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

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

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

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