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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 3 8 2 5 2 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 3 8 2 5 2

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