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())
array = [int(x) for x in input().split(' ')]
maxa = max(array)
mina = min(array)
if maxa - mina > 1:
    print('No')
elif maxa == mina:
    if n >= 2 * maxa:
        print('Yes')
    elif maxa == n-1:
        print('Yes')
    else:
        print('No')
else:
    sum = 0
    for j in array:
        if j == mina:
            sum += 1
    if sum >= maxa:
        print('No')
        exit()
    if 2*(maxa - sum) <= n - sum:
        print('Yes')
    else:
        print('No')
