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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 2 1 5 7 6 9 1 4 3 7 3 6 4 3 0 0 0 5 2
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