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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1 3 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 1 3 0 0 0 0 0 0 0 0 0 0 0 0

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