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(){
  long long n,i,a,ans=0,p[222222];
  cin>>n;
  for(i=1;i<=n;i++){
    cin>>a;
    p[a]=i;
  }
  set<long long> s;
  set<long long> s2;
  s.insert(0);
  s.insert(n+1);
  s2.insert(0);
  s2.insert(-n-1);
  for(i=1;i<=n;i++){
    auto itr1=s2.lower_bound(-p[i]);
    auto itr2=s.upper_bound(p[i]);
    ans+=(*itr2-p[i])*(p[i]+*itr1)*i;
    s.insert(p[i]);
s2.insert(-p[i]);
  }
  cout<<ans<<endl;
}
