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:  9 9 4 7 2 3 5 7 8 2 7 3 8 6 8 9 7 3
Output: 4 7 2 3 5 7 8 2 7 3 8 6 8 9 7 3 9 9

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

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

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