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

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

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

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