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 <iostream>
#include <set>
using namespace std;
int main(void){
    int n, b[200001];
    set<int> s={0};
    long long c=0;
    cin>>n;
    for(int i=1;i<=n;i++){
        int a;
        cin>>a;
        b[a]=i;
    }
    s.insert(n+1);
    for(int i=1;i<=n;i++){
        auto it=s.lower_bound(b[i]);
        long long p=(*it)-b[i],q;
        //cout<<i<<" "<<b[i]<<" "<<(*it);
        it--;
        //cout<<" "<<(*it)<<endl;
        q=b[i]-(*it);
        c+=p*q*i;
        //cout<<c<<endl;
        s.insert(b[i]);
    }
    cout<<c<<endl;
}