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

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

Example 3:
Input:  5 5 5 4 4 8 7 1 5 8 0 0 0 0 0 0 0 0 0 0
Output: 4 4 8 7 1 5 8 0 0 0 0 0 0 0 0 0 0 5 5 5

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
3 1 1 7 9 9 9 0 9 2 7 5 3 3 9 6 9 7 3 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