Counting Pairs with Target Sum

Given two integer intervals \([a,b]\) and \([c,d]\), an integer is chosen uniformly at random from each interval. Determine the probability that the sum equals \(e\). However, instead of outputting the probability, output the value obtained by multiplying this probability with \((b-a+1)(d-c+1)\). This result is guaranteed to be an integer, and in fact it represents the number of pairs \((x,y)\) such that \(x \in [a,b]\), \(y \in [c,d]\), and \(x+y=e\).

Note: All inputs are integers and it is given that \(a \le b\) and \(c \le d\).

inputFormat

The input consists of a single line containing five space-separated integers: \(a\), \(b\), \(c\), \(d\), and \(e\).

outputFormat

Output a single integer, which is the number of pairs \((x,y)\) such that \(x \in [a,b]\), \(y \in [c,d]\), and \(x+y = e\).

sample

1 3 1 3 4

3