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

def read_data():
    N = int(input())
    As = list(map(int, input().split()))
    return N, As

def solve(N, As):
    x = max(As)
    y = min(As)
    if x - y > 1:
        return False
    if x == y:
        if x == N - 1:
            return True
        if x * 2 <= N:
            return True
        return False
    n_solo = As.count(y)
    if x < n_solo + 1:
        return False
    n_group = x - n_solo
    if n_group * 2 <= N - n_solo:
        return True
    return False

N, As = read_data()
if solve(N, As):
    print('Yes')
else:
    print('No')
