Truck Parking Fees

Interview

Time limit1sMemory limit128 MB

Summary

Given per-truck rates depending on how many of three trucks overlap in time, compute the total parking fee over discrete minute intervals.

Level: Easy3 of 10
Topics: Simulation, Implementation
Solved: No attempts yet

Problem

A driver owns three trucks. The parking lot charges a discounted per-truck fee depending on how many of the trucks are parked at the same time.

If exactly one truck is parked, the fee is A won per minute for that truck. If exactly two trucks are parked, the fee is B won per minute for each truck. If all three trucks are parked, the fee is C won per minute for each truck.

Given A, B, C and the arrival and departure times of the three trucks, compute the total parking fee. A truck is considered parked from its arrival time up to, but not including, its departure time.

Input

The first line contains the parking fees A, B, and C separated by spaces. (1 <= C <= B <= A <= 100)

Each of the next three lines contains two integers: the arrival time and departure time of one truck. The arrival time is always earlier than the departure time, and every time is an integer from 1 to 100 inclusive.

Output

Print the total parking fee for the three trucks.

Examples2

Example 1
Input
```
5 3 1
1 6
3 5
2 8
```
Expected output
```
33
```
Example 2
Input
```
10 8 6
15 30
25 50
70 80
```
Expected output
```
480
```