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())
arr=list(map(int,input().split()))
min_,max_=min(arr),max(arr)
ans=None

if max_-min_ > 1:
    ans=False
elif max_-min_ == 1:
    """
    A=max_
    y=len([a for a in arr if a==max_])
    x=N-y
    nc=A-x
    ans=(A-x)>0 and y >=2*(A-x)
    """
    
    y=len([a for a in arr if a==max_])
    x=N-y
    nc=max_-x
    ans=nc>0 and y>=2*nc

else:
    ans=N>=2*min_ or min_+1==N

print("Yes" if ans else "No")
