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

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

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

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