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

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

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

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