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

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

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

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