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 - 1:
        print('Yes')
    elif 2 * a[0] <= N:
        print('Yes')
    else:
        print('No')
else:
    al = 0
    na = 0
    for i in range(N):
        if a[i] == ma - 1:
            al += 1
        else:
            na += 1

    if al < ma and 2 * (ma - al) <= na:
        print('Yes')
    else:
        print('No')