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;
using ll = long long;

int main(int argc, char const* argv[])
{
  int N; cin >> N;
  vector<int> a(N); for (int i = 0; i < N; i++) cin >> a[i];
  vector<int> b(N + 1); for (int i = 0; i < N; i++) b[a[i]] = i;
  ll ans {};
  set<int> s { -1, N };
  for (int i = 1; i <= N; i++) {
    s.insert(b[i]);
    auto itr = s.find(b[i]);
    int l, r;
    itr--; l = *itr; itr++;
    itr++; r = *itr; itr--;
    ans += (ll)i * (*itr - l) * (r - *itr);
  }
  cout << ans << endl;
  return 0;
}
