Simple Intuitive Approach
IntuitionSince low scores always become 0 after changing, it is important to make the high score small.ApproachSince the high score is the gap between the large
# Intuition
<!-- Describe your first thoughts on how to solve this problem. -->
Since low scores always become 0 after changing, it is important to make the high score small.

# Approach
<!-- Describe your approach to solving the problem. -->
Since the high score is the gap between the largest and smallest values, to reduce this gap, you need to make the largest value smaller or the smallest value larger.


# Complexity
- Time complexity: $$O(NlogN)$$
<!-- Add your time complexity here, e.g. $$O(n)$$ -->

- Space complexity: $$O(N)$$
<!-- Add your space complexity here, e.g. $$O(n)$$ -->

# Code
```cpp []
class Solution {
public:
    int minimizeSum(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int n = nums.size();
        // case 1. remove the two biggests.
        int ans1 = nums[n-3] - nums[0];
        // case 2. remove the two lowests.
        int ans2 = nums[n-1] - nums[2];
        // case 3. remove the biggest and the lowest.
        int ans3 = nums[n-2] - nums[1];
        return min({ans1, ans2, ans3});
    }
};
```
['C++']