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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 2 3 3 4 1 7 7 8 7 2 8 1 1 4 5 9 8 6 2 3 6 9 1 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