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

using namespace std;

int main(){
    int N; cin >> N;
    vector<int> a(N);
    for(auto& t : a) cin >> t;
    vector<int> pos(N);
    for(int i=0;i<N;i++) pos[a[i]-1] = i;
    long long res = 0;
    set<int> S;
    S.insert(-1);
    S.insert(N);
    for(int i=0;i<N;i++){
        int p = pos[i];
        auto it = S.upper_bound(p);
        long long m = 1;
        m *= *it-p;
        --it;
        m *= p-*it;
        res += (i+1)*m;
        S.insert(p);
    }
    cout << res << endl;
}