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

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

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

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