One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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>
typedef long long ll; 
 
using namespace std;
using P = pair<int, int>;

int main() {
	int N;
	cin >> N;
	vector<ll> a(N);
	vector<int> indx(N + 1);
	for (int i = 0; i < N; ++i) {
		cin >> a[i];
		indx[a[i]] = i;
	}

	ll res = 0;
	set<int> st;
	st.insert(-1);
	st.insert(N);
	for (int i = 1; i <= N; ++i) {
		auto it = st.lower_bound(indx[i]);
		
		ll r = (*it) - indx[i];
		it--;
		ll l = indx[i] - (*it);
		ll tmp = i * l * r;
		res += tmp;

		st.insert(indx[i]);
	}

	cout << res << endl;

	return 0;
}
