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
import sys
input = sys.stdin.readline

from collections import Counter

N = int(input())
A = list(map(int, input().split()))

C = Counter(A)
if len(C) == 1:
    X = A[0]
    if N >= 2*X or N == X + 1:
        ans = "Yes"
    else:
        ans = "No"
elif len(C) == 2:
    Xs = sorted(C.keys())
    if Xs[0] + 1 != Xs[1]:
        ans = "No"
    else:
        X = Xs[0]
        if C[X] <= X and C[X+1] >= 2*(X-C[X]+1):
            ans = "Yes"
        else:
            ans = "No"
else:
    ans = "No"

print(ans)