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

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

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

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