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:  4 6 6 6 9 9 2 3 1 7 9 8 1 9 8 5 7 3 9 8
Output: 6 6 9 9 2 3 1 7 9 8 1 9 8 5 7 3 9 8 4 6

Example 2:
Input:  3 0 0 0 0 0 0 0 0 0 6 8 6 3 3 4 4 6 6 4
Output: 0 0 0 0 0 0 0 0 6 8 6 3 3 4 4 6 6 4 3 0

Example 3:
Input:  2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 4 1
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 4 1 2 2

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