You are given a strictly increasing zero indexed integer array nums of length $n$, and an array queries where each query is given as queries[i] $= [l_i, r_i]$.

For any index i, its closest neighbor is defined as the adjacent index j (where $|i - j| = 1$) that minimizes $|$nums[i] $-$ nums[j]$|$. If both adjacent indices have the same difference, either may be chosen as the closest neighbor.

When moving directly from index i to an adjacent index j:

• The cost is $1$ if j is the closest neighbor of i.

• The cost is $|$nums[i] $-$ nums[j]$|$ otherwise.

For each query queries[i] $= [l_i, r_i]$, determine the minimum total cost to travel from index l_i to index r_i by moving only between adjacent indices.

Return an integer array ans where ans[i] is the minimum cost for the $i$th query.

Constraints:

• $2 \leq$ nums.length $\leq 10^5$

• $-10^9 \leq$ nums[i] $\leq 10^9$

• nums is strictly increasing

• $1 \leq$ queries.length $\leq 10^5$

• queries[i] $= [l_i, r_i]$

• $0 \leq l_i, r_i <$ nums.length

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.