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 8 9 6 9 5 3 1 6 3 6 1 1 9 9 6 2 7 1
Output: 1 0 0 0 0 0 0 0 0 0 8 9 6 9 5 3 1 6 3 6 1 1 9 9 6 2 7

Example 2:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 6 8 9
Output: 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 6 8

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

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