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

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

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

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