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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php

$cat_count = trim(fgets(STDIN));

$string = trim(fgets(STDIN));


$array = explode(" ", $string);

$counts = array();

$MAX = 0;

foreach ($array as $item)
{
	$counts[$item] ++;
}

ksort($counts);

if (count($counts) > 2)
{
	echo "No\n";
	die();
}


$high		 = max(array_keys($counts));
$high_count	 = $counts[$high];
$low		 = max(array_keys($counts)) - 1;
$low_count	 = $counts[$low];




//all cats say the same thing
if ($low_count === null)
{
	//all unique -> number is one less than number of cats
	if (($high + 1) == $cat_count)
	{
		echo "Yes\n";
		die();
	}

	//all non-unique
	if ($high <= ($cat_count / 2))
	{
		echo "Yes\n";
		die();
	}
}
else
{
	$unique_hat_count = $low_count;


	$total_hat_colors = $high;

	$non_unqiue_colors	 = $total_hat_colors - $unique_hat_count;
	$non_unqiue_cats	 = $cat_count - $unique_hat_count;
	

	if (($non_unqiue_cats != 0) && ($non_unqiue_colors == 0))
	{
		echo "No\n";
		die();
	}
	
		if (($non_unqiue_cats == 0) && ($non_unqiue_colors != 0))
	{
		echo "No\n";
		die();
	}
	

	if ($non_unqiue_colors <= ($non_unqiue_cats / 2))
	{
		echo "Yes\n";
		die();
	}
}


echo "No\n";