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;

const int Maxn = 200005;

int wh[Maxn];
int n;
set <int> S;
ll res;

int main()
{
    scanf("%d", &n);
    S.insert(0); S.insert(n + 1);
    for (int i = 1; i <= n; i++) {
        int a; scanf("%d", &a);
        wh[a] = i;
    }
    for (int i = 1; i <= n; i++) {
        int ind = wh[i];
        auto it2 = S.upper_bound(ind);
        auto it1 = it2; it1--;
        res += ll(ind - *it1) * ll(*it2 - ind) * i;
        S.insert(ind);
    }
    cout << res << endl;
    return 0;
}
