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 <set>
#include <algorithm>
#include <vector>

using namespace std;

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

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

    set<int> po;
    po.insert(-1);
    po.insert(N);
    int64_t ans = 0;
    for(int i = 0; i < N; ++i){
        auto it = po.lower_bound(data[i]);
        ans += int64_t(i+1) * (*it - data[i]) * (data[i] - *(--it));
        po.insert(data[i]);
    }
    cout << ans << endl;
}