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()))
max_A = max(A)
min_A = min(A)
if max_A - min_A >= 2:
    print("No")
elif max_A - min_A == 1:  # 他の猫とと色がかぶらない猫と、色が被る猫の両方が存在する
    M = A.count(max_A)
    print("Yes") if N - M + 1 <= max_A <= (N - M) + M // 2 else print("No")
else:  # 他の猫とと色がかぶらない猫が存在しない or 皆違う色
    print("Yes") if max_A <= N // 2 or max_A == N - 1 else print("No")
