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

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

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

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