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

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

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

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