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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

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