------
## 最终结论
Here's the Python code to solve the problem as described:

```python
def minimum_total_time(n, a):
    # Sort the array 'a'
    a.sort()
    
    # Initialize total_time
    total_time = 0
    
    # Calculate the minimum possible total time
    for i in range(n):
        total_time += a[i] * a[n - i - 1]
    
    # Return the result modulo 10007
    return total_time % 10007

# Read input values
n = int(input().strip())
a = [int(input().strip()) for _ in range(n)]

# Calculate and print the result
print(minimum_total_time(n, a))
```

This code reads the number of tasks `n` and their associated difficulty/laziness levels into an array `a`. It then sorts this array and calculates the minimum possible total time by multiplying elements from both ends of the sorted array. Finally, it returns this total time modulo 10,007.