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;
const ll MOD = 1e9 + 7;
map<int,int> a;
set<int> s;

int main(){
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    a[x] = i;
  }
  ll ans = 0;
  s.insert(-1);
  s.insert(n);
  for (int i = 1; i <= n; i++) {
    int pos = a[i];
    auto it = s.lower_bound(pos);
    int r = *it;
    it--;
    int l = *it;
    s.insert(pos);
    ans += (ll)i * (r - pos) * (pos - l);
  }
  cout << ans << endl;
  return 0;
}
