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

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

Example 3:
Input:  0 0 0 2 5 4 9 5 5 4 4 2 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 5 4 9 5 5 4 4 2 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2

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