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

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

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

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