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
input = sys.stdin.readline

from collections import Counter

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

x = min(A)
y = max(A)

if x == y:
    # 全員がnon-uniqueな色 or 全員がuniqueな色
    bl = (x <= N//2) or (x == N-1)
elif y != x + 1:
    bl = False
else:
    a = A.count(x)
    b = A.count(y)
    # a人：unique color
    # b人：non-unique color
    # b人でc種類あるとする
    c = y - a
    bl = (1 <= c <= b//2)

answer = 'Yes' if bl else 'No'
print(answer)