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<cstdio>
using namespace std;

int N, a[200000], idx[200001];


int main(){
    cin >> N;
    for(int i = 0; i < N; i++){
        cin >> a[i];
        idx[a[i]] = i;
    }
    set<int> st;
    st.insert(-1);
    st.insert(N);
    long long ans = 0;
    for(int i = 1; i <= N; i++){
        int j = idx[i];
        set<int>::iterator itr = st.upper_bound(j);
        int r = *itr;
        int l = *(--itr);
        ans += (long long)i * (r-j) * (j-l);
        st.insert(j);
    }
    cout << ans << endl;

}