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())
s=input().split()
l=[int(s[i]) for i in range(n)]
l.sort()
if l[0]==l[-1]:
    if l[0]<=n//2 or l[0]==n-1:
        print("Yes")
    else:
        print("No")
elif l[-1]-l[0]>1:
    print("No")
else:
    a=l.count(l[0])
    b=l.count(l[-1])
    if a+1<=l[-1]<=a+b//2:
        print("Yes")
    else:
        print("No")
