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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
8 1 5 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 9 1 4
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