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;
using ll = long long;
using ull = unsigned long long;
#define MOD 1000000007

int a[200010],r[200010],l[200010];

int main(){
  int n;
  cin>>n;
  for(int i=0;i<n;i++) cin>>a[i+1];
  stack<int> s;
  for(int i=0;i<=n+1;i++){
    while(!s.empty()&&a[s.top()]>a[i]){
      r[s.top()]=i;
      s.pop();
    }
    if(!s.empty()) l[i]=s.top();
    s.push(i);
  }
  ll ans=0;
  for(int i=1;i<=n;i++){
    ans+=1LL*a[i]*(r[i]-i)*(i-l[i]);
  }
  cout<<ans<<endl;
  return 0;
}