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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 3 6 6 7 7
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