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:  4 9 0 0 1 4 0 0 8 0 8 0 1 7 0 0 8
Output: 0 0 0 0 0 0 0 0 4 9 1 4 8 8 1 7 8

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

Example 3:
Input:  1 3 6 0 0 0 0 0 9 5 1 0 9 5 6 7 6
Output: 0 0 0 0 0 0 1 3 6 9 5 1 9 5 6 7 6

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