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>

#define SZ(x) ((int(x.size())))

typedef long long ll;

using namespace std;

const int maxn = 200*1000+10;
int n;
stack <pair <int, int> > s;
ll sum, t[maxn], x, ans;

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	s.push ({-1, -1});
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		cin >> x;
		while (x < s.top().first)
		{
			sum -= t[s.top().second] * s.top().first;
			s.pop();
		}
		t[i] = i - s.top().second;
		sum += t[i] * x;
		ans += sum;
		s.push ({x, i});
	}
	cout << ans;
	return 0;
}