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

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

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

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