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;
						
#define fast_cin() ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0)
#define endl '\n'
#define int long long
				
int32_t main() {
	fast_cin();  
	int n; cin >> n;
	vector<int> a(n), pos(n);
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
		--a[i], pos[a[i]] = i;
	}
	set<int> st = {-1, n};
	int ans = 0;
	for (int i = 0; i < n; ++i) {
		int j = pos[i];
		int l = *(--st.lower_bound(j));
		int r = *st.lower_bound(j);
		ans += (j - l) * (r - j) * (i + 1);
		st.insert(j); 
	}
	cout << ans << endl;
	return 0;
}