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(){
    ll n;
    cin >> n;
    vector<ll> a(n);
    set<ll> st={-1,n};
    map<ll,ll> mp;
    ll ans = 0,l=0,r=n-1;
    for(int i = 0;i < n;i ++){
        ll a0;
        cin >> a0;
        a[i] = a0;
        mp[a0] = i;
    }
    for(int i = 1;i <= n;i ++){
        ll j = mp[i];
        auto itr = st.upper_bound(j);
        r = *itr-1;
        itr --;
        l = *itr+1;
        ans += (r-j+1)*(j-l+1)*i;
        st.insert(j);
    }
    cout << ans << endl;
    return 0;
}