#include <iostream>
#include <algorithm>
#include <climits>
#include <vector>
#include <set>
using namespace std;
using ll = long long;

int main(){
  int n; cin >> n;
  ll a[n+1], b[n+1];
  for(int i=1; i<=n; i++){
    cin >> a[i];
    b[a[i]] = i;
  }

  ll ans = 0;
  set<ll> s; 
  s.insert(0); s.insert(n+1);
  for(int i=1; i<=n; i++){
    auto itr = s.upper_bound(b[i]);
    ans += (*itr-b[i]) * (b[i]-*(--itr)) * i;
    s.insert(b[i]);
  }
  
  cout << ans << endl;

  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

Constraints

* 1 ≦ N ≦ 200,000
* (a_1, a_2, ..., a_N) is a permutation of (1, 2, ..., N).

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the answer.

Note that the answer may not fit into a 32-bit integer.

Examples

Input

3
2 1 3


Output

9


Input

4
1 3 2 4


Output

19


Input

8
5 4 8 1 2 6 7 3


Output

85

### Response

```cpp
#include <iostream>
#include <algorithm>
#include <climits>
#include <vector>
#include <set>
using namespace std;
using ll = long long;

int main(){
  int n; cin >> n;
  ll a[n+1], b[n+1];
  for(int i=1; i<=n; i++){
    cin >> a[i];
    b[a[i]] = i;
  }

  ll ans = 0;
  set<ll> s; 
  s.insert(0); s.insert(n+1);
  for(int i=1; i<=n; i++){
    auto itr = s.upper_bound(b[i]);
    ans += (*itr-b[i]) * (b[i]-*(--itr)) * i;
    s.insert(b[i]);
  }
  
  cout << ans << endl;

  return 0;
}

```