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

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

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

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