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

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

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