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

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

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

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