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;

int n;
ll a[200000], c[200000];
set<int> s;

int main()
{
	cin >> n;
	for (ll i = 0;i < n;i++) cin >> a[i];

	for (ll i = 0;i < n;i++) c[a[i] - 1] = i;

	long long ans = 0;
	s.insert(-1); s.insert(n);
	for (ll i = 0;i < n;i++) {
		auto itr = s.lower_bound(c[i]);
		ll right = *itr, left = *(--itr);

		ans += (i + 1) * (c[i] - left) * (right - c[i]);
		s.insert(c[i]);
	}

	cout << ans << endl;

    return 0;
}

