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;
const ll MOD=(ll)1e9+7;


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

    ll ans=0ll;;
    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;
        --itr;
        l=*itr;
        ans+=i*(place[i]-l)*(r-place[i]);
        used.insert(place[i]);
    }

    cout<<ans<<endl;

    return 0;
}