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

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 6 4 6 0 0 0
Output: 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 6 4

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

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