<|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:  4 1 4 9 2 1 8 9 7 2 6 3 0 0 0 4 1 8 3 6 9 6 4 6 8 5
Output: 9 2 1 8 9 7 2 6 3 0 0 0 4 1 8 3 6 9 6 4 6 8 5 4 1 4

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

Example 3:
Input:  4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 4 0 0

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