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

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

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

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