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<iostream>
#include<cstdio>
#define int long long
using namespace std;
int n,top,minn;
const int N=1000010;
int a[N],zhan[N],r[N],l[N];
long long ans;
signed main()
{
	cin>>n;
	for(int i=1;i<=n;++i)scanf("%lld",&a[i]);
	for(int i=1;i<=n;++i)r[i]=n+1,l[i]=0;
	for(int i=1;i<=n;++i)
	{
		while(top&&a[zhan[top]]>a[i])r[zhan[top--]]=i;
		l[i]=zhan[top];
		zhan[++top]=i;
	}
	for(int i=1;i<=n;++i)ans+=(r[i]-i)*(i-l[i])*a[i];
	cout<<ans;
	return 0;
}
/*
8
5 4 8 1 2 6 7 3
*/