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

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

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

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