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 <fstream>
using namespace std;
const int nmax=200005;
int poz[nmax],st[nmax],dr[nmax];
long long tot,i;
int n,x;
int main()
{
   // freopen("data.in","r",stdin);
    cin>>n;
    for(i=1;i<=n;i++)
    {
        cin>>x;
        poz[x]=i;
    }
    for(i=n;i>=1;i--)
    {
        x=poz[i];
        st[x]=dr[x]=x;
        if(st[x-1]) st[x]=st[x-1];
        if(dr[x+1]) dr[x]=dr[x+1];
        dr[st[x]]=dr[x];
        st[dr[x]]=st[x];
        tot+=1LL*(x-st[x]+1)*(dr[x]-x+1)*i;
    }
    cout<<tot;
    return 0;
}
