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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 8 0 0 0 0 0 4 1 7 7 1 1 3 3 9 3 8 5 2 6 3 2 1 7 4 7 8
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