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

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

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

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