You are given an integer n and an integer array limit of length m.

You want to divide a strip of length n into two segments and paint each segment with a distinct color from index $0$ to m $- 1$.

A configuration is determined by choosing an ordered pair of distinct color indices (i, j) where i $\neq$ j, and an integer length x such that:

• The first segment has length x, painted with color i, with $1 \leq x \leq$ limit[i].

• The second segment has length n $- x$, painted with color j, with $1 \leq$ n $- x \leq$ limit[j].

Return the total number of valid ways to paint the strip.

Constraints:

• $2 \leq$ n $\leq 10^9$

• $2 \leq$ m $==$ limit.length $\leq 10^5$

• $1 \leq$ limit[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.