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>
#define REP(i, a, n) for(int i = a; i < n; i++)
using namespace std;


int N, a[200000], p[200001];
set<int> s;
long sum;

int main(void) {
  cin >> N;
  REP(i, 0, N) cin >> a[i];

  REP(i, 0, N) {
    p[a[i]] = i + 1;
  }

  sum = 0;
  s.insert(0);
  s.insert(N + 1);
  REP(i, 1, N + 1) {
    set<int>::iterator itr = s.lower_bound(p[i]);
    int r = *itr;
    int l = *(--itr);
    sum += (long) i * (r - p[i]) * (p[i] - l);
    s.insert(p[i]);
  }

  cout << sum << endl;

  return 0;
}
