[CODE ONLY][DEBUG OUTPUT] PYTHON USING Lynn's SOLUTION
Debug outputCode
# Debug output
```
nums: [16, 6, 3]
Maximum number in nums: 16
Initialized DP table:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
At index=2: [16, 6] ...3... []
	Target difference: 1, Calculated difference: 2
		Frequency for diff 2 updated for num 3: 1 (max of 0 and 1)
	Target difference: 2, Calculated difference: 1
		Frequency for diff 1 updated for num 3: 1 (max of 0 and 1)
	Target difference: 3, Calculated difference: 0
		Frequency for diff 0 updated for num 3: 1 (max of 0 and 1)
	Target difference: 4, Calculated difference: 1
		Frequency for diff 1 updated for num 3: 1 (max of 1 and 1)
	Target difference: 5, Calculated difference: 2
		Frequency for diff 2 updated for num 3: 1 (max of 1 and 1)
	Target difference: 6, Calculated difference: 3
		Frequency for diff 3 updated for num 3: 1 (max of 0 and 1)
	Target difference: 7, Calculated difference: 4
		Frequency for diff 4 updated for num 3: 1 (max of 0 and 1)
	Target difference: 8, Calculated difference: 5
		Frequency for diff 5 updated for num 3: 1 (max of 0 and 1)
	Target difference: 9, Calculated difference: 6
		Frequency for diff 6 updated for num 3: 1 (max of 0 and 1)
	Target difference: 10, Calculated difference: 7
		Frequency for diff 7 updated for num 3: 1 (max of 0 and 1)
	Target difference: 11, Calculated difference: 8
		Frequency for diff 8 updated for num 3: 1 (max of 0 and 1)
	Target difference: 12, Calculated difference: 9
		Frequency for diff 9 updated for num 3: 1 (max of 0 and 1)
	Target difference: 13, Calculated difference: 10
		Frequency for diff 10 updated for num 3: 1 (max of 0 and 1)
	Target difference: 14, Calculated difference: 11
		Frequency for diff 11 updated for num 3: 1 (max of 0 and 1)
	Target difference: 15, Calculated difference: 12
		Frequency for diff 12 updated for num 3: 1 (max of 0 and 1)
	Target difference: 16, Calculated difference: 13
		Frequency for diff 13 updated for num 3: 1 (max of 0 and 1)
		Propagating max for diff 1: 1 (max of 1 and 1)
		Propagating max for diff 2: 1 (max of 1 and 1)
		Propagating max for diff 3: 1 (max of 1 and 1)
		Propagating max for diff 4: 1 (max of 1 and 1)
		Propagating max for diff 5: 1 (max of 1 and 1)
		Propagating max for diff 6: 1 (max of 1 and 1)
		Propagating max for diff 7: 1 (max of 1 and 1)
		Propagating max for diff 8: 1 (max of 1 and 1)
		Propagating max for diff 9: 1 (max of 1 and 1)
		Propagating max for diff 10: 1 (max of 1 and 1)
		Propagating max for diff 11: 1 (max of 1 and 1)
		Propagating max for diff 12: 1 (max of 1 and 1)
		Propagating max for diff 13: 1 (max of 1 and 1)
		Propagating max for diff 14: 1 (max of 0 and 1)
		Propagating max for diff 15: 1 (max of 0 and 1)
DP table after processing number 3:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
At index=1: [16] ...6... [3]
	Target difference: 1, Calculated difference: 5
		Frequency for diff 5 updated for num 6: 1 (max of 0 and 1)
	Target difference: 2, Calculated difference: 4
		Frequency for diff 4 updated for num 6: 1 (max of 0 and 1)
	Target difference: 3, Calculated difference: 3
		Frequency for diff 3 updated for num 6: 2 (max of 0 and 2)
	Target difference: 4, Calculated difference: 2
		Frequency for diff 2 updated for num 6: 1 (max of 0 and 1)
	Target difference: 5, Calculated difference: 1
		Frequency for diff 1 updated for num 6: 1 (max of 0 and 1)
	Target difference: 6, Calculated difference: 0
		Frequency for diff 0 updated for num 6: 1 (max of 0 and 1)
	Target difference: 7, Calculated difference: 1
		Frequency for diff 1 updated for num 6: 1 (max of 1 and 1)
	Target difference: 8, Calculated difference: 2
		Frequency for diff 2 updated for num 6: 1 (max of 1 and 1)
	Target difference: 9, Calculated difference: 3
		Frequency for diff 3 updated for num 6: 2 (max of 2 and 1)
	Target difference: 10, Calculated difference: 4
		Frequency for diff 4 updated for num 6: 1 (max of 1 and 1)
	Target difference: 11, Calculated difference: 5
		Frequency for diff 5 updated for num 6: 1 (max of 1 and 1)
	Target difference: 12, Calculated difference: 6
		Frequency for diff 6 updated for num 6: 1 (max of 0 and 1)
	Target difference: 13, Calculated difference: 7
		Frequency for diff 7 updated for num 6: 1 (max of 0 and 1)
	Target difference: 14, Calculated difference: 8
		Frequency for diff 8 updated for num 6: 1 (max of 0 and 1)
	Target difference: 15, Calculated difference: 9
		Frequency for diff 9 updated for num 6: 1 (max of 0 and 1)
	Target difference: 16, Calculated difference: 10
		Frequency for diff 10 updated for num 6: 1 (max of 0 and 1)
		Propagating max for diff 1: 1 (max of 1 and 1)
		Propagating max for diff 2: 1 (max of 1 and 1)
		Propagating max for diff 3: 2 (max of 2 and 1)
		Propagating max for diff 4: 2 (max of 1 and 2)
		Propagating max for diff 5: 2 (max of 1 and 2)
		Propagating max for diff 6: 2 (max of 1 and 2)
		Propagating max for diff 7: 2 (max of 1 and 2)
		Propagating max for diff 8: 2 (max of 1 and 2)
		Propagating max for diff 9: 2 (max of 1 and 2)
		Propagating max for diff 10: 2 (max of 1 and 2)
		Propagating max for diff 11: 2 (max of 0 and 2)
		Propagating max for diff 12: 2 (max of 0 and 2)
		Propagating max for diff 13: 2 (max of 0 and 2)
		Propagating max for diff 14: 2 (max of 0 and 2)
		Propagating max for diff 15: 2 (max of 0 and 2)
DP table after processing number 6:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
At index=0: [] ...16... [6, 3]
	Target difference: 1, Calculated difference: 15
		Frequency for diff 15 updated for num 16: 1 (max of 0 and 1)
	Target difference: 2, Calculated difference: 14
		Frequency for diff 14 updated for num 16: 1 (max of 0 and 1)
	Target difference: 3, Calculated difference: 13
		Frequency for diff 13 updated for num 16: 2 (max of 0 and 2)
	Target difference: 4, Calculated difference: 12
		Frequency for diff 12 updated for num 16: 1 (max of 0 and 1)
	Target difference: 5, Calculated difference: 11
		Frequency for diff 11 updated for num 16: 1 (max of 0 and 1)
	Target difference: 6, Calculated difference: 10
		Frequency for diff 10 updated for num 16: 3 (max of 0 and 3)
	Target difference: 7, Calculated difference: 9
		Frequency for diff 9 updated for num 16: 1 (max of 0 and 1)
	Target difference: 8, Calculated difference: 8
		Frequency for diff 8 updated for num 16: 1 (max of 0 and 1)
	Target difference: 9, Calculated difference: 7
		Frequency for diff 7 updated for num 16: 1 (max of 0 and 1)
	Target difference: 10, Calculated difference: 6
		Frequency for diff 6 updated for num 16: 1 (max of 0 and 1)
	Target difference: 11, Calculated difference: 5
		Frequency for diff 5 updated for num 16: 1 (max of 0 and 1)
	Target difference: 12, Calculated difference: 4
		Frequency for diff 4 updated for num 16: 1 (max of 0 and 1)
	Target difference: 13, Calculated difference: 3
		Frequency for diff 3 updated for num 16: 1 (max of 0 and 1)
	Target difference: 14, Calculated difference: 2
		Frequency for diff 2 updated for num 16: 1 (max of 0 and 1)
	Target difference: 15, Calculated difference: 1
		Frequency for diff 1 updated for num 16: 1 (max of 0 and 1)
	Target difference: 16, Calculated difference: 0
		Frequency for diff 0 updated for num 16: 1 (max of 0 and 1)
		Propagating max for diff 1: 1 (max of 1 and 1)
		Propagating max for diff 2: 1 (max of 1 and 1)
		Propagating max for diff 3: 1 (max of 1 and 1)
		Propagating max for diff 4: 1 (max of 1 and 1)
		Propagating max for diff 5: 1 (max of 1 and 1)
		Propagating max for diff 6: 1 (max of 1 and 1)
		Propagating max for diff 7: 1 (max of 1 and 1)
		Propagating max for diff 8: 1 (max of 1 and 1)
		Propagating max for diff 9: 1 (max of 1 and 1)
		Propagating max for diff 10: 3 (max of 3 and 1)
		Propagating max for diff 11: 3 (max of 1 and 3)
		Propagating max for diff 12: 3 (max of 1 and 3)
		Propagating max for diff 13: 3 (max of 2 and 3)
		Propagating max for diff 14: 3 (max of 1 and 3)
		Propagating max for diff 15: 3 (max of 1 and 3)
DP table after processing number 16:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3]
Final DP table:
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3]
Maximum frequency: 3
```

# Code
```python3 []
# USING Lynn's solution AND Gemini
# LINK: https://leetcode.com/problems/longest-subsequence-with-decreasing-adjacent-difference/solutions/6238595/python-2d-dp

class Solution:
    def longestSubsequence(self, nums: List[int]) -> int:
        # print(f'nums: {nums}')
        max_num = max(nums)  # Find the maximum number in nums.  This determines the table size.
        # print(f"Maximum number in nums: {max_num}")

        dp = [ [0] * max_num for _ in range(max_num + 1)]  # Initialize DP table. dp[num][diff] stores the max frequency of 'diff' using 'num' and smaller numbers.
        # def _printDP(message: str):
        #     print(message)
        #     for row in dp:
        #         print(row)
    
        # _printDP("Initialized DP table:")

        for i in range(len(nums) - 1, -1, -1):  # Iterate through nums from right to left.  This order ensures we build solutions from smaller numbers to larger ones.
            num = nums[i]  # The current number being considered.
            # print(f"At index={i}: {nums[:i]} ...{nums[i]}... {nums[i+1:]}")

            for target_diff in range(1, max_num + 1):  # Iterate through all possible target differences.
                diff = abs(num - target_diff)  # Calculate the absolute difference between current number and target.
                # print(f"\tTarget difference: {target_diff}, Calculated difference: {diff}")
                current_freq = dp[num][diff]
                previous_freq = dp[target_diff][diff] + 1
                dp[num][diff] = max(current_freq, previous_freq)  # Update the frequency for this difference. We take the max to consider cases where the current number gives a higher frequency, or a previous number did.
                # print(f"\t\tFrequency for diff {diff} updated for num {num}: {dp[num][diff]} (max of {current_freq} and {previous_freq})")

            for diff in range(1, max_num):  # Iterate through all possible differences.
                prev_max = dp[num][diff]
                dp[num][diff] = max(dp[num][diff], dp[num][diff - 1])  # Propagate maximum frequencies for smaller differences. We do this because a smaller difference is more likely to exist.
                # print(f"\t\tPropagating max for diff {diff}: {dp[num][diff]} (max of {prev_max} and {dp[num][diff-1]})")

            # _printDP(f"DP table after processing number {num}:")

        # Find the maximum frequency across all numbers and differences.
        max_freq = 0
        for i in range(max_num + 1):
            max_freq = max(max_freq, max(dp[i]))

        # _printDP(f"Final DP table:")
        # print(f"Maximum frequency: {max_freq}")

        return max_freq

```
['Python3']