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 6 2 9 7 8 8 6 5 9 7 5 4 7 2 1 6 8 8 6 6 0
Output: 0 0 0 0 0 0 0 0 0 6 2 9 7 8 8 6 5 9 7 5 4 7 2 1 6 8 8 6 6

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

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

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