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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 8 4 0 0 0 0 7 4 1 9 1 9 9 8 1 1 4 1 5 3 9 5 6 8 8 8 6
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