<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], target: int) -> int:
        # dp[sum] represent current longest sequence that add up to sum
        dp = [float('-inf')] * (target+1) ### initial value CANNOT BE any negative value
        ### this is to ensure when sum_target - num has never been met, i.e. when dp[sum_target - num] = -inf, -inf +1 is still -inf
        ### otherwise dp[never_met_target]+1 = -some_negative_value+1  which gradually grows bigger and wrongly that it is more and more meetable

        dp[0] = 0 # need zero num to sum to target of 0
        for num in nums:
            ##for sum_target in range(target, -1, -1):  if go negative python will interpret as indexing from back to front
            # from large to small using the same element in the subsequence multiple times
            for sum_target in range(target, num-1, -1):  #at least target = num otherwise sum_target-num not in dp
                # subsequence does not need to maintain order
                # new sum is including current number
                dp[sum_target] = max(dp[sum_target], dp[sum_target-num]+1)
            #print(dp)
        return dp[target] if dp[target] != float('-inf') else -1
17257