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

Example 2:
Input:  0 7 1 7 6 4 2 2 7 4 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 7 1 7 6 4 2 2 7 4 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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