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

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

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

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