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 <bits/stdc++.h>

using namespace std;

int n;
int arr[200100];
int ord[200100];
set<int> s;

int main() {
    int i;
    long long res = 0;
    scanf("%d",&n);
    for (i=0;i<n;i++) scanf("%d",&arr[i]);
    for (i=0;i<n;i++) ord[arr[i]] = i;
    s.insert(-1); s.insert(n);
    for (i=1;i<=n;i++) {
        res += 1LL*i*((*s.upper_bound(ord[i]))-ord[i])*(ord[i]-(*(--s.lower_bound(ord[i]))));
        s.insert(ord[i]);
    }
    printf("%lld\n",res);

    return 0;
}
