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

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

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

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