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

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

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

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 7 4 4 2 1 7 7 3 1 1 7 2 6 0 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