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()))
a_max = max(a)
a_min = min(a)
if a_max > a_min+1:
    print('No')
    exit()
k = a_max
if a_max == a_min:
    if k == n-1 or 2*k <= n:
        print('Yes')
    else:
        print('No')
else:
    uni = a.count(k-1)
    if k >= uni + 1 and k <= uni + (n-uni)//2:
        print('Yes')
    else:
        print('No')