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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 1 2 3 3 3 7 6 2 0 0
Output: 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 1 2 3 3 3 7 6

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 2 5 8 0 0 8 8 2 5 6 3 3 3 7 4 9 3 8 9 2 9 1 3 7 7 7 2 8
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