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>
#include <set>
using namespace std;

typedef long long ll;
ll A[200010],B[200010];
ll N;

int main(){
	cin >> N;
	for(int i=1;i<=N;i++){
		cin >> A[i];
		B[A[i]] = i;
	}
	set<ll> s,t;
	ll ans = 0;
	s.insert(0);
	t.insert(N+1);
	for(int i=1;i<=N;i++){
		s.insert(-B[i]);
		t.insert(B[i]);
		set<ll>::iterator it = s.upper_bound(-B[i]); 
		set<ll>::iterator it2 = t.upper_bound(B[i]);
		ll l = -*it;
		ll r = *it2;
		ans += i*(B[i]-l)*(r-B[i]);
	}
	cout << ans << endl;
}