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

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

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

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 1 1 5 4 6
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