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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 4 7 6 9 5 9 7 0 0 0 0 0 0 0 0 0 2 7 8 7 9 4 8 4 1 6
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