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

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

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

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