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

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

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

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