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;
#define ll long long
#define nn 65536*4
#define lf double
int bel[nn];
set<int> s;
int n;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		int x;scanf("%d",&x);
		s.insert(i);bel[x]=i;
	}
	s.insert(0);s.insert(n+1);
	ll ans=0;
	for(int i=n;i>=1;i--)
	{
		s.erase(bel[i]);
		set<int>::iterator it=s.lower_bound(bel[i]);
		int r=*it,l=*(--it);
		ans=ans+1ll*i*(r-bel[i])*(bel[i]-l);
	}
	cout<<ans;
	return 0;
} 