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;
int main(){
  int n;
  cin >> n;
  vector<long long> p(n+1);
  for(int i=1;i<n+1;i++){
    int a;
    cin >> a;
    p[a] = i;
  }
  set<long long> st;
  st.insert(0);
  st.insert(n+1);
  long long ans = 0;
  for(int i=1;i<n+1;i++){
    auto r = st.lower_bound(p[i]);
    auto l = r;
    l--;
    ans += (*r - p[i]) * (p[i] - *l) * i;
    st.insert(p[i]);
  }
  cout << ans << endl;
}