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 7 2 5 8 2 9 5 3 8 0 3 7 7 9 1 1 1 2
Output: 8 2 9 5 3 8 0 3 7 7 9 1 1 1 2 9 7 2 5

Example 2:
Input:  8 5 9 6 5 6 3 5 1 4 0 0 0 8 1 9 6 7 8
Output: 5 6 3 5 1 4 0 0 0 8 1 9 6 7 8 8 5 9 6

Example 3:
Input:  4 6 7 6 2 8 7 9 7 0 0 7 6 6 8 5 6 1 3
Output: 2 8 7 9 7 0 0 7 6 6 8 5 6 1 3 4 6 7 6

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 0 0 0 0 0 0 0 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