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:  6 0 9 0 0 7 1 0 0 0 7 9 6 9 7 0
Output: 0 0 0 0 0 0 0 6 9 7 1 7 9 6 9 7

Example 2:
Input:  5 0 0 1 0 3 6 0 0 3 9 0 0 0 9 0
Output: 0 0 0 0 0 0 0 0 0 5 1 3 6 3 9 9

Example 3:
Input:  1 9 8 6 5 3 6 1 0 0 1 4 0 0 5 8
Output: 0 0 0 0 1 9 8 6 5 3 6 1 1 4 5 8

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