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

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

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

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