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=list(map(int,input().split()))
b=sorted(a)
c=0
if(b[n-1]-b[0]>1):
    print('No')
elif(b[n-1]-b[0]==0):
    if(1<=b[0]<=n//2 or b[0]==n-1):
        print('Yes')
    else:
        print('No')
else:
    for i in range(n-1):
        if(b[i]<b[i+1]):
            c=i
            break
    if(c==n-2):
        print('No')
    elif(c+1<=b[0]<=c+(n-c-1)//2):
        print('Yes')        
    else:
        print('No')