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 3 6 1 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 6 2 9 3 8 6
Output: 6 1 9 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 6 2 9 3 8 6 6 3

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

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

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