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 int long long
using namespace std;

signed main() {
    int N;
    cin >> N;

    vector<int> a(N), idx(N);
    for (int i = 0; i < N; i++) {
        cin >> a[i];
        idx[a[i] - 1] = i;
    }

    set<int> se;
    se.insert({-1, N});

    int ans = 0;
    for (int i = 0; i < N; i++) {
        auto it = se.lower_bound(idx[i]);
        int r = *it - idx[i];
        int l = idx[i] - *--it;
        ans += l * r * a[idx[i]];
        se.insert(idx[i]);
    }
    cout << ans << endl;
}
