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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 2 4 1 8 6 1 3 1 1 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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