<|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:  8 5 1 3 3 0 0 0 0 0 0 0 0 0 7 2 5 9 1 4 4 1
Output: 1 3 3 0 0 0 0 0 0 0 0 0 7 2 5 9 1 4 4 1 8 5

Example 2:
Input:  3 7 6 6 8 2 0 0 0 0 0 0 0 0 0 0 3 4 7 4 2 2
Output: 6 6 8 2 0 0 0 0 0 0 0 0 0 0 3 4 7 4 2 2 3 7

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 8 5 3 6 7 2 4 2 1 0 0 0 0 0 0 0 2 4 4 6 9
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