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:  1 3 2 9 8 3 7 0 0 0 0 0 1 7 7 3 1 2
Output: 1 2 1 3 2 9 8 3 7 0 0 0 0 0 1 7 7 3

Example 2:
Input:  9 7 8 4 0 0 0 0 0 0 0 0 0 0 0 5 8 2
Output: 8 2 9 7 8 4 0 0 0 0 0 0 0 0 0 0 0 5

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 9 3 3 3 2 2 8 2 8 8 6 0 0 0 0 0 5
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