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

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

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

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