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;
    set<int> s;
    vector<int> b(n);
    int ans = 0;
    for(int i = 0; i < n; i++){
        int a; cin >> a;
        a--;
        b[a] = i;
    }

    s.insert(-1);
    s.insert(n);

    for(int i = 0; i < n; i++){
        
        auto nx = s.upper_bound(b[i]);
        auto pr = nx;
        pr--;
        ans += (i + 1) * (*nx - b[i]) * (b[i] - *pr);
        s.insert(b[i]);
    }

    cout << ans << endl;

    return 0;
    
}