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 main()
{
	int64_t n;
	cin >> n;
	vector<int64_t> as(n);
	for (auto &a : as)
	{
		cin >> a;
	}
	vector<pair<int64_t, int64_t>> v(n);
	for (int64_t i = 0; i < n; i++)
	{
		v[i] = {as[i], i};
	}
	sort(v.begin(), v.end());
	set<int64_t> st;
	st.insert(-1);
	st.insert(n);
	int64_t ans = 0;
	for (auto &p : v)
	{
		auto itr = st.lower_bound(p.second);
		int r = *itr, l = *(--itr);
		ans += p.first * (r - p.second) * (p.second - l);
		st.insert(p.second);
	}
	cout << ans << endl;
	return 0;
}