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

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

Example 3:
Input:  6 1 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 7 7
Output: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 1 7 7 6 1 5

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