Sums of Blue and Red Cubes

Interview

Time limit2sMemory limit1024 MB

Summary

Count the pairs (x, y) with x and y each taken from the integers a to b whose sum lies between c and d inclusive.

Level: Medium4 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

Krosh received several gifts on a holiday. Barash and Losyash each gave him a set of cubes. Barash gave blue cubes and Losyash gave red cubes. Each set has one cube for every integer from $a$ to $b$ inclusive, and no two cubes in the same set share a number.

Krosh chooses two numbers $c$ and $d$ . He then picks one blue cube and one red cube so that the sum of their numbers is between $c$ and $d$ inclusive. Count the number of ways to do this.

Input

The input is a single line with four integers $a$ , $b$ , $c$ , and $d$ . $0 \le a \le b \le 10^9$ , $0 \le c \le d \le 2 \cdot 10^9$ .

Output

Print one integer: the number of ways to choose one blue cube and one red cube so that their sum is in the given range.

Examples2

Example 1
Input
```
3 6 7 9
```
Expected output
```
9
```
Example 2
Input
```
1 1 10 10
```
Expected output
```
0
```