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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 6 8 3 3 9 2 9 5 6 5 6 4 7 9 3 6 2 6 3 0 0 3 1 2 1 3
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