LogiQuest

71. Count Inversions

HardMerge SortDivide and Conquer

An inversion is a pair i < j with a[i] > a[j]. Print the number of inversions.

Input format

Line 1: n Line 2: n integers

Output format

The number of inversions.

Example 1

Input

5
2 4 1 3 5

Output

3

Example 2

Input

3
1 2 3

Output

0

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 7 test cases, most of them hidden.

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