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

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

Example 3:
Input:  2 9 3 1 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 9 1 9 9 5 3 3
Output: 1 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 9 1 9 9 5 3 3 2 9 3

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