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:  7 2 7 3 6 8 7 3 3 6 6 0 0 0 0 0 0 0 0 0 0 0 0 6 7
Output: 7 7 2 7 3 6 8 7 3 3 6 6 0 0 0 0 0 0 0 0 0 0 0 0 6

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

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

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