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

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

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