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

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

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

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