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

Example 2:
Input:  0 4 8 8 4 8 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 8 4 8 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8

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

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