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

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

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

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