Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Python (2.7.6) (judge verdict: Wrong Answer)

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 (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'