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
N = int(input())
a = list(map(int, input().split()))
a.sort()
if a[-1] - a[0] > 1:
  print("No")
  exit(0)

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

table = [0] * N
for i in range(N):
  if a[i] == a[0]: table[i] = i + 1
l = max(table) + 1
r = l + table.count(0) // 2

if a[-1] in range(l, r): print("Yes")
else: print("No")