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

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

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

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