<p>You are given a <strong>0-indexed</strong> array of integers <code>nums</code>, and an integer <code>target</code>.</p>

<p>Return <em>the <strong>length of the longest subsequence</strong> of</em> <code>nums</code> <em>that sums up to</em> <code>target</code>. <em>If no such subsequence exists, return</em> <code>-1</code>.</p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5], target = 9
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are 3 subsequences with a sum equal to 9: [4,5], [1,3,5], and [2,3,4]. The longest subsequences are [1,3,5], and [2,3,4]. Hence, the answer is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,1,3,2,1,5], target = 7
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 5 subsequences with a sum equal to 7: [4,3], [4,1,2], [4,2,1], [1,1,5], and [1,3,2,1]. The longest subsequence is [1,3,2,1]. Hence, the answer is 4.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,5,4,5], target = 3
<strong>Output:</strong> -1
<strong>Explanation:</strong> It can be shown that nums has no subsequence that sums up to 3.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution:
    def lengthOfLongestSubsequence(self, nums: List[int],   # Ex: nums = [4,1,3,2,1]  target = 7
                                    target: int) -> int:
                                                            #  num  dp 
                                                            #  ---  ------------
        (dp:= [0]).extend([-1] * target)                    #  -->   [0,-1,-1,-1, 1,-1,-1,-1]
        for num in nums:                                    #   4    [0,-1,-1,-1, 1,-1,-1,-1]
            for i in reversed(range(num, target+1)):        #   1    [0, 1,-1,-1, 1, 2,-1,-1]
                nxt = dp[i - num] + 1                       #   3    [0, 1,-1, 1, 2, 2,-1, 2]
                dp[i] = max(nxt, dp[i]) if nxt else dp[i]   #   2    [0, 1,-1, 1, 2, 2,-1, 2]
                                                            #   1    [0, 1, 2, 2, 3, 3, 3, 4]
        return dp[-1]                                       #                               \_ return 4
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