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

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

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

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