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

    long long res = 0;
    set<int> S;
    S.insert(-1);
    S.insert(N);

    for(int i=0; i<N; ++i) {
        auto itr = S.lower_bound(index[i]);
        long long r = *itr;
        --itr;
        long long l = *itr;
        res += (r - index[i]) * (index[i] - l) * (i + 1);
        S.insert(index[i]);
    }

    cout << res << endl;
}