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

N = int(input())
a = [int(i) for i in input().split()]

def solve() :
    c = Counter(a)
    if len(c.keys()) > 2 :
        return 'No'
    
    if len(c.keys()) == 2 :
        if max(c.keys()) - min(c.keys()) != 1 :
            return 'No'
            
        mk, Mk = min(c.keys()), max(c.keys())
        mv, Mv = c[mk], c[Mk]
        n = N - mv
        m = Mk - mv
        if 0 < m * 2 <= n :
            return 'Yes'
        else :
            return 'No'
    else :
        n = N
        m = list(c.keys())[0]
        if m * 2 <= n or m == n - 1 :
            return 'Yes'
        else :
            return 'No' 

print(solve())
