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

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

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

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