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()))

# Yesならば aの任意の2要素の差は高々1である
# 小さい方の値を発言している猫はそれぞれ異なる帽子を被る必要がある
# 大きい方の値を発言している猫は同じ帽子を被る猫が少なくとも他に一匹存在する必要がある
L = min(a)
R = max(a)
ans = (
    'Yes' if R - L == 0 and (N >= 2 * L or N == L + 1) or
    R - L == 1 and 2 * (L + 1) - N <= sum(x == L for x in a) <= L else
    'No'
)

print(ans)
