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

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

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

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