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

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

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

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