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

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

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

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