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>
long long n, a, x, ans;
long long l[200002];
long long r[200002];
long long p[200002];
int main() {
	scanf("%lld", &n);
	for (long long i = 1; i <= n; i++) {
		l[i] = i - 1;
		r[i] = i + 1;
	}
	for (long long i = 1; i <= n; i++) {
		scanf("%lld", &a);
		p[a] = i;
	}
	for (int i = n; i; i--) {
		x = p[i];
		ans += i * (r[x] - x) * (x - l[x]);
		l[r[x]] = l[x];
		r[l[x]] = r[x];
	}
	printf("%lld\n", ans);
}