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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 4 7 0 0 0 8 3 9 7 7 9 2 5 5 6 3 6 5 7 7 9 8 6 6 8 7 2 6 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