** 9 + 7


def inpl(): return list(map(int, input().split()))


def solve():
    N = int(input())
    A = inpl()

    max_a = max(A)
    min_a = min(A)
    num_cnt = Counter(A)

    if max_a - min_a > 1:
        return 'No'

    if len(num_cnt) == 1:
        if max_a == N - 1 or 2 * max_a <= N:
            return 'Yes'
        else:
            return 'No'

    not_alone = num_cnt[max_a]
    alone = num_cnt[min_a]
    if not_alone >= (max_a - alone) * 2 and alone < max_a:
        return 'Yes'

    return 'No'


print(solve())
