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

signed main(){
	int n;cin>>n;
	vector<int> a(n),l(n),r(n);
	for(auto&& w:a)cin>>w;
	for(int i=0;i<n;i++){
		l[i]=i;
		while(l[i]>0 && a[l[i]-1]>a[i]){
			l[i]=l[l[i]-1];
		}		
	}
	for(int i=n-1;i>=0;i--){
		r[i]=i;
		while(r[i]<n-1 && a[r[i]+1]>a[i]){
			r[i]=r[r[i]+1];
		}		
	}
	int ans=0ll;
	for(int i=0;i<n;i++){
		ans+=a[i]*(i-l[i]+1)*(r[i]-i+1);
	}
	cout<<ans<<endl;
}