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<cstdio>
#include<vector>
#include<set>

using namespace std;

int main(){
	int n;
	scanf("%d", &n);
	vector<int> a(n), b(n);
	for(int i = 0; i < n; i++){
		scanf("%d", &a[i]);
		b[a[i] - 1] = i + 1;
	}
	long long ans = 0;
	set<int> s = {0, n + 1};
	for(int i = 0; i < n; i++){
		int t = b[i];
		s.insert(t);
		auto it = s.find(t);
		auto l = it, r = it;
		l--; r++;
		ans += (long long)(i + 1) * (t - *l) * (*r - t);
	}
	printf("%lld\n", ans);
	return 0;
}