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

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

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

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