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

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

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

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