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

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

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

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