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 <algorithm>
#include <iostream>
#include <set>
using namespace std;
int main(){
  int N;
  cin >> N;
  int A[N], id[N+1];
  for(int i = 0; i < N; ++i){
    cin >> A[i];
    id[A[i]] = i;
  }
  long long int ans = 0LL;
  set<int> S;
  S.insert(N);
  S.insert(-1);
  for(int i = 1; i <= N; ++i){
    S.insert(id[i]);
    set<int>::iterator itr = S.find(id[i]), l = itr, r = itr;
    --l;
    ++r;
    ans += (long long int)(id[i] - *l)*(*r - id[i])*i;
  }
  cout << ans << endl;
  return 0;
}
