One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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 <algorithm>
#include <set>
using namespace std;
typedef long long ll;
int n;
ll ans;
set<ll>o;
ll a[200005];
int main(void){
    scanf("%d",&n);
    o.insert(0);
    o.insert(n+1);
    for(int i=0;i<n;i++){
        ll x;
        scanf("%lld",&x);
        a[x]=i+1;
    }
    for(ll i=1;i<=n;i++){
        auto itr=o.upper_bound(a[i]);
        ll r=*itr;
        itr--;
        ll l=*itr;
        ans+=i*(a[i]-l)*(r-a[i]);
        o.insert(a[i]);
    }
    printf("%lld\n",ans);
}