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;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
ll ans = 0;

int main()
{
ll n ;
cin >> n ;
vector<ll> a(n);
rep(i,n){
  ll r;
  cin >> r;
  a[r-1]=i+1;
}
set<ll> s;
s.insert(0);
s.insert(n+1);
rep(i,n){
  auto itr=s.insert(a[i]).first;
  auto itr1=itr;itr1++;
  auto itr2=itr;itr2--;
  ans+=(i+1)*(*itr1-*itr)*(*itr-*itr2);
}
cout << ans << endl;
return 0;
}