A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 8 9 5 7 5 1 5 7 2 4 0 0 0 4 7 5 9 1 2 7 1 1 3 5 9
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>.
Assistant: Let me solve this step by step.
<think>
user