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
N=int(input())
A=[int(i) for i in input().split()]
M=max(A)
m=min(A)
if M-m>=2:
    print("No")
elif M-m==1:
    x=0
    y=0
    for i in range(N):
        if A[i]==m:
            x+=1
        else:
            y+=1
    if x<M and 2*(M-x)<=y:
        print("Yes")
    else:
        print("No")
else:
    if 2*M<=N or M==N-1:
        print("Yes")
    else:
        print("No")
