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;

#define for_(i,a,b) for(int i=(a);i<(b);++i)
typedef long long lint;

int N, a[200005], b[200005];

int main() {
	cin >> N;
	for_(i,0,N) {
		cin >> a[i];
		b[a[i]] = i;
	}
	
	lint ans = 0;
	set< lint > index = {-1,N};
	for_(i,1,N+1) {
		auto R = index.upper_bound(b[i]);
		auto L = R; --L;
		index.insert(b[i]);
		ans += ((*R) - b[i]) * (b[i] - (*L)) * i;
	}
	cout << ans << endl;
}