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

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

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

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 9 4 5 4 1 3 3 2 2 4 8 0 0 0 0 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