You are given an array of integers 'A' of length 'M', representing amplifiers. Each amplifier 'A[i]' amplifies the input signal such that:

Output signal = A[i] * input signal

Amplifiers can only be connected to adjacent amplifiers in 'A'. The task is to select the maximum number of amplifiers to amplify a signal of strength 1 to exactly 'S'. Return the number of amplifiers used, or -1 if it is not possible.

Example:

• Input: M = 3, A = {2, 3, 4}, S = 123
• Output: -1
• Input: M = 5, A = {1, 2, 3, 4, 6}, S = 12
• Output: 2
• Input: M = 5, A = {2, 1, 3, 4, 6}, S = 12
• Output: 3

You are given a binary message 'S' of length 'N', which is an encoded version of a lowercase alphabetic string. You also have an array 'A' of 'M' binary strings, each representing a 5-bit binary string of a lowercase alphabet. The message 'S' arrived in a scrambled manner. The task is to find the lexicographically smallest possible lowercase alphabetic string that the message could represent.

Example:

• Input:
  • S = "0000100101"
  • N = 10
  • A = {"00000", "00001", "00010", "00011"}
  • M = 4
• Output: 'bd'
• Input:
  • S = "0000100101"
  • N = 10
  • A = {"01010", "10000", "01100", "00000"}
  • M = 4
• Output: 'ab'

Given a list of rectangles with width and height, the task was to stack these rectangles to maximize the height of the stacked rectangles. Each rectangle must have a width and height less than or equal to the rectangle below it.

Example:

• Input: Rectangles = [(1, 2), (2, 3), (3, 4), (4, 5)]
• Output: 4
• Input: Rectangles = [(1, 2), (2, 1), (3, 4), (4, 3)]
• Output: 2