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:  8 4 3 9 7 6 4 4 3 3 4 5 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7
Output: 0 2 7 8 4 3 9 7 6 4 4 3 3 4 5 7 3 0 0 0 0 0 0 0 0 0 0 0 0

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

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

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