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;

#define rep(i,m,n) for(long long i=m;i<n;i++)

typedef long long ll;

int main(){
   cin.tie(nullptr);
  ios::sync_with_stdio(false);

 ll n;
  cin >> n;
  vector<ll> p(n);
  rep(i,0,n){
    ll a;
    cin >> a;
    a--;
    p[a]=i;
  }
  
  set<ll> s;
  s.insert(-1);
  s.insert(n);
  ll res=0;
  
  rep(i,0,n){
    auto v=s.lower_bound(p[i]);
    ll r=*v-p[i];
    v--;
    ll l=p[i]-*v;
    s.insert(p[i]);
    res+=(i+1)*l*r;
  }
  cout << res << endl;
}
