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

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

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

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