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

Example 2:
Input:  0 0 0 0 5 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 5 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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