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

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

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

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