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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 1 2 7 1 9 9 3 4 4 5 5 8 3 7 6 1 3 9 4 1 3 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>.
Assistant: Let me solve this step by step.
<think>
user