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

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

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

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