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>
#define rep(i, n) for (int i = 0; i < (n); i++)
using ll = long long;
using namespace std;

int main() {
    int n; cin >> n;
    vector<int> a(n); rep(i,n) { cin >> a[i]; a[i]--; }
    vector<int> aa(n); rep(i,n) aa[a[i]] = i;

    ll ans = 0ll;
    set<int> data;
    data.insert(-1);
    data.insert(n);
    rep(i,n) {
        auto iter = data.upper_bound(aa[i]);
        ans += (ll)(i+1) * (ll)(*iter - aa[i]) * (ll)(aa[i] - *prev(iter));
        data.insert(aa[i]);
    }
    cout << ans << endl;
    return 0;
}