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 = sorted(list(map(int,input().split())),reverse=True)
if A[0]==A[-1] and (A[0]==1 or A[0]==N-1):
    print("Yes")
else:
    k = A[0]
    cnt = A.count(k-1)
    n = N-cnt
    k -= cnt
    if k<=0:
        print("No")
    else:
        n -= 2*k
        if n>=0:
            print("Yes")
        else:
            print("No")