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()))
a.sort()
if a[0] == a[-1]:
    if a[0] == N-1 or a[0] <= N//2:
        print("Yes")
    else:
        print("No")
    exit()

if a[0] < a[-1]-1:
    print("No")
    exit()

o = 0
t = 0
for i in range(N):
    if a[i] != a[0]:
        o = i
        t = N-i
        break

if t//2 + o >= a[-1] > o:
    print("Yes")
else:
    print("No")

