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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 4 7 4 1 2 7 7 4 8 9 0 0 0 0 0 0 0 0 0 0 2 8 6 5 2 2 4
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