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;

const int MAXN = 200005;

int N, a[MAXN];

int main(){
	scanf("%d", &N);
	
	stack < pair <int, int> > s;
	long long res = 0, cur = 0;
	
	for(int i = 0; i < N; i++){
		scanf("%d", &a[i]);
		
		int cnt = 1;
		while(!s.empty()){
			pair <int, int> t = s.top();
			if(t.first < a[i])break;
			
			s.pop();
			cur -= 1LL * t.first * t.second;
			cnt += t.second;
		}
		s.push(make_pair(a[i], cnt));
		cur += 1LL * a[i] * cnt;
		
		res += cur;
	}
	
	printf("%lld\n", res);
	
	return 0;
}
