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>
using namespace std;
#include<algorithm>
#include<vector>
#include<set>
#define mod  998244353
#define int long long int
int32_t main()
{
	int n;
	cin>>n;
	int j,arr[n+1];
	for(j=1;j<=n;j++)
	    cin>>arr[j];
	int answer=0;
	int position[n+1];
	for(j=1;j<=n;j++)
	{
		position[arr[j]]=j;
	}
	set<int> s;
	s.insert(0);
	s.insert(n+1);
	for(j=1;j<=n;j++)
	{
		int x=position[j];
		auto it=s.upper_bound(x);
		int right=*it;
		right--;
		it--;
		int left=*it;
		left++;
		answer+=j*(x-left+1)*(right-x+1);
		s.insert(x);

	}
	cout<<answer<<endl;
}
