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;
long long n, a, s, l, r, b[200005];
set<int> st;
int main() {
	int i;
	scanf("%d", &n);
	for(i=1; i<=n; i++) scanf("%d", &a), b[a] = i;;
	st.insert(0);
	st.insert(n+1);
	for(i=1; i<=n; i++) {
		l = *(--st.lower_bound(b[i]));
		r = *st.lower_bound(b[i]);
		s += i * (b[i]-l) * (r-b[i]);
		st.insert(b[i]);
	}
	printf("%lld", s);
	return 0;
}