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>
#define endl '\n'
#define N 200005
using namespace std;

struct kieu{long gt,vt;};
kieu st[N];
long  a[N], n,so,kq;

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);
	cin>>n;
	st[0]={0,0}; so=0;
	for(long i=1;i<=n;++i) cin>>a[i];
	for(long i=1;i<=n+1;++i){
		while(a[i]<st[so].gt){
			kq+=st[so].gt*(i-st[so].vt)*(st[so].vt-st[so-1].vt);
			--so;
		}
		st[++so]={a[i],i};
	}
	cout<<kq;
}