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
def main():
    from collections import Counter as ct
    n=int(input())
    a=ct(list(map(int,input().split())))
    if len(a.keys()) not in [1,2]:
        print("No")
        return 0
    if len(a.keys())==1:
        a=list(a.items())
        if a==[(n-1,n)]:
            print("Yes")
            return 0
        if 2*a[0][0]<=a[0][1]:
            print("Yes")
        else:
            print("No")
        return 0
    i=min(a.keys())
    iv=a[i]
    j=max(a.keys())
    jv=a[j]
    if j-i!=1:
        print("No")
        return 0
    if iv>i:
        print("No")
        return 0
    k=2*(i-iv+1)
    if jv>=k:
        print("Yes")
    else:
        print("No")
main()