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<cstdio>
#include<cstring>
using namespace std;
const int N=4e5+500;
int n,w[N],q[N];
int main()
{
    scanf("%d",&n);int top=0;long long ans=0,s=0;
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&w[i]);
        while(top&&w[i]<w[q[top]])s-=1ll*(q[top]-q[top-1])*w[q[top]],--top;
        q[++top]=i,s+=1ll*w[i]*(q[top]-q[top-1]);
        ans+=s;
    }
    cout<<ans<<endl;
}