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

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

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

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