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

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

Example 3:
Input:  7 1 3 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 3
Output: 2 3 7 1 3 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

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