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

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

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

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