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
def printans(t):
    print(t)
    sys.exit()

N=int(input())
A=[int(i) for i in input().split()]

if all([a==A[0] for a in A]):#全部同じ
    shurui=A[0]
    if shurui==N-1 or shurui*2<=N:
        printans("Yes")
    else:printans("No")
else:#少ないやつは自分だけの色、そいつら以外で上と同じ処理
    maxshurui = max(A)
    if all([a in (maxshurui,maxshurui-1) for a in A]):
        unique = A.count(maxshurui-1)
        shurui = maxshurui-unique
        if shurui<=0:
            printans("No")
        if shurui*2<=N-unique:
            printans("Yes")
        else:printans("No")
    else:printans("No")