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

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

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