Professor X has to solve the perennial problem of the budget for school picnic Each student is identified by a unique Roll Number $$$(r[i])$$$ and a Unique Identification Number$$$(a[i])$$$. The total amount of the trip will be calculated as the sum of the cost of each of the rounds as long as there are at least two students remaining in the class. In a single round:

• Professor will select two students in his class, let them be $$$p$$$ and $$$q$$$.

• Choose Unique Identification Number $$$(a[p])$$$ of one and Roll Number$$$(r[q])$$$ of the other. Add the value $$$a[p] \cdot r[q]$$$ to the amount of trip. Or another option is vice versa, $$$a[q] \cdot r[p].$$$

• Return one (say $$$p$$$) back to the class, while the other (say $$$q$$$) will go and sit in the bus outside or vice versa, i.e., return $$$q$$$ to the class and $$$p$$$ goes and sits in the bus. Note $$$p$$$ and $$$q$$$ are indexes of the students.

In the last round, both students will go to the bus.

The professor needs your help. You need to find the minimum possible amount of the trip, considering all the possible ways in which the student can be selected and organized. Help him out.

As this amount can be very large find its mod with 10^9+7.