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

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

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

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