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;
typedef long long ll;
int main(){
  ll n,i,j,k,ans=0;cin>>n;
  ll a[n];
  set<ll>  s1,s2;
  map<ll,ll> m;
  for(i=0;i<n;i++) cin>>a[i],m[a[i]]=i+1;
  ll l=0,r=n+1;
  s1.insert(l);
  s1.insert(r);
  s2.insert(-l);
  s2.insert(-r);
  for(i=1;i<=n;i++){
    k=m[i];
    
    l=*s1.lower_bound(k);
    r=-*s2.lower_bound(-k);
    //cout <<i<<":"<<k<<":"<<l<<":"<<r<<":"<<i*(k-l)*(r-k)<< endl;
    
    ans+=i*(k-l)*(r-k);
    s1.insert(k);
    s2.insert(-k);
  }
  cout << ans << endl;
  return 0;
}
