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

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

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

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