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

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

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

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