One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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 <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
int n, a[N];
int D[N], R[N], L[N];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", a + i);
    int top = 0;
    D[0] = 0;
    for (int i = 1; i <= n; i++) {
        while (top > 0 && a[D[top]] >= a[i]) R[D[top--]] = i - 1;
        L[i] = D[top] + 1;
        D[++top] = i;
    }
    while (top) R[D[top--]] = n;
    long long res = 0;
    for (int i = 1; i <= n; i++) {
        res += 1LL * (i - L[i] + 1) * (R[i] - i + 1) * a[i];
    }
    cout << res << endl;
}
