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 6 7 0 0 0 0 0 0 0 0 0 0 0 8 8 7 1 6 6 1
Output: 7 0 0 0 0 0 0 0 0 0 0 0 8 8 7 1 6 6 1 1 6

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

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

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