You wish to buy video games from the famous online video game store Mist.

Usually, all games are sold at the same price, p dollars. However, they are planning to have the seasonal Halloween Sale next month in which you can buy games at a cheaper price. Specifically, the first game you buy during the sale will be sold at p dollars, but every subsequent game you buy will be sold at exactly d dollars less than the cost of the previous one you bought. This will continue until the cost becomes less than or equal to m dollars, after which every game you buy will cost m dollars each.

For example, if p = 20, d = 3 and m = 6, then the following are the costs of the first 11 games you buy, in order:

20, 17, 14, 11, 8, 6, 6, 6, 6, 6, 6

You have s dollars in your Mist wallet. How many games can you buy during the Halloween Sale?

We define the distance between two array values as the number of indices between the two values. Given a, find the minimum distance between any pair of equal elements in the array. If no such value exists, print -1.

For example, if a = [3, 2, 1, 2, 3], there are two matching pairs of values: 3 and 2. The indices of the 3‘s are i = 0 and j = 4, so their distance is d[i, j] = |j - i| = 4. The indices of the 2‘s are i = 1 and j = 3, so their distance is d[i, j] = |j - i| = 2.

Given a sequence of integers a, a triplet (a[i], a[j], a[k]) is beautiful if:

• i < j < k
• a[j] - a[i] = a[k] - a[j] = d

Given an increasing sequenc of integers and the value of d, count the number of beautiful triplets in the sequence.

For example, the sequence arr = [2, 2, 3, 4, 5] and d = 1. There are three beautiful triplets, by index: [i, j, k] = [0, 2, 3], [1, 2, 3], [2, 3, 4]. To test the first triplet, arr[j] - arr[i] = 3 - 2 = 1 and arr[k] = arr[j] = 4 - 3 = 1.

A modified Kaprekar number is a positive whole number with a special property. If you square it, then split the number into two integers and sum those integers, you have the same value you started with.

Consider a positive whole number n with d digits. We square n to arrive at a number that is either 2 x d digits long or (2 x d) - 1 digits long. Split the string representation of the square into two parts, l and r. The right hand part, r must be d digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get n.

For example, if n = 5, d = 1 then . We split that into two strings and convert them back to integers 2 and 5. We test , so this is not a modified Kaprekar number. If n = 9, still d = 1, and . This gives us 1 + 8 = 9, the original n.

Note: r may have leading zeros.

An English text needs to be encrypted using the following encryption scheme.
First, the spaces are removed from the text. Let L be the length of this text.
Then, characters are written into a grid, whose rows and columns have the following constraints:

For example, the sentence
s = if man was meant to stay on the ground god would have given us roots, after removing spaces is 54 characters long. is between 7 and 8, so it is written in the form of a grid with 7 rows and 8 columns.