D - Count Triangles CodeForces - 1355C

CodeForces - 1355C

Like any unknown mathematician, Yuri has favourite numbers: AA, BB, CC, and DD, where A≤B≤C≤DA≤B≤C≤D. Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides xx, yy, and zz exist, such that A≤x≤B≤y≤C≤z≤DA≤x≤B≤y≤C≤z≤D holds?

Yuri is preparing problems for a new contest now, so he is very busy. That's why he asked you to calculate the number of triangles with described property.

The triangle is called non-degenerate if and only if its vertices are not collinear.

Input

The first line contains four integers: AA, BB, CC and DD (1≤A≤B≤C≤D≤5⋅1051≤A≤B≤C≤D≤5⋅105) — Yuri's favourite numbers.

Output

Print the number of non-degenerate triangles with integer sides xx, yy, and zz such that the inequality A≤x≤B≤y≤C≤z≤DA≤x≤B≤y≤C≤z≤D holds.

Examples

Input

1 2 3 4

Output

4

Input

1 2 2 5

Output

3

Input

500000 500000 500000 500000

Output

1

Note

In the first example Yuri can make up triangles with sides (1,3,3)(1,3,3), (2,2,3)(2,2,3), (2,3,3)(2,3,3) and (2,3,4)(2,3,4).

In the second example Yuri can make up triangles with sides (1,2,2)(1,2,2), (2,2,2)(2,2,2) and (2,2,3)(2,2,3).

In the third example Yuri can make up only one equilateral triangle with sides equal to 5⋅1055⋅105.

题意：给定四个整数a,b,c,d，要求a≤x≤b,b≤y≤c,c≤z≤d，求这样的x,y,z一共能构成多少个三角形。

题解：反正千万别想着暴力能过就是了，直接看代码吧。

#include
#include
using namespace std;
typedef long long ll;
int main(){
	ll a, b, c, d, ans=0;
	scanf("%lld%lld%lld%lld", &a, &b, &c, &d);
	for(ll i=a+b; i<=b+c; i++){
		if(i>c){//a+b>c才能构成三角形 
			ll minz=c, maxz=min(i-1, d);
			ll miny=max(i-b, b), maxy=min(i-a, c);
			//确定a，求y和z的范围，范围相乘得三角形数量 
			ans += (maxz-minz+1)*(maxy-miny+1);	
		}
		
	}
	printf("%lld\n", ans);
	return 0;
}