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<cstdio>
#include<set>
using namespace std;

int main(){
    long n,a[200000],b[200001],x,ans=0,l,r;
    multiset<long> s;
    scanf("%ld",&n);
    for(long i=0;i<n;i++){
        scanf("%ld",&a[i]);
        b[a[i]]=i;
    }
    s.insert((long)-1);
    s.insert(n);
    for(long i=1;i<=n;i++){
        set<long>::iterator itr=s.lower_bound(b[i]);
        r=*itr;
        l=*(--itr);
        x=(b[i]-l)*(r-b[i]);
        ans+=x*i;
        s.insert(b[i]);
    }
    printf("%ld\n",ans);
}