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

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

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

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