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
import bisect
n=int(input())
a=list(map(int,input().split()))
s=max(a)-min(a)
if s>=2:
    print("No")
elif s==0:
    if a[0]==n-1 or n//a[0]>=2:
        print("Yes")
    else:
        print("No")
else:
    a.sort()
    x=bisect.bisect_right(a,a[0])
    if x+1<=a[-1]<=x+(n-x)//2 and n-x>=2:
        print("Yes")
    else:
        print("No")