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 0 0 0 0 0 0 0 0 0 0 0 0 9 5 4 2 8 3 5 7 7 2 8 5 1 2 3
Output: 1 2 3 2 5 0 0 0 0 0 0 0 0 0 0 0 0 9 5 4 2 8 3 5 7 7 2 8 5

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

Example 3:
Input:  2 5 9 1 9 0 0 0 0 0 0 2 4 4 2 8 8 2 6 2 6 2 7 4 5 9 1 7 9
Output: 1 7 9 2 5 9 1 9 0 0 0 0 0 0 2 4 4 2 8 8 2 6 2 6 2 7 4 5 9

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 6 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 5 5 6 5 9 4 5 7
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