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

Example 2:
Input:  1 6 8 7 2 2 0 0 0 0 9 8 4 3 4 5 4 5 9 3 6 3 2 5 7 5 3
Output: 5 7 5 3 1 6 8 7 2 2 0 0 0 0 9 8 4 3 4 5 4 5 9 3 6 3 2

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

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 3 4 9 4 6 6 8 9 6 1 6 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