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 long long ll;

int main(){
	int n, a;
	cin >> n;
	int t[n+1];
	set<ll> s;
	ll ans = 0;
	for(int i = 0; i < n; i++)cin >> a, t[a] = i+1;
	for(int i = 1; i <= n; i++){
		ll l, u;
		auto itr = s.upper_bound(t[i]);
		if(itr == s.end())l = n+1;
		else l = *itr;
		if(itr == s.begin())u = 0;
		else u = *(--itr);
		s.insert(t[i]);
		ans += (t[i]-u)*(l-t[i])*i;
	}
	cout << ans << endl;
    return 0;
}