#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main(void) {
  ll n;
  cin >> n;
  
  vector<ll> a(n), b(n + 1);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[a[i]] = i + 1;
  }

  ll ans = 0;
  set<ll> stl, str;
  stl.insert(0); str.insert(0);
  stl.insert(-(n + 1)); str.insert(n + 1);
  for (int i = 1; i <= n; i++) {
    ll l = *stl.upper_bound(-b[i]), r = *str.upper_bound(b[i]);
    ans += (b[i] + l) * (r - b[i]) * (ll)i;
    stl.insert(-b[i]); str.insert(b[i]);
  }
  cout << ans << endl;

  return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

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 <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main(void) {
  ll n;
  cin >> n;
  
  vector<ll> a(n), b(n + 1);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[a[i]] = i + 1;
  }

  ll ans = 0;
  set<ll> stl, str;
  stl.insert(0); str.insert(0);
  stl.insert(-(n + 1)); str.insert(n + 1);
  for (int i = 1; i <= n; i++) {
    ll l = *stl.upper_bound(-b[i]), r = *str.upper_bound(b[i]);
    ans += (b[i] + l) * (r - b[i]) * (ll)i;
    stl.insert(-b[i]); str.insert(b[i]);
  }
  cout << ans << endl;

  return 0;
}
```