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 -*-
from collections import Counter
def inpl(): return map(int, input().split())
N = int(input())
A = list(map(int, input().split()))

C = Counter(A)

if len(C) >= 3:
    print("No")
elif len(C) == 1:
    for k, v in C.items():
        if k == N-1 or N >= 2*k:
            print("Yes")
        else:
            print("No")
else:
    k = sorted(C.keys())[0]
    v = C[k]
    X = N - v
    if (k+1-v) * 2 <= C[k+1] and v <= k:
        print("Yes")
    else:
        print("No")