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 LL;
int a[200005];
int l[200005], r[200005];

int pos[200005];
set<int> s;
set<int>::iterator its;
int main(){
	LL ans = 0;
	int n;
	scanf("%d", &n);
	s.insert(0);
	s.insert(n+1);
	for(int i=1;i<=n;i++){
		scanf("%d", &a[i]);
		pos[a[i]] = i;
	}	
	for(int i=1;i<=n;i++){
		int p = pos[i];
		its = s.lower_bound(p);
		r[p] = *its;
		its--;
		l[p] = *its;

		s.insert(p);
	}
	for(int i=1;i<=n;i++){
		int le = i-l[i];
		int ri = r[i]-i;
		ans += (LL)le*ri*a[i];
	}
	printf("%lld\n", ans);
}