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

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

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

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