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

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

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

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