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:  0 6 6 2 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 6 6 2 4 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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

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