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

Example 2:
Input:  7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 6 4
Output: 1 3 6 4 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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