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;
long long n,i,k,a[200001],b[200001],ans;
set<int>s;
int main()
{
    cin>>n;
    s.insert(0);
    s.insert(n+1);
    for(i=1;i<=n;i++){
       cin>>a[i];
        b[a[i]]=i;
    }
    for(i=1;i<=n;i++){
       auto it=s.lower_bound(b[i]);
       k=*it;
       it--;
       ans+=(k-b[i])*(b[i]-*it)*i;
       s.insert(b[i]);
    }
    cout<<ans<<endl;
    return 0;
       
}