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;
using ll = long long;

int main() {
    ll N;
    cin >> N;
    vector<ll> a(N), pos(N + 2, -1);
    for (ll i = 0; i < N; i++) {
        cin >> a[i];
        pos[a[i]] = i;
    }

    ll ans = 0;

    set<ll> st;
    st.insert(-1);
    st.insert(N);
    for (ll i = 1; i <= N; i++) {
        auto itr = st.lower_bound(pos[i]);
        ll r_value = *itr;
        itr--;
        ll l_value = *itr;

        ans += i * (pos[i] - l_value) * (r_value - pos[i]);

        st.insert(pos[i]);
    }

    cout << ans << endl;
}