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Formatted question description: https://leetcode.ca/all/2297.html

# 2297. Jump Game VIII

## Description

You are given a **0-indexed** integer array `nums`

of length `n`

. You are initially standing at index `0`

. You can jump from index `i`

to index `j`

where `i < j`

if:

`nums[i] <= nums[j]`

and`nums[k] < nums[i]`

for all indexes`k`

in the range`i < k < j`

, or`nums[i] > nums[j]`

and`nums[k] >= nums[i]`

for all indexes`k`

in the range`i < k < j`

.

You are also given an integer array `costs`

of length `n`

where `costs[i]`

denotes the cost of jumping **to** index `i`

.

Return *the minimum cost to jump to the index *

`n - 1`

.

**Example 1:**

Input:nums = [3,2,4,4,1], costs = [3,7,6,4,2]Output:8Explanation:You start at index 0. - Jump to index 2 with a cost of costs[2] = 6. - Jump to index 4 with a cost of costs[4] = 2. The total cost is 8. It can be proven that 8 is the minimum cost needed. Two other possible paths are from index 0 -> 1 -> 4 and index 0 -> 2 -> 3 -> 4. These have a total cost of 9 and 12, respectively.

**Example 2:**

Input:nums = [0,1,2], costs = [1,1,1]Output:2Explanation:Start at index 0. - Jump to index 1 with a cost of costs[1] = 1. - Jump to index 2 with a cost of costs[2] = 1. The total cost is 2. Note that you cannot jump directly from index 0 to index 2 because nums[0] <= nums[1].

**Constraints:**

`n == nums.length == costs.length`

`1 <= n <= 10`

^{5}`0 <= nums[i], costs[i] <= 10`

^{5}