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;

typedef unsigned long long ull;
typedef long long ll;

int main(){
	int n;
	cin >> n;
	ll a[n+1];
	for(int i=1; i<=n; i++){
		ll t;
		cin >> t;
		a[t]=i;
	}

	set<ll> s;
	s.insert(0);
	s.insert(n+1);
	ll ans=0;
	for(int i=1; i<=n; i++){
		set<ll>::iterator itr=s.lower_bound(a[i]), itl=itr--;
		ll l=*itl, r=*itr;
		ans+=i*(a[i]-l)*(r-a[i]);
		s.insert(a[i]);
	}
	cout << ans << endl;
	return 0;
}