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

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

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

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