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

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

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

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