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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$n = intval(fgets(STDIN));
$A = array_map("intval", explode(" ", trim(fgets(STDIN))));
$max = max($A);
$min = min($A);
if($max - $min > 1){
    echo "No";exit;
}
if($max==$min){
//全員aloneか全員aloneではない
    if($max == $n - 1){//全員aloneな場合
        echo "Yes";exit;
    }else{
        //全員aloneではないので、$maxが大きすぎてはいけない
        if($max <= intdiv($n, 2)){
            echo "Yes";exit;
        }else{
            echo "No";exit;
        }
    }
}else{
    $maxCount = 0;
    foreach($A as $a){
        if($a == $max)$maxCount++;
    }
    $minCount = $n - $maxCount;
    //一部aloneな場合
    if($max > intdiv($maxCount, 2) + $minCount){//aloneではない猫をK匹とすると、その部分の色の数はfloor($K/2)以下である
        echo "No";exit;
    }elseif($maxCount<2){//aloneでない猫は必ず2匹以上いる
        echo "No";exit;
    }elseif($max < 1+$minCount){//色数は1＋aloneな猫の数以上である
        echo "No";exit;
    }else{
        echo "Yes";exit;
    }
}