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<iostream>
#include<set>
using namespace std;
using ll = long long;

int Q[200500];

int main() {
	set<int>s;
	int  n;
	cin >> n;
	for (int i = 0; i < n; i++) {
		int x;
		cin >> x;
		Q[x] = i;
	}
	s.insert(-1);
	s.insert(n);
	ll ans = 0;
	for (int v = 1; v <= n; v++) {
		int p = Q[v];//v番目の数
		auto it = s.upper_bound(p);
		int r = *it;
		int l = *(--it);
		ans += v * 1ll * (r - p) * 1ll * (p - l);
		s.insert(p);
	}
	cout << ans << endl;
}