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

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

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

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