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