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
n = int(input())
a = list(map(int,input().split()))
b = list(a)
b.sort()
if b[n-1]-b[0] >=2:
    print("No")
else:
    b = sum(a)%n
    c = int((sum(a)-b)/n)
    if b == 0:
        if 2*c > n and n != c+1:
            print("No")
        else:
            print("Yes")
    else:
        if b == 1:
            print("No")
        else:
            if n - b/2 >= c+1 and n <= c+b:
                print("Yes")
            else:
                print("No")