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

Example 2:
Input:  4 2 6 0 0 0 0 0 0 3 4 4 8 6 7 3 2 7 8 7 7 2 3 7 8
Output: 7 8 4 2 6 0 0 0 0 0 0 3 4 4 8 6 7 3 2 7 8 7 7 2 3

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