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>
#define ll long long
using namespace std;

int main() {
    int n;
    cin >> n;
    int a[n + 1];
    for (int i = 1; i <= n; i++) {
        int t;
        cin >> t;
        a[t] = i;
    }
    ll sum = 0LL;
    set<int> s;
    s.insert(0);
    s.insert(n + 1);
    for (int i = 1; i <= n; i++) {
        auto iter = s.lower_bound(a[i]);
        int r = *iter;
        int l = *--iter;
        s.insert(a[i]);
        sum += 1LL * (a[i] - l) * (r - a[i]) * i;
    }
    cout << sum << endl;
    return 0;
}
