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

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

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

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 6 9 2 6 2 8 2 9 9 5 6 3 3 6 0 0 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