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152

Count Inversions

Difficulty: MEDIUM
Contributed By
Avg. time to solve
40 min
Success Rate
55%

Problem Statement

For a given integer array/list 'ARR' of size 'N' containing all distinct values, find the total number of 'Inversions' that may exist.

An inversion is defined for a pair of integers in the array/list when the following two conditions are met.

A pair ('ARR[i]', 'ARR[j]') is said to be an inversion when:

1. 'ARR[i] > 'ARR[j]' 
2. 'i' < 'j'

Where 'i' and 'j' denote the indices ranging from [0, 'N').
Input format :
The first line of input contains an integer 'N', denoting the size of the array.

The second line of input contains 'N' integers separated by a single space, denoting the elements of the array 'ARR'.
Output format :
Print a single line containing a single integer that denotes the total count of inversions in the input array.
Note:
You are not required to print anything, it has been already taken care of. Just implement the given function.  
Constraints :
1 <= N <= 10^5 
1 <= ARR[i] <= 10^9

Where 'ARR[i]' denotes the array element at 'ith' index.

Time Limit: 1 sec
Sample Input 1 :
3
3 2 1
Sample Output 1 :
3
Explanation of Sample Output 1:
We have a total of 3 pairs which satisfy the condition of inversion. (3, 2), (2, 1) and (3, 1).
Sample Input 2 :
5
2 5 1 3 4
Sample Output 2 :
4
Explanation of Sample Output 1:
We have a total of 4 pairs which satisfy the condition of inversion. (2, 1), (5, 1), (5, 3) and (5, 4).
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