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

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

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

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