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 sys
input=sys.stdin.readline
sys.setrecursionlimit(10**9)
n=int(input())
A=list(map(int,input().split()))
a,b=max(A),min(A)
if a-b>1:
    print('No')
elif a==b:
    print('Yes' if a<=n//2 or a==n-1 else 'No')
else:
    c=A.count(b)
    print('Yes' if 1<=a-c<=(n-c)//2 else 'No')