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(){
    int n;
    cin >> n;
    long long a;
    long long b[n+1];
    for(int i = 0;i<n;i++){
        cin >> a;
        b[a]=i+1;
    }
    set<int> st;
    st.insert(0);
    st.insert(n+1);
    long long ans = 0;
    long long l,r;
    for(int i = 1;i<=n;i++){
        auto itr = st.upper_bound(b[i]);
        r = *itr;
        itr--;
        l = *itr;
        ans+=i*(b[i]-l)*(r-b[i]);
        st.insert(b[i]);
    }
    cout << ans << endl;
}