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
from collections import Counter
from sys import exit
def No():
    print('No')
    exit()
def Yes():
    print('Yes')
    exit()

N = int(input())
A = list(map(int, input().split()))
if max(A) - min(A) > 1:
    No()
if len(set(A)) == 1:
    if A == [N-1]*N:
        Yes()
    a = A[0]
    if a <= N//2:
        Yes()
    No()
mA = min(A)
S = max(A)
B = Counter(A)[mA]
if B + 1 <= S <= (N - B)//2 + B:
    Yes()
No()