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

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

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

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