# Array Pairs

### Problem Statement :

```Consider an array of n  integers, A = [ a1, a2, . . . . an] . Find and print the total number of (i , j)  pairs such that ai * aj <= max(ai, ai+1, . . . aj) where i <  j.

Input Format

The first line contains an integer, n , denoting the number of elements in the array.
The second line consists of n space-separated integers describing the respective values of a1, a2 , . . . an .```

### Solution :

```                            ```Solution in C :

In C++ :

#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i=0;i<n;i++)
#define ll long long int
#define f first
#define s second
#define pi pair<ll,ll>
#define pii pair<pi,ll>
#define f first
#define s second
#define pb push_back
#define mod 1000000007
#define mp make_pair
#define pb push_back
#define rep(i,n) for(int i=0;i<n;i++)

int N;
int A[1000011];
int L[1000011];
int R[1000011];
vector<int>g[1000011];
ll bt[1000011];
int maxn;
void update(int ind, int val) {
while(ind <= maxn) {
bt[ind] += val;
ind += (ind & -ind);
}
}
ll query(int ind) {
ll ans = 0;
while(ind > 0) {
ans += bt[ind];
ind -= (ind & -ind);
}
return ans;
}
vector<int>V;
int find_ind(int x) {
if(V.back() <= x) return V.size();
return upper_bound(V.begin(), V.end(), x) - V.begin();
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);

cin >> N;
set<int>S;
unordered_map<int, int>M;

for(int i = 1; i <= N; i++) {
cin >> A[i];
assert(A[i] >= 1 and A[i] <= 1000000000);
S.insert(A[i]);
}
vector<pi>window;
for(int i = 1; i <= N; i++) {
while(window.size() > 0 and window.back().f < A[i]) window.pop_back();
if(window.size() == 0) L[i] = 1;
else {
L[i] = window.back().s + 1;
}
window.pb(mp(A[i], i));
}
window.clear();
for(int i = N; i >= 1; i--) {
while(window.size() > 0 and window.back().f <= A[i]) window.pop_back();
if(window.size() == 0) R[i] = N;
else {
R[i] = window.back().s - 1;
}
window.pb(mp(A[i], i));
}

for(int i = 1; i <= N; i++) {
if(i - L[i] <= R[i] - i) {
for(int j = L[i]; j < i; j++) {
g[i - 1].pb(-A[i] / A[j]);
g[R[i]].pb(A[i] / A[j]);
//S.insert(A[i]/A[j]);
}

g[i].pb(-1);
g[R[i]].pb(1);
} else {

for(int j = i + 1; j <= R[i]; j++) {
g[L[i] - 1].pb(-A[i] / A[j]);
g[i].pb(A[i] / A[j]);
//S.insert(A[i]/A[j]);
}

g[L[i] - 1].pb(-1);
g[i - 1].pb(1);
}
}
maxn = S.size() + 2;
int cnt = 1;
for(set<int>::iterator it = S.begin(); it != S.end(); it++) {
M[*it] = cnt++;
}
ll ans = 0;
int r;
V = vector<int>(S.begin(), S.end());
for(int i = 1; i <= N; i++) {
update(M[A[i]], 1);
for(int j = 0; j < g[i].size(); j++) {
r = find_ind(abs(g[i][j]));
if(g[i][j] < 0) {
ans -= query(r);
} else {
ans += query(r);
}
}
}
cout << ans;
}```
```

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