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;
typedef long long ll;
int main(){
  ll n,ans=0,r,l;
  cin >> n;
  ll a[n+1],b[n+1];
  set<ll> s;
  s.insert(0);
  s.insert(n+1);
  for(int i=1;i<=n;i++){
    cin >> a[i];
    b[a[i]]=i;
  }
  for(int i=1;i<=n;i++){
    auto it= s.upper_bound(b[i]);
    ans += (*it - b[i])*(b[i]- *(--it))*i;
    s.insert(b[i]);
  }
  cout << ans << endl;
}
