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

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

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

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