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

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

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

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