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

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

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

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