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>

typedef long long LL;
const int MN = 200005;

int N, A[MN], L[MN], R[MN];
int stk[MN], tp;
LL Ans;

int main() {
	scanf("%d", &N);
	for (int i = 1; i <= N; ++i) scanf("%d", &A[i]);
	stk[tp = 1] = 0;
	for (int i = 1; i <= N; ++i) {
		while (A[stk[tp]] > A[i]) R[stk[tp--]] = i;
		L[i] = stk[tp], stk[++tp] = i;
	}
	while (tp) R[stk[tp--]] = N + 1;
	for (int i = 1; i <= N; ++i) Ans += (LL)(i - L[i]) * (R[i] - i) * A[i];
	printf("%lld\n", Ans);
	return 0;
}