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
input = sys.stdin.readline

def main():
    n = int(input())
    a = list(map(int, input().split()))
    
    M, m = max(a), min(a)
    c = a.count(m)
    C = a.count(M)
    
    if M == m:
        if n//2 >= m or m == n-1:
            judge = True
        else:
            judge = False
    else:
        if M - m > 1:
            judge = False
        elif M - c <= 0:
            judge = False
        elif n-c >= (M-c)*2:
            judge = True
        else:
            judge = False
        
    
    print("Yes" if judge else "No")
    
    
    
if __name__ == "__main__":
    main()
