One day, Snuke was given a permutation of length N, a_1, a_2, ..., a_N, from his friend.

Find the following:

<image>

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 rep(i,n) for(int i=0;i<n;i++)
#define MOD (int)1e9+7
#define int long long
int a[222222], b[222222];
set<int>st;
signed main() {
	int n, ans = 0;
	cin >> n;
	rep(i, n) {
		cin >> a[i];
		b[a[i] - 1] = i;
	}
	st.insert(-1);
	st.insert(n);
	rep(i, n) {
		auto itr= st.lower_bound(b[i]);
		int right = (*itr) - b[i];
		itr--;
		int left = b[i] - (*itr);
		ans += a[b[i]] * right*left;
		st.insert(b[i]);
	}
	cout << ans << endl;
	return 0;
}