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

Example 2:
Input:  2 6 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
Output: 0 0 0 8 2 6 6 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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

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