<|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 8 3 8 0 0 0 0 0 0 0 5 4 3 1 2
Output: 3 1 2 6 8 3 8 0 0 0 0 0 0 0 5 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
1 4 9 3 2 0 0 1 2 3 7 7 6 6 6 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user