Problem Statement

Given an array of n positive integers, assuming 0-based indexing, its cost is calculated using the following formula:

给定一个包含 nnn 个正整数的数组（假设使用基于 0 的索引），其成本计算公式如下：

Here, len(arr) represents the size of the array.

You need to insert any integer at any location of the array such that the cost of the array is minimized. Find the minimum possible cost of the array after inserting exactly one element.

其中，len(arr)\text{len(arr)}len(arr) 表示数组的大小。

需要在数组的任意位置插入一个整数，使得数组的成本最小化。找到插入一个元素后数组的最小可能成本。

It can be proven that 49 is the minimum cost possible. Return 49.

Function Description

Complete the function getMinimumCost as follows:

def getMinimumCost(arr):
    # Write your code here

Input:

• An integer array arr representing the initial array.

Output:

• A long integer representing the minimum possible cost after inserting exactly one element.

Constraints:

Example Analysis

Example Array: [1, 3, 5, 2, 10]

Let's analyze the example provided:

The minimum cost achieved after inserting an element is 49, demonstrating the effectiveness of the optimal insertion strategy.

Summary

This problem challenges you to find the optimal insertion point to minimize the array's cost after a single insertion. The approach involves calculating costs for potential insertion points and determining the minimum.

这个问题的挑战在于找到最佳插入点，使插入一个元素后的数组成本最小化。该方法涉及计算潜在插入点的成本并确定最小值。

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