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 = trim(fgets(STDIN));
    $a = explode(" ", trim(fgets(STDIN)));
    sort($a);
    
    $ans = false;
    $f = true;
    for($i=0; $i<$n; $i++){
        if($a[$i] != 1) $f = false;
    }
    if($f) $ans = true;
    $f = true;
    for($i=0; $i<$n; $i++){
        if($a[$i] != $n - 1) $f = false;
    }
    if($f) $ans = true;
    
    if(!$ans){
        $ans = true;
        $x = 0;
        for($i=0; $i<$n; $i++){
            if($a[$i] != $a[0]){
                if($a[$i] == $a[0] + 1){
                    $x = $i;
                    break;
                } else {
                    $ans = false;
                    break;
                }
            }
        }
        while(++$i<$n){
            if($a[$i] != $a[0] + 1){
                $ans = false;
            }
        }
        if($ans){
            if($x==0){
                if(0<$a[0] && $a[0]<=floor(($n-$x)/2));
                else $ans = false;
            } else {
                if($x<=$a[0] && $a[0]+1<=$x+floor(($n-$x)/2));
                else $ans = false;
            }
        }
        
    }
    
    if($ans) echo "Yes";
    else echo "No";
    
?>