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;

int n,i,a[2000005];

deque <pair<int, int> > b;

int main(){
	scanf("%d", &n);
	for(i = 0; i < n; i++)
	scanf("%d", &a[i]);
	
	long long res = 0;
	long long s = 0;
	
	for(i = 0; i < n; i++){
		int cnt = 1;
		while(b.size() && b.back().first > a[i]){
			s -= (long long)b.back().second * b.back().first;
			cnt += b.back().second;
			b.pop_back();
		}
		
		s += (long long)cnt * a[i];
		res += s;
		b.push_back({a[i], cnt});
	}
	
	printf("%lld\n", res);
}
