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

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

Example 3:
Input:  8 6 2 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 2 4 4 1 2 2 6 6
Output: 3 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 2 4 4 1 2 2 6 6 8 6 2 6

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 5
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