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
sys.setrecursionlimit(pow(10, 6))


def main():
    n = int(input())
    a = list(sorted(map(int, input().split())))
    
    if a[0] == a[-1]:
        if (a[0] == n-1 or a[0]*2 <= n):
            print("Yes")
        else:
            print("No")
    elif a[-1] - a[0] > 1:
        print("No")
    else:
        minc = 0
        for _a in a:
            if _a == a[0]:
                minc += 1
            else:
                break
        if minc <= a[0] and n-minc>=2*(a[-1]-minc):
            print("Yes")
        else:
            print("No")


if __name__ == '__main__':
    main()
