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;
#ifdef LOCAL_DEBUG
  #include "LOCAL_DEBUG.hpp"
#endif
#define int long long

signed main(){

  int n; cin >> n;
  vector<int> a(n+1);
  for(int i = 1; i <= n; i++) cin >> a[i];

  vector<int> idx(n+1);
  for(int i = 1; i <= n; i++){
    idx[a[i]] = i;
  }

  set<int> st = {0, n+1};
  int ans = 0;
  for(int i = 1; i <= n; i++){
    auto pos = st.lower_bound(idx[i]);
    int right = *pos, left = *(--pos);
    ans += i * (idx[i] - left) * (right - idx[i]);
    st.insert(idx[i]);
  }
  cout << ans << endl;

  return 0;
}
