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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 6 4 6 2 8 5 1 6 2 8 5 2 2 5 8 1 0 0 0 0 0 0 0 0 0 2 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