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<stdio.h>
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i,x,n) for (int i = x;i < n;++i)

int x[200001];

int main() {
	int n;
	scanf("%d", &n);
	ll an = 0;
	f(i, 0, n) {
		int t;
		scanf("%d", &t);
		x[t] = i;
	}
	set<int> s;
	s.insert(-1);
	s.insert(n);
	f(i, 1, n + 1) {
		int l, r;
		set<int>::const_iterator it = s.lower_bound(x[i]);
		r = *it;
		l = *(--it);
		an += (ll)(x[i] - l) * (r - x[i]) * i;
		s.insert(x[i]);
	}
	printf("%lld", an);
}