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Problem of the day

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').
```

Detailed explanation

```
1 <= N <= 10^5
1 <= ARR[i] <= 10^9
Where 'ARR[i]' denotes the array element at 'ith' index.
Time Limit: 1 sec
```

```
3
3 2 1
```

```
3
```

```
We have a total of 3 pairs which satisfy the condition of inversion. (3, 2), (2, 1) and (3, 1).
```

```
5
2 5 1 3 4
```

```
4
```

```
We have a total of 4 pairs which satisfy the condition of inversion. (2, 1), (5, 1), (5, 3) and (5, 4).
```

```
1. Start with the brute force approach.
2. Use a modified merge sort.
3. Iterate through the elements in sorted order and use a Fenwick tree to track the inversions.
```