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 collections as co
n = int(raw_input())
aa = map(int, raw_input().split())

c = co.Counter(aa).most_common()

if len(c) > 2:
  print 'No'
  exit()

if len(c) == 1:
  cc = c[0][0]
  if cc == n-1:
    print 'Yes'
  elif cc*2 <= n:
    print 'Yes'
  else:
    print 'No'
  exit()

l = c[0]
s = c[1]
if l[0] < s[0]:
  l,s = s,l

if l[0] != s[0] + 1:
  print 'No'
  exit()

if (n-l[0])+1 <= l[1] <= (n-l[0])*2:
# if (n-l[0])+1 <= l[1] <= (n-l[0])*2 and n-(n-l[0])*2 <= s[1] <= l[0] - 1:
  print 'Yes'
else:
  print 'No'