#include <iostream>
#include <set>
#include <vector>
using namespace std;
typedef long long lli;
lli n;
vector<lli> x;
set<lli> s;
lli ans = 0;
int main(){
    cin >> n;
    x = vector<lli> (n+1);
    for(lli i = 1;i <= n;i++){
        lli a;
        cin >> a;
        x[a] = i;
    }
    s.insert(0);s.insert(n+1);
    for(lli i = 1;i <= n;i++){
        auto itr = s.lower_bound(x[i]);
        ans += i * (*itr - x[i]) * (x[i] - *(--itr));
        s.insert(x[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 <set>
#include <vector>
using namespace std;
typedef long long lli;
lli n;
vector<lli> x;
set<lli> s;
lli ans = 0;
int main(){
    cin >> n;
    x = vector<lli> (n+1);
    for(lli i = 1;i <= n;i++){
        lli a;
        cin >> a;
        x[a] = i;
    }
    s.insert(0);s.insert(n+1);
    for(lli i = 1;i <= n;i++){
        auto itr = s.lower_bound(x[i]);
        ans += i * (*itr - x[i]) * (x[i] - *(--itr));
        s.insert(x[i]);
    }
    cout << ans << endl;
    return 0;
}
```