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

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

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

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