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

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

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

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