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

Example 2:
Input:  0 0 0 0 0 0 0 3 4 9 3 7 5 9 1 7 3 6 5 4 9 0 0 0 0 0 0 0 0
Output: 0 0 0 0 0 0 0 0 0 3 4 9 3 7 5 9 1 7 3 6 5 4 9 0 0 0 0 0 0

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

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