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

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

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