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

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

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

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