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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 2 4 1 1 5 6 2 3 7 4 5 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