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 9 5 5 9 4 6 9 3 5 0 0 3 6 2 5 7 5
Output: 5 9 4 6 9 3 5 0 0 3 6 2 5 7 5 2 9 5

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

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

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