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

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

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

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