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

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

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

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