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
// Rafael Saddatimov
#include <bits/stdc++.h>
#define MAX 200005
using namespace std;

int pos[MAX];
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) {
        int x;
        scanf("%d", &x);
        pos[x] = i;
    }
    set<int> s;
    long long res = 0;
    s.insert(0);
    s.insert(n + 1);
    for (int i = 1; i <= n; ++i) {
        auto it = s.lower_bound(pos[i]);
        int r = *it, l = *(--it);
        res += 1LL * i * (r - pos[i]) * (pos[i] - l);
        s.insert(pos[i]);
    }
    printf("%lld\n", res);
    return 0;
}
