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:  0 4 3 6 8 3 8 2 5 5 8 3 7 8 5 5 2 2 1
Output: 0 1 2 2 5 5 8 7 3 8 5 5 2 8 3 8 6 3 4

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

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

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