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

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

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