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

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

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

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