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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 9 1 5 8 8 0 0 0 0 0 0 0 0 0 4 1 3 6 2 3 3 4 7 9 7 3 3 6 3
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