<|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:  2 6 9 8 4 0 0 0 0 0 0 2 2 4 6 3
Output: 3 2 6 9 8 4 0 0 0 0 0 0 2 2 4 6

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
2 3 8 4 7 7 6 6 3 1 6 9 0 0 3 7
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