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>
typedef long long ll;
using namespace std;
ll ans;
ll n;
ll a[200005];
int main() {
  cin >> n;
  for(int i = 0; i < n; i++) {
    int t;
    cin >> t;
    a[t] = i;
  }

  set<ll> s;
  s.insert(-1), s.insert(n);

  for(int i = 1; i <= n; i++) {
    ll j = a[i];
    auto it = s.lower_bound(j);
    ll r = *it;
    it--;
    ll l = *it;
    ans += ll(i) * (r - j) * (j - l);
    s.insert(j);
  }

  cout << ans << endl;
}
 
  
