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

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

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

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