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 6 5 5 2 1 6 6
Output: 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 5 5 2 1

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

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

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