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

int main() {
  long n,ans=0;
  cin >> n;
  vector<long> a(n);
  vector<long> b(n);
  for(long i=0;i<n;i++) cin >> a[i];
  for(long i=0;i<n;i++) b[a[i]-1]=i;
  set<long> aaa={-1,n};
  for(long i=0;i<n;i++) {
    auto itr=aaa.upper_bound(b[i]);
    long x=*itr-b[i];
    itr--;
    long y=b[i]-*itr;
    ans+=x*y*(i+1);
    aaa.insert(b[i]);
  }

  cout << ans << endl;
}
### Prompt

Generate a Cpp solution to 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 <bits/stdc++.h>
using namespace std;

int main() {
  long n,ans=0;
  cin >> n;
  vector<long> a(n);
  vector<long> b(n);
  for(long i=0;i<n;i++) cin >> a[i];
  for(long i=0;i<n;i++) b[a[i]-1]=i;
  set<long> aaa={-1,n};
  for(long i=0;i<n;i++) {
    auto itr=aaa.upper_bound(b[i]);
    long x=*itr-b[i];
    itr--;
    long y=b[i]-*itr;
    ans+=x*y*(i+1);
    aaa.insert(b[i]);
  }

  cout << ans << endl;
}
```