text

Consider a text with n characters. The characters used in the text are lower case English alphabet letters and the character *. Two words in the text are separated by one or more * characters.

Task

a) Determine the positions in the text of words that contain a maximum length sequence comprised of letters in strictly ascending alphabetical order.
b) Letters from this text are used to mark with letters the vertices of a regular polygon. The same letter cannot be used for marking two different vertices of a polygon. For the given text determine the maximum number of vertices of a regular polygon that can be marked using these letters.

Input data

Input file text.in contains on the first line the positive integer n, and on the second line the text characters without any spaces between them.

Output data

Output file text.out will contain on the first line the number of words with the property from point a). The second line will contain the positions of words with the property from point a), in ascending order, any two consecutive positions being separated by a space. The third line will contain the number requested in point b).

Constraints

Example
text.in text.out Explanation
40
abcdayz***abcabcdey**pqrs**mnpqruab**aba

2
2 4
14

At point a) we have words abcabcdey and mnpqruab on positions 2 and 4 which contain strictly ascending sequences of maximum length abcdey, and respectively mnpqru.
At point b) marking the regular polygon vertices with the most vertices would use letters a, b, c, d, e, m, n, p, r, s, u, x, y, z.

Time limit: 0.1 seconds/test

prof. Doru Popescu Anastasiu
"Radu Greceanu" National College - Slatina
Contact:dopopan@yahoo.com