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

Example 2:
Input:  5 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6

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

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