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 0 0 0 0 0 0 0 9 9 5 9 1 1 7 8 7 1 8 9 8 8 0
Output: 8 0 0 0 0 0 0 0 0 0 9 9 5 9 1 1 7 8 7 1 8 9 8

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

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

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