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

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

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

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