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

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

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

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 7 3 1 1 4 2 7 7 7 7 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