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()
{
    int n;
    cin >> n;
    vector<int> a(n), p(n);
    for(int i = 0; i < n; i++) {
        cin >> a[i];
        p[--a[i]] = i;
    }

    set<int> st;
    st.insert(-1), st.insert(n);
    ll ans = 0;
    for(int i = 0; i < n; i++) {
        auto itr = st.lower_bound(p[i]);
        int r = *itr - p[i];
        itr--;
        int l = p[i] - *itr;
        ans += (ll)(i + 1) * r * l;
        st.insert(p[i]);
    }
    cout << ans << endl;
}