Given intervals $[a, b]$ and $[c, d]$, count the number of ordered pairs of co-prime integers $(x, y)$ such that $a \le x \le b$ and $c \le y \le d$. Coprime integers have no common factor greater than $1$.

-----Input-----
The input consists of a single line of four space-separated integers $a$, $b$, $c$, and $d$. These integers satisfy the bounds ($1 \le a \le b \le 10^7$, $1 \le c \le d \le 10^7$).

-----Output-----
Print a single integer: the number of coprime pairs $(x,y)$ with $a \le x \le b, c\le y \le d$.

-----Examples-----
Sample Input 1:
1 5 1 5
Sample Output 1:
19

Sample Input 2:
12 12 1 12
Sample Output 2:
4

Source: kattis | Difficulty: HARD


Solutions: