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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 1 6 0 0 0 0 0 0 0 0 0 0 0 1 5 4 1 7 4 6 9 8 1 7 4 6 6 3 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