One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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;
#define ll long long
const ll N=5e5;

  ll n,A;
  ll a[N],l[N],k[N],r[N];
ll cmp(ll x,ll y)
{
  return a[x]>a[y];
}

int main()
{
  cin>>n;
  for (ll i=0;++i<=n;)
    scanf("%d",a+i),
	  l[i]=i-1,k[i]=i,r[i]=i+1;
  sort(k+1,k+n+1,cmp);
  for (ll i=0;++i<=n;)
    {
      A+=a[k[i]]*(r[k[i]]-k[i])*(k[i]-l[k[i]]);
      r[l[k[i]]]=r[k[i]];
      l[r[k[i]]]=l[k[i]];
    }
  cout<<A;
  exit(0);
}