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

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

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

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