You are given a $0$ indexed array of positive integers heights representing the heights of buildings.

You are also given a $2$D array queries, where queries[i] = [a_i, b_i]. In the $i$th query, Alice is located at building a_i and Bob is located at building b_i.

A person at building i can move to building j if and only if i < j and heights[i] < heights[j].

For each query, determine the index of the leftmost building where Alice and Bob can both meet. A person can either stay at their starting building or move to a building with a greater index and strictly greater height.

Return an array ans where ans[i] is the index of the leftmost building where Alice and Bob can meet for the $i$th query, or $-1$ if they cannot meet at any building.

Constraints:

• $1 \leq$ heights.length $\leq 5 \times 10^4$

• $1 \leq$ heights[i] $\leq 10^9$

• $1 \leq$ queries.length $\leq 5 \times 10^4$

• queries[i] $= [a_i, b_i]$

• $0 \leq a_i, b_i \leq$ heights.length $- 1$

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.