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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
5 6 4 8 3 1 0 0 0 0 4 4 8 7 2 9 4 9 1 7 7 5
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