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;

using ll=long long;

int main()
{
	for(int n;cin>>n && n;){
		vector<int> a(n),b(n);
		for(int i=0;i<n;i++)
			cin>>a[i],b[--a[i]]=i;
		map<int,int> range;
		range[0]=n;
		ll res=0;
		for(int x=0;x<n;x++){
			int i=b[x];
			auto it=--range.upper_bound(i);
			int l=it->first,r=it->second;
			res+=ll(x+1)*(i-l+1)*(r-i);
			range.erase(it);
			if(l<i) range[l]=i;
			if(i+1<r) range[i+1]=r;
		}
		cout<<res<<endl;
	}
}
