<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:
        # 1 2 3 4 5
        # 1.  3.  5
        #   2 3 4
        # F[i][t] -> longest subseq len that ends at idx i and sums to t 
        L = len(nums)
        F = [[-float('inf')]*(target+1) for _ in range(len(nums))]
        # F[0]=0
        for i in range(len(nums)):
            F[i][0] = 0
        # print("F",F)
        for i, num in enumerate(nums):
            for t in range(1, target+1):
                # print("i",i,"t", t,"num", num, 'F[i-1][t-num]', F[i-1][t-num],
                # 'F[i-1][t]',F[i-1][t])
                if t>=num:
                    F[i][t] = max(F[i-1][t], F[i-1][t-num]+1)
                    # print('F[i][t]',F[i][t])
                # else:
                F[i][t] = max(F[i][t], F[i-1][t])
                # print("i",i,"t", t,"num", num, F[i][t])

        max_res = -1
        for i in range(len(nums)):
            max_res = max(max_res, F[i][target])
            # F[i][0] = 0
        return max_res
        # return res if res != -float('inf') else -1


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