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

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

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

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