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# 1403. Minimum Subsequence in Non-Increasing Order

<https://leetcode.com/problems/minimum-subsequence-in-non-increasing-order>

## Description

Given the array `nums`, obtain a subsequence of the array whose sum of elements is **strictly greater** than the sum of the non included elements in such subsequence.&#x20;

If there are multiple solutions, return the subsequence with **minimum size** and if there still exist multiple solutions, return the subsequence with the **maximum total sum** of all its elements. A subsequence of an array can be obtained by erasing some (possibly zero) elements from the array.&#x20;

Note that the solution with the given constraints is guaranteed to be **unique**. Also return the answer sorted in **non-increasing** order.

**Example 1:**

```

**Input:** nums = [4,3,10,9,8]
**Output:** [10,9] 
**Explanation:** The subsequences [10,9] and [10,8] are minimal such that the sum of their elements is strictly greater than the sum of elements not included, however, the subsequence [10,9] has the maximum total sum of its elements. 
```

**Example 2:**

```

**Input:** nums = [4,4,7,6,7]
**Output:** [7,7,6] 
**Explanation:** The subsequence [7,7] has the sum of its elements equal to 14 which is not strictly greater than the sum of elements not included (14 = 4 + 4 + 6). Therefore, the subsequence [7,6,7] is the minimal satisfying the conditions. Note the subsequence has to returned in non-decreasing order.  
```

**Example 3:**

```

**Input:** nums = [6]
**Output:** [6]
```

**Constraints:**

* `1 <= nums.length <= 500`
* `1 <= nums[i] <= 100`

## ac

```java
```