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 <cstdio>
int N, a[200001], p[200001], L[200002], R[200002], F[200002];
long long O, C;
int main()
{
	scanf("%d", &N);
	for (int i = 1; i <= N; i++)
	{
		scanf("%d", a + i);
		p[a[i]] = i;
	}
	for (int i = 1; i <= N; i++)
	{
		L[i] = R[i] = i;
		F[i] = 0;
	}
	for (int i = N; i; i--)
	{
		int u = p[i];
		int LM = F[u - 1] ? L[u - 1] : u, RM = F[u + 1] ? R[u + 1] : u;
		F[u] = 1;
		R[LM] = RM;
		L[RM] = LM;;
		O += C += (long long)(u - LM) * (RM - u) + RM - LM + 1;
	}
	printf("%lld\n", O);
	return 0;
}
