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

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

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

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