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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.TreeSet;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		sa = br.readLine().split(" ");
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[Integer.parseInt(sa[i]) - 1] = i;
		}
		br.close();

		TreeSet<Integer> set = new TreeSet<Integer>();
		set.add(-1);
		set.add(n);
		long ans = 0;
		for (int i = 0; i < n; i++) {
			long x = a[i] - set.lower(a[i]);
			long y = set.higher(a[i]) - a[i];
			ans += x * y * (i + 1);
			set.add(a[i]);
		}
		System.out.println(ans);
	}
}
