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

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

Example 3:
Input:  7 7 4 4 9 9 2 8 3 9 2 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 9
Output: 4 4 9 9 2 8 3 9 2 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 9 7 7

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 5 7 9 3 9 0 0 0 0 0 0 0 0 1 1 2 9 8 2 4 1 3 7 3 1 8 1 8
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