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

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

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

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