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;
    ll place[N + 1];
    for (int i = 1; i <= N; i++) {
        ll a;
        cin >> a;
        place[a] = i;
    }
    ll ans = 0;
    set<ll> used = {0, N + 1};
    for (int i = 1; i <= N; i++) {
        ll r, l;
        auto itr = used.lower_bound(place[i]);
        r = *itr;
        l = *(--itr);
        ans += i * (place[i] - l) * (r - place[i]);
        used.insert(place[i]);
    }
    cout << ans << endl;
}