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
from collections import Counter

N = int(input())
*a, = map(int, input().split())
v = sum(a)
c = Counter(a)

for n in range(N+1)[::-1]:
    if v-(N-1)*n>=0 and (v-(N-1)*n)%N==0:
        k = (v-(N-1)*n)//N
        if (k==0 and n==N) or (k and (N-n)%k==0):
            if c[n+k]==N-n and c[n+k-1]==n:
                print("Yes")
                break
else:
    print("No")
