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

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

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

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