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

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

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

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