<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

Example 3:
Input:  5 5 5 4 9 0 0 0 0 0 0 0 1 2 5 1
Output: 5 1 5 5 5 4 9 0 0 0 0 0 0 0 1 2

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
9 4 5 4 0 0 0 0 0 0 0 1 6 4 1 8
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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user