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

Example 2:
Input:  5 0 0 2 3 2 3 2 6 3 5 9 4 9 5
Output: 4 9 5 5 0 0 2 3 2 3 2 6 3 5 9

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 2 5 4 0 4 7 4 6 4 6 2 3 1 3
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