题目描述

About 44 days are left before $\textit{College Scholastic Ability Test}$ is held. This exam aims to measure students' achievement of National Curriculum standards and scholastic ability required for college education. (http://www.kice.re.kr/sub/info.do?m=0205&s=english)

One of the subjects covered by this test is Mathematics, which consists of 21 multiple choice questions and 9 short-answer questions. The answer of each short-answer question is guaranteed to be a $\textit{unique positive integer below 1\,000}$, as you can see from the answer sheet below.

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However, the organizers might want to give students short-answer questions with non-integer answers, such as $2\sqrt{3}$ or $\frac{5}{3}$. Usually, the workaround is to write the answer in a canonical form, and then sum up all the integers inside that form and ask students to write that number instead.

In particular, when the answer is a positive rational number $\frac{a}{b}$, the organizers usually ask students to reduce it and sum up the numerator and the denominator of the reduced fraction. For example, when the answer is $\frac{18}{10}$, the student should reduce it to $\frac{9}{5}$ and write the final answer as $9 + 5 = 14$.

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However, when the answer is $\frac{521}{500}$, the reduced fraction is also $\frac{521}{500}$, so the student should write the final answer as $521 + 500 = 1021$. But this shouldn't happen, since all the answers for the short-answer questions are below 1,000. To avoid this situation, the organizers should make sure that after reducing the fraction, the sum of the numerator and the denominator shouldn't exceed $999$. Let's call such fractions as $\textit{Suneung Fractions}$. For example, $\frac{1996}{2}$ and $\frac{18}{10}$ are $\textit{Suneung fractions}$, while $\frac{1998}{2}$ and $\frac{521}{500}$ are not.

Suppose that, this year, one of the organizers wrote a problem, and the answer to that problem is $\frac{x}{y}$. Since the problem is not finalized yet, the only thing we know is $A \le x \le B$ and $C \le y \le D$ holds, for given $A, B, C, D$. The organizers want to know, among all the pairs $(x, y)$, how many of $\frac{x}{y}$ is a $\textit{Suneung fraction}$. Write a program that counts this number.

输入格式

The first and only line contains four space-separated integers $A, B, C$ and $D$ ($1 \le A \le B \le 10^{12}$, $1 \le C \le D \le 10^{12}$)

输出格式

Print the number of integral pairs $(x, y)$ ($A \le x \le B$, $C \le y \le D$), where $\frac{x}{y}$ is a $\textit{Suneung fraction}$.

5 8 3 6

16

2018 2019 2018 2019

2