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.util.Scanner;
import java.util.TreeSet;

public class Main {

	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		int N = sc.nextInt();
		int[] A = new int[N];
		int[] P = new int[N + 1];
		for (int i = 0; i < N; ++i) {
			A[i] = Integer.parseInt(sc.next());
			P[A[i]] = i;
		}
		long ans = 0;
		TreeSet<Integer> used = new TreeSet<>();
		used.add(-1);
		used.add(N);
		for (int i = 1; i <= N; ++i) {
			int pos = P[i];
			int lo = used.lower(pos);
			int hi = used.higher(pos);
			ans += (long) i * (pos - lo) * (hi - pos);
			used.add(pos);
		}
		System.out.println(ans);
	}
}
