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>
using namespace std;
typedef long long ll;

int main(){
    int N;  cin >> N;
    vector<int> a(N,0), pos(N+1,0);
    for(int i=0; i<N; i++){
        cin >> a[i];
        pos[a[i]] = i;
    }

    ll ans = 0;
    set<int> st;
    st.insert(-1);
    st.insert(N);
    for(ll i=1; i<=N; i++){
        auto itr = st.lower_bound(pos[i]);
        ll right = *itr;
        itr--;
        ll left = *itr;
        ans += i*(right-pos[i])*(pos[i]-left);
        st.insert(pos[i]);
    }
    cout << ans << endl;
}
