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())
la = list(map(int, input().split()))

m = max(la)
if (m == N - 1) and (len(set(la)) == 1):
    print('Yes')
else:
    d = N - m
    cnt = la.count(m)
    if ((cnt >= d + 1) and (cnt <= 2 * d)):
        if cnt < N:
            if (len(set(la)) == 2) and min(la) == m - 1:
                print('Yes')
            else:
                print('No')
        else:
            print('Yes')
    else:
        print('No')
    
    
