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

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

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

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