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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 7 6 3 9 6 4 2 8 3 8 9 5 4 5 1 1 2 0 4 8 3 8 9 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