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: Wrong Answer)

n =gets.to_i
a = gets.split.map(&:to_i)
count = []
num = []
n.times do |i|
	if num.count(a[i]) == 0
		num << a[i]
		count[num.index(a[i])] = 1
	else
		count[num.index(a[i])] += 1
	end
end

if num.length == 1
	if num[0]* 2 <= n
		puts "Yes"
	else
		puts "No"
	end
elsif num.length > 2 || (num[0] - num[1]).abs > 1
	puts "No"
else
	if num[0] < num[1]
		min_num = num[0]
		min_count = count[0]
		max_count = count[1]
	elsif
		min_num = num[1]
		min_count = count[1]
		max_count = count[0]
	end
	if min_count <= min_num && (min_num+1) <= (min_count + max_count / 2)
		puts "Yes"
	else
		puts "No"
	end
end