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

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

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

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