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

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

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

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