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

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

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

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 0 0 0 0 0 0 0 0 0 0 0 0 6 6 1
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