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

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

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

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