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

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

Example 3:
Input:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 4 4 3 4 7 8 5 5
Output: 7 8 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 4 4 3 4

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