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

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

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

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