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>
using namespace std;
int main(void){
    int n;
    int b[200001];
    long long ans = 0;
    set<int> s;
    cin >> n;
    for(int i=1;i<=n;i++){
        int a;
        cin >> a;
        b[a] = i;
    }
    s.insert(0);
    s.insert(n+1);
    for(int i=1;i<=n;i++){
        int left, right;
        auto itr = s.lower_bound(b[i]);
        right = *itr--;
        left = *itr;
        ans += (long long) (b[i] - left) * (right - b[i]) * i;
        s.insert(b[i]);
    }
    cout << ans << endl;
}
