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 int long long
const int N=200005;
int n,l[N],r[N],a[N],b[N],ans;
signed main(){
	scanf("%lld",&n);
	for (int i=1;i<=n;i++)scanf("%lld",&a[i]);
	int tot=0;
	for (int i=1;i<=n;i++){
		while (tot&&a[i]<a[b[tot]])tot--;
		l[i]=b[tot];
		b[++tot]=i;
	}
	tot=1;b[1]=n+1;
	for (int i=n;i;i--){
		while (tot>1&&a[i]<a[b[tot]])tot--;
		r[i]=b[tot];
		b[++tot]=i;
	}
	//for (int i=1;i<=n;i++)printf("%lld %lld\n",l[i],r[i]);
	for (int i=1;i<=n;i++)ans+=(r[i]-i)*(i-l[i])*a[i];
	printf("%lld",ans);
} 