In this problem, you have to analyze a particular sorting algorithm. The algorithm processes a sequence of $n$ distinct integers by swapping two adjacent sequence elements until the sequence is sorted in ascending order. For the input sequence

9 1 0 5 4 ,

Ultra-QuickSort produces the output

0 1 4 5 9 .

Your task is to determine how many swap operations Ultra-QuickSort needs to perform in order to sort a given input sequence.

-----Input-----
Input begins with a line that contains a single integer $1 \le n \le 500000$ – the length of the input sequence. Each of the the following $n$ lines contains a single integer $0 \le a[i] \le 999999999$, the $i$-th input sequence element.

-----Output-----
Prints a single line containing an integer number op, the minimum number of swap operations necessary to sort the given input sequence.

-----Examples-----
Sample Input:
5
9
1
0
5
4
Sample Output:
6

Source: kattis | Difficulty: MEDIUM


Solutions: