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

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

Example 3:
Input:  6 7 8 7 4 6 6 3 7 0 0 0 0 0 0 5 3 7 5
Output: 8 7 4 6 6 3 7 0 0 0 0 0 0 5 3 7 5 6 7

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