Mike is growing tired of searching for strings, and has instead become interested in breaking them apart! Given a string ~S~, he wants to break it into any number of subsequences. Each character in ~S~ should belong to exactly one subsequence.

The ~i~-th letter in the English alphabet is assigned the value ~i~ (e.g. A~\to 1~, B~\to 2~, ..., Z~\to 26~).

For each subsequence, let ~v_{c_i}~ and ~v_{c_j}~ be the value of the first and last characters. Then, the score of the subsequence is equal to ~(v_{c_i}-v_{c_j})(v_{c_i}+v_{c_j})~. Note that scores can be negative. For example, the sequence HELLO will have a score of ~(8-15)(8+15) = -161~.

The total score of a string is equal to the sum of all the scores of its subsequences. To satisfy Mike's curiosity, you want to determine all the possible total scores for a given string.

Constraints

~1 \le N \le 250~

~S~ only consists of uppercase letters A...Z.

Subtask 1 [10%]

~1 \le N \le 5~

Subtask 2 [10%]

~S~ only consists of uppercase letters A and B.

Subtask 3 [30%]

~1 \le N \le 50~

Subtask 4 [50%]

No additional constraints.

Input Specification

The first line contains one integer ~N~, the length of the string.

The second line contains the string ~S~.

Output Specification

On the first line, output a single integer ~M~, the total number of possible scores.

On the next ~M~ lines, output the possible scores sorted in ascending order.

Sample Input 1

3
ADB

Sample Output 1

4
-15
-3
0
12

Explanation for Sample Output 1

There are five possible ways to break up the string into subsequences:

AD B

The total score for the first arrangement is ~(1-4)(1+4) + (2-2)(2+2) = -15~.

AB D

The total score for the second arrangement is ~(1-2)(1+2) + (4-4)(4+4) = -3~.

A D B

The total score for the third arrangement is ~(1-1)(1+1) + (4-4)(4+4) + (2-2)(2+2) = 0~.

A DB

The total score for the fourth arrangement is ~(1-1)(1+1) + (4-2)(4+2) = 12~.

ADB

The total score for the fifth arrangement is ~(1-2)(1+2) = -3~, which results in the same total score as the second arrangement.

Sample Input 2

3
AAC

Sample Output 2

2
-8
0

Explanation for Sample Output 2

One way to achieve a total score of ~-8~ is by breaking the string into the following subsequences:

A AC

One way to achieve a total score of ~0~ is by breaking the string into the following subsequences:

AA C

Sample Input 3

4
ABAB

Sample Output 3

4
-6
-3
0
3

Sample Input 4

4
JHVM

Sample Output 4

9
-489
-420
-384
-105
-69
0
36
315
351