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

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

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

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