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;cin >> n;
  vector<ll> a(n),b(n);
  for(int i=0;i<n;i++){
    cin >> a[i];
    a[i]--;
    b[a[i]]=i;
  }
  set<ll> st,st2;
  ll ans=0;
  st.insert(-1);
  st.insert(n);
  st2.insert(1);
  st2.insert(-n);
  for(int i=0;i<n;i++){
    auto itr=st.upper_bound(b[i]);
    auto itr2=st2.upper_bound(-b[i]);
    ans+=(*itr-b[i])*(b[i]+*itr2)*(i+1);
    st.insert(b[i]);
    st2.insert(-b[i]);
  }
  cout << ans << endl;
}