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

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

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

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