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(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++) cin >> a[i];
	vector<int> pos(n);
	for(int i = 0; i < n; i++){
		pos[a[i]-1] = i;
	}

	set<int> idx;
	idx.insert(-1); idx.insert(n);
	ll ans = 0;
	for(int i = 0; i < n; i++){
		idx.insert(pos[i]);
		int a = *prev(idx.find(pos[i]));
		int b = *next(idx.find(pos[i]));
		ans += 1ll * (i+1) * (pos[i] - a) * (b - pos[i]);
	}
	cout << ans << '\n';
}