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()))
    
    if (max(a)-min(a) >= 2):
        print("No")
    else:
        count = [0,0]
        t = min(a)
        for num in a:
            if num == t:
                count[0] += 1
            else:
                count[1] += 1
        if (count[0]*count[1] == 0):
            if (2*a[0] <= N or a[0] == N-1):
                print("Yes")
            else:
                print("No")
        else:
            if (count[0] < t+1 and 2*(t+1-count[0]) <= count[1]):
                print("Yes")
            else:
                print("No")

if __name__ == "__main__":
    main()
