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()))

ma = max(a)
mi = min(a)
if ma-mi >= 2:
    print('No')
elif ma == mi:
    if a[0] <= N//2 or a[0] == N-1:
        print('Yes')
    else:
        print('No')
else:
    maxnum = a.count(ma)
    minnum = a.count(mi)
    #if max(a) == minnum:
    #    print('No')
    if minnum + 1 <= ma <= minnum + maxnum//2:
        print('Yes')
    else:
        print('No')
