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 Ruby (2.3.3) (judge verdict: Accepted)

def solve(n,a)
  a.sort!
  return false if a[-1]-a[0] >= 2

  cnt = [0,0]
  a.each do |v|
    cnt[v-a[0]] += 1
  end

  if cnt[1] == 0 
    if a[0] == n-1 || a[0] <= n/2
      return true
    else
      return false
    end
  elsif cnt[1] == 1
    return false
  else
    kind = [cnt[0]+1,cnt[0]+cnt[1]/2]
    if kind.min <= a[-1] && a[-1] <= kind.max
      return true
    else
      return false
    end
  end
end

n = gets.to_i
a = gets.split.map(&:to_i)

puts solve(n,a) ? "Yes" : "No"