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

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

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

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