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

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

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

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