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

Find the following:

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

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

    long res=0;
    set<int> s={-1, n};
    for(int i=1; i<=n; ++i) {
        int k=p[i];
        auto it=s.upper_bound(k);
        long R=*it;
        long L=*--it;
        res+=(k-L)*(R-k)*i;
        s.insert(k);
    }
    cout<<res<<endl;
}
