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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 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 4 1 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