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

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

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

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