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

n = int(input())
a = list(map(int,input().split()))
mi,ma = 10 ** 6,0
cnt = [0] * n
for v in a:
    cnt[v] += 1
    mi = min(mi,v)
    ma = max(ma,v)
if ma - mi >= 2:
    print("No")
    sys.exit()
if mi != ma:
    if cnt[mi] == ma or (n - cnt[mi]) // (ma - cnt[mi]) < 2:
        print("No")
    else:
        print("Yes")
else:
    if mi == n - 1 or mi * 2 <= n:
        print("Yes")
    else:
        print("No")
