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
import sys
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    A = list(map(int,input().split()))

    a = max(A)
    if not all(0 <= a - b <= 1 for b in A):
        print('No')
        return
    
    cnt = sum(0 if a == b else 1 for b in A)
    if cnt == 0 and (2*a <= N or a + 1 == N):
        print('Yes')
    elif a == cnt == N:
        print('Yes')
    elif a - cnt > 0 and (a - cnt)*2 <= N - cnt:
        print('Yes')
    else:
        print('No')

if __name__ == '__main__':
    main()