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

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

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

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