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

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

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

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