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;

typedef long long ll;

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);

  int n; cin>>n;
  vector<ll> p(n);
  for (int i=0; i<n; i++) cin>>p[i];
  map<ll,ll> idx;
  for (int i=0; i<n; i++) idx[p[i]]=i+1;

  ll ret=0;
  set<ll> st={0,n+1};
  for (ll i=1; i<=n; i++) {
    ll cur=idx[i];
    set<ll>::iterator it=st.upper_bound(cur);
    ll r=(*it), l=(*(--it));
    ret+=(cur-l)*(r-cur)*i;
    st.insert(cur);
  }
  cout << ret << endl;
  return 0;
}