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

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

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

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