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 <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int d[200001];
int main(void){
    int n;
    cin>>n;
    for(int i=0;i<n;i++){
        int a;
        cin>>a;
        d[a]=i;
    }
    ll ans=0;
    set<ll> s; 
    s.insert(-1),s.insert(n);
    for(int i=0;i<n;i++){
        auto cnt=s.lower_bound(d[i+1]);
        ll l=*cnt;
        cnt--;
        ll r=*cnt;
        ans+=(i+1)*(l-d[i+1])*(d[i+1]-r);
        s.insert(d[i+1]);
        
        
    }
    cout<<ans<<endl;
}
