Company: DPWORLD

Given a series of integer intervals, determine the size of the smallest set that contains at least 2 integers within each interval.

Example:
first = [0, 1, 2]
last = [2, 3, 3]

The intervals start at first[i] and end at last[i].
- Interval 0: [0, 2] → contains 1 and 2
- Interval 1: [1, 3] → contains 2 and 3
- Interval 2: [2, 3] → contains 2 and 3

To satisfy all intervals , we must select integers such that each interval has at least 2 of them.
The smallest such set is {1, 2, 3}, and the answer is 3.

Function Description
Complete the function `interval` with the following parameters:
- `int first[]`: each element represents the start of interval[i]
- `int last[]`: each element represents the end of interval[i]

Returns:
- `int`: the size of the smallest set such that every interval contains at least two integers from it

Constraints:
- 1 ≤ n ≤ 10^5
- 0 ≤ first[i] < last[i] ≤ 10^9

Input Format for Custom Testing:

The first line contains the integer n, the number of intervals.
The second line contains n integers representing the array `first`.
The third line contains n integers representing the array `last`.

Sample Input 0
4
3 2 0 4
5 4 2 6

Explanation:
The intervals are:
- [3, 5]
- [2, 4]
- [0, 2]
- [4, 6]

The smallest set containing at least 2 integers in each interval might be {1, 2, 3, 4, 5}.
The correct set would be calculated by the function, and its size would be returned. Show More

A forklift operator navigates products within an automotive parts warehouse. The dashboard displays a real-time map showing open and blocked sections as an n x m matrix of 1's (open) and 0's (blocked). The operator starts at the top-left corner of the map at warehouse[0][0] and aims to reach the bottom-right corner at warehouse[n-1][m-1]. Movements can only be made to the right or downward. Given the warehouse map, calculate the number of distinct paths from warehouse[0][0] to warehouse[n-1][m-1]. Return the result modulo (10^9 + 7).

Example:
warehouse =
[1, 1, 0, 1],
[1, 1, 1, 1]

This matrix shows open (1) and blocked (0) sections of the warehouse. It is only possible to travel through open sections, so no path can go through the section at (0, 2). There are 2 possible paths from warehouse[0][0] to warehouse[1][3], and 2 modulo (10^9 + 7) = 2.

Function Description
Complete the function `numPaths` in the editor with the following parameter(s):
- `warehouse[n][m]`: a two-dimensional array of integers with n rows and m columns

Returns
- `int`: the number of paths through the matrix, modulo (10^9 + 7)

Constraints
- 1 ≤ n, m ≤ 1000
- Each cell in matrix warehouse contains either a 0 or a 1 Show More