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>
#include <vector>
#include <cstdio>

using namespace std;

int a[200001];
int pos[200001];

typedef long long ll;

int main() {

	int N;

	scanf("%d",&N);

	int i;

	for (i = 0; i < N; i++) {
		scanf(" %d",&a[i]);
		pos[a[i]] = i + 1;
	}

	set<int>data;

	data.insert(0);
	data.insert(N+1);

	ll sum = 0;

	for (i = 1; i <= N; i++) {
		data.insert(pos[i]);
		set<int>::iterator it = data.find(pos[i]);
		ll r = *(++it) - pos[i];
		--it;
		ll l = pos[i] - (*(--it));
		sum += (ll)i*r*l;
	}
	printf("%lld\n",sum);

	return 0;
}