<|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 4 1 6 1 6 7 4 3 0 0 0 0 0 0 0 0 0 1 4 1
Output: 6 1 6 7 4 3 0 0 0 0 0 0 0 0 0 1 4 1 3 4 1

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

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

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