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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 2 4 0 0 8 7 5 5 4 5 7 5 9 2 7 4 3 4 6 4 9 6 8 6 4 6 5 4 1
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