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

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

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

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