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:  3 6 6 9 8 3 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 7
Output: 8 7 3 6 6 9 8 3 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 8

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

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

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