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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 6 9 6 4 7 9 9 0 0 0 0 0 0 0 0 1 2 8 1 9 7 3
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