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 <bits/stdc++.h>
using namespace std;

int main(){
    long long i,n,a,b[200010],ans=0;
    set<long long> s;
    cin >> n;
    for(i=1;i<=n;i++){
        cin >> a;
        b[a] = i;
    }
    s.insert(0);
    s.insert(n+1);
    for(i=1;i<=n;i++){
        auto x = s.upper_bound(b[i]);
        auto y = x--;
        ans += i*(*x-b[i])*(b[i]-*(y));
        s.insert(b[i]);
    }
    cout << ans << endl;
}