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

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

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

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