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

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

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

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