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

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

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

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