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:  2 5 8 2 0 0 9 6 9 9 5 4 3 3 3
Output: 5 8 2 0 0 9 6 9 9 5 4 3 3 3 2

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 3 0 8 3 8 6 4 4 6 2 1 4 7 9
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