#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main(void){
    ll n,l,r; cin>>n;
    set <ll> st;
    vector <ll> d(200010);
    for(int i=0;i<n;i++){
        int a; cin>>a;
        d[a]=i;
    }
    ll ans=0;
    st.insert(-1);
    st.insert(n);
    for(ll i=1;i<=n;i++){
        l=*(--st.lower_bound(d[i]));
        r=*(st.lower_bound(d[i]));
        ans += i*(d[i]-l)*(r-d[i]);
        st.insert(d[i]);
    }
    cout<<ans<<endl;
}
### Prompt

Create a solution in CPP for 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;
using ll = long long;
int main(void){
    ll n,l,r; cin>>n;
    set <ll> st;
    vector <ll> d(200010);
    for(int i=0;i<n;i++){
        int a; cin>>a;
        d[a]=i;
    }
    ll ans=0;
    st.insert(-1);
    st.insert(n);
    for(ll i=1;i<=n;i++){
        l=*(--st.lower_bound(d[i]));
        r=*(st.lower_bound(d[i]));
        ans += i*(d[i]-l)*(r-d[i]);
        st.insert(d[i]);
    }
    cout<<ans<<endl;
}
```