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 ll long long
ll n,a[200010],l[200010],r[200010];
ll s[200010],tol=0;
signed main(){
	std::ios::sync_with_stdio(false);
	cin>>n;
	for(ll i=1;i<=n;i++){
		cin>>a[i];
		l[i]=0;
		r[i]=n+1;
	}
	for(ll i=1;i<=n;i++){
		while(tol&&a[s[tol]]>a[i]){
			r[s[tol]]=i;
			tol--;
		}
		l[i]=s[tol];
		tol++;
		s[tol]=i;
	}
	ll ans=0;
	for(ll i=1;i<=n;i++){
		ans+=(i-l[i])*(r[i]-i)*a[i];
	}
	cout<<ans;
	
	
	
	
	
	return 0;
}