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
from collections import Counter


def solve(n, cnt):
    if len(cnt) == 1:
        a = next(iter(cnt))
        return (a == n - 1) or (1 <= a <= n // 2)
    a1, a2 = min(cnt), max(cnt)
    if a2 - a1 > 1:
        return False
    c1, c2 = cnt[a1], cnt[a2]
    return c1 < a2 and a2 - c1 <= c2 // 2


n = int(input())
cnt = Counter(map(int, input().split()))

print('Yes' if solve(n, cnt) else 'No')
