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 <iostream>
#include <algorithm>
#include <set>

using namespace std;

int main() {
    long n;
    cin >> n;
    long perm[n];
    for (long i=0; i<n; i++) {
        int a;
        cin >> a; a--;
        perm[a] = i;
    }
    set<long> used;
    used.insert(-1);
    used.insert(n);
    long sum = 0;
    for (long i=0; i<n; i++) {
        long p = perm[i];
        auto itr1 = used.upper_bound(p), itr2 = itr1;
        itr1--;
        sum += (*itr2 - p) * (p - *itr1) * (i + 1);
        used.insert(p);
    }
    cout << sum << '\n';
    return 0;
}