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# Solution: Maximum Sum Increasing Subsequence

## Problem Statement

Given a number sequence, find the increasing subsequence with the highest sum. Write a method that returns the highest sum.

**Example 1:**

```
Input: {4,1,2,6,10,1,12}
Output: 32
Explanation: The increaseing sequence is {4,6,10,12}.
Please note the difference, as the LIS is {1,2,6,10,12} which has a sum of '31'.
```

**Example 2:**

```
Input: {-4,10,3,7,15}
Output: 25
Explanation: The increaseing sequences are {10, 15} and {3,7,15}.
```

**Constraints:**

`1 <= nums.length <= 2500`

- -10<sup>4</sup> <= nums[i] <= 10<sup>4</sup>

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