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

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

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

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