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 s64;
#define rep(i,l,r) for(int i=l;i<=r;++i)
const int N=2e5+5;
int a[N],st[N],top;s64 dp[N];

int main()
{
	//freopen("1.in","r",stdin);
	int n;
	cin>>n;
	rep(i,1,n)scanf("%d",a+i);
	s64 ans=0;
	rep(i,1,n)
	{
		while(a[st[top]]>a[i])--top;
		dp[i]=dp[st[top]]+(s64)a[i]*(i-st[top]);
		st[++top]=i;
		ans+=dp[i];
	}
	cout<<ans;
}