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 N;
#define MAX_N 200000
int A[MAX_N], B[MAX_N];
set<int> known;
long long res;

int main() {
  cin >> N;
  for(int i = 0; i < N; ++i) {
    cin >> A[i]; --A[i]; B[A[i]] = i;
  }
  known.insert(-1); known.insert(N);
  for(int i = 0; i < N; ++i) {
    long long mid = B[i];
    auto it = known.upper_bound(mid); long long hi = *it;
    --it; long long lo = *it;
    known.insert(mid);
    res += (i + 1) * (mid - lo) * (hi - mid);
  }
  cout << res << endl;
  return 0;
}
