<|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 0 0 0 0 0 0 4 8 2 5 2 2 3 2 3 7
Output: 0 0 0 0 0 0 0 0 7 3 2 3 2 2 5 2 8 4

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

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

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