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

Example 2:
Input:  7 3 6 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
Output: 6 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 7 3

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 5 8 3 2 6 2 6 8 4 5 2 6 7 3 2 2 4 7 4 6 3 3 9 5 0 0 0 0 7
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