Lilah has a string, s, of lowercase English letters that she repeated infinitely many times.

Given an integer, n, find and print the number of letter a’s in the first n letters of Lilah’s infinite string.

For example, if the string s = ‘abcac’ and n = 10, the substring we consider is abcacabcac, the first 10 characters of her infinite string. There are 4 occurrences of a in the substring.

Your local library needs your help! Given the expected and actual return dates for a library book, create a program that calculates the fine (if any). The fee structure is as follows:

1. If the book is returned on or before the expected return date, no fine will be charged (i.e.: fine = 0.
2. If the book is returned after the expected return day but still within the same calendar month and year as the expected return date, fine = 15 Hackos x (the number of days late).
3. If the book is returned after the expected return month but still within the same calendar year as the expected return date, the fine = 500 Hackos x (the number months late).
4. If the book is returned after the calendar year in which it was expected, there is a fixed fine of 10000 Hackos.

Charges are based only on the least precise measure of lateness. For example, whether a book is due January 1, 2017 or December 31, 2017, if it is returned January 1, 2018, that is a year late and the fine would be 10000 Hackos.

Watson likes to challenge Sherlock’s math ability. He will provide a starting and ending value describing a range of integers. Sherlock must determine the number of square integers within that range, inclusive of the endpoints.

Note: A square integer is an integer which is the square of an integer, e.g. 1, 4, 9, 16, 25.

For example, the range is a = 24 and b = 49, inclusive. There are three square integers in the range: 25, 36 and 49.

You have a string of lowercase English alphabetic letters. You can perform two types of operations on the string:

1. Append a lowercase English alphabetic letter to the end of the string.
2. Delete the last character in the string. Performing this operation on an empty string results in an empty string.

Given an integer, k, and two strings, s and t, determine whether or not you can convert s to t by performing exactly k of the above operations on s. If it’s possible, print Yes. Otherwise, print No.

For example, strings s = [a, b, c] and t = [d, e, f]. Our number of moves, k = 6. To convert s to t, we first delete all of the characters in 3 moves. Next we add each of the characters of t in order. On the move, you will have the matching string. If there had been more moves available, they could have been eliminated by performing multiple deletions on an empty string. If there were fewer than 6 moves, we would not have succeeded in creating the new string.

An integer d is a divisor of an integer n if the remainder of n / d = 0.

Given an integer, for each digit that makes up the integer determine whether it is a divisor. Count the number of divisors occurring within the integer.

Note: Each digit is considered to be unique, so each occurrence of the same digit should be counted (e.g. for n = 111, 1 is a divisor of 111 each time it occurs so the answer is 3).