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

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

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

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