You are given a $2 ext{D}$ integer array ranges where ranges[i] = [start_i, end_i] represents an inclusive range from start_i to end_i.

You want to partition ranges into $2$ groups, where each group may be empty, such that:

• Each range belongs to exactly one group.

• Any two overlapping ranges must belong to the same group.

Two ranges overlap if they have at least one common number.

Return the total number of ways to split ranges into $2$ groups. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ ranges.length $\leq 10^5$

• ranges[i].length $= 2$

• $0 \leq$ start_i $\leq$ end_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.