<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  5 3 9 2 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3
Output: 9 2 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 5 3

Example 2:
Input:  1 7 0 0 0 0 0 0 0 5 4 2 3 9 8 7 9 5 7 2 4
Output: 0 0 0 0 0 0 0 5 4 2 3 9 8 7 9 5 7 2 4 1 7

Example 3:
Input:  0 7 5 3 7 5 9 1 7 8 9 4 5 9 3 4 6 7 2 9 0
Output: 5 3 7 5 9 1 7 8 9 4 5 9 3 4 6 7 2 9 0 0 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 3 3 6 8 1 0 0 4 2 4 7 8 3 4 7 5 6 2 1 6
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user