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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 7 4 8 3 1 0 6 2 5 2 8 1 4 8 5 4 7 1 3 5 7 1 8 2 3 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