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;
const int N=200010;
map<int,bool>mp;
map<int,bool>::iterator t;
int n;
long long ans,num;
int a[N],pos[N];
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		pos[a[i]]=i;
	}
	mp[0]=1;mp[n+1]=1;
	for(int i=1;i<=n;i++)
	{
		t=mp.lower_bound(pos[i]);
		num=t->first-pos[i];
		t--;
		num*=pos[i]-t->first;
		ans+=num*i;
		mp[pos[i]]=1;
	}
	printf("%lld\n",ans);
	return 0;
}