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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 6 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 4 9 6 1 5 5 8
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