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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 7 6 6 7 0 0 0 4 1 7 7 5 4 4 5 9 3 9 1 1 1 7 9 3 6 7 6
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