Problem:
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The Number of Inversions

For a given sequence $A = \{a_0, a_1, ... a_{n-1}\}$, the number of pairs $(i, j)$ where $a_i > a_j$ and $i < j$, is called the number of inversions. The number of inversions is equal to the number of swaps of Bubble Sort defined in the following program:

bubbleSort(A)
cnt = 0 // the number of inversions
for i = 0 to A.length-1
for j = A.length-1 downto i+1
if A[j] < A[j-1]
swap(A[j], A[j-1])
cnt++

return cnt

For the given sequence $A$, print the number of inversions of $A$. Note that you should not use the above program, which brings Time Limit Exceeded.

Input

In the first line, an integer $n$, the number of elements in $A$, is given. In the second line, the elements $a_i$ ($i = 0, 1, .. n-1$) are given separated by space characters.

output

Print the number of inversions in a line.

Constraints

$ 1 \leq n \leq 200,000$

$ 0 \leq a_i \leq 10^9$

$a_i$ are all different

Sample Input 1

5
3 5 2 1 4

Sample Output 1

6

Sample Input 2

3
3 1 2

Sample Output 2

2

Solution in C++ (judge verdict: Accepted)

#include<iostream>

using namespace std;

typedef long long ll;

const long maxn=200005;
const ll maxv=1e9+5;

long sum=0;

void Merge(ll*a,long left,long mid,long right)
{
    long n1=mid-left,n2=right-mid;
    ll *L,*R;
    L=new ll [n1+1];R=new ll [n2+1];
    for(long i=0;i<n1;i++)
        L[i]=a[left+i];
    for(long j=0;j<n2;j++)
        R[j]=a[mid+j];
    L[n1]=R[n2]=maxv;
    long m=0,n=0;
    for(long i=left;i<right;i++)
    {
        if(L[m]<=R[n]){a[i]=L[m];m++;}
        else
        {
            sum+=n1-m;
            a[i]=R[n];
            n++;
        }
    }
}

void Merge_Sort(ll*a,long left,long right)
{
    if(left<right-1)
    {
        long mid=(left+right)/2;
        Merge_Sort(a,left,mid);
        Merge_Sort(a,mid,right);
        Merge(a,left,mid,right);
    }
}


int main()
{
    long n;
    ll a[maxn];
    cin>>n;
    for(long i=0;i<n;i++)
        cin>>a[i];
    Merge_Sort(a,0,n);
    cout<<sum<<endl;
    return 0;
}