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())
lists=list(map(int,input().split()))
from collections import Counter
a=dict(Counter(lists))
if len(a)==1:
    if n>=lists[0]*2 or lists[0]==n-1:
        print("Yes")
    else:
        print("No")
    
elif len(a)==2:
    P=list(a.keys())
    Q=list(a.values())
    x,y=min(P),max(P) #x=k+l-1,y=k+l
    c,d=a[x],a[y]#c=k,d=?
    if 2*y-c<=n and c>0 and y>c and y-x==1:
        print("Yes")
    else:
        print("No")

    
else:
    print("No")