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

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

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

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