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;
#define ll long long

int main(){
    int N;
    cin >> N;
    vector<int> b(N);
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        b[a-1] = i;
    }
    set<int> ar;
    ar.insert(-1);
    ar.insert(N);
    ll ans = 0;
    for (int i = 0; i < N; i++) {
        ll t = b[i];
        auto it1 = ar.lower_bound(t);
        auto it2 = it1;
        it1--;
        ans += (ll)(t-(*it1)) * ((*it2)-t) * (i+1);
        ar.insert(t);
    }
    cout << ans << endl;
    return 0;
}