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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 0 0 0 6 1 6 5 7 3 9 6 3 5 1 8 7 2 2
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