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:  3 4 8 4 5 4 7 7 1 5 5 5 2 6 1 0 0 0 0 0 0 0 0 0 0 2 7 6 7
Output: 5 4 7 7 1 5 5 5 2 6 1 0 0 0 0 0 0 0 0 0 0 2 7 6 7 3 4 8 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 5 1 2 9 9 5 6 6 7 5 8 5 3 5 3 3 7 2 8 0 0 0 0
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