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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 5 4 0 0 0 0 0 0 9 7 5 2 7 1 2 9 5 9 2 1 9 4 2 5 7 4 4 1 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