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<bits/stdc++.h>
using namespace std;
int n;
int a[2100000];
int l[2100000];
int r[2100000];
long long ans=0;
int main()
{
	scanf("%d",&n);
    r[0]=1;
    l[n+1]=n;
    for(int i=1;i<=n;i++)
    {
       	int x;
       	scanf("%d",&x);
        l[i]=i-1;
        r[i]=i+1;
        a[x]=i;
    }
    for(int i=n;i>=1;i--)
    {
        ans+=1LL*i*(a[i]-l[a[i]])*(r[a[i]]-a[i]);
        r[l[a[i]]]=r[a[i]];
		l[r[a[i]]]=l[a[i]];
    }
	printf("%lld\n",ans);
    return 0;
}