<|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:  3 3 4 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9 5 2 5 1 9 9 2
Output: 9 9 2 3 3 4 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9 5 2 5 1

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 0 0 0 0 0 0 0 0 0 0 0 0 4 8 8 9 4 6 2 1 6 5 9 2 1 1 4 2
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