#include <bits/stdc++.h>
using namespace std;

const int N = 202020;
int a[N], pr[N], ne[N], pos[N];

int main()
{
	int n;
	cin >> n;
	for (int i = 1; i <= n; ++i){
		cin >> a[i];
		pos[a[i]] = i;
	}

	for (int i = 0; i <= n + 1; ++i){
		pr[i] = i - 1;
		ne[i] = i + 1;
	}

	long long ans = 0;
	for (int i = n; i >= 1; i--){
		int j = pos[i];
		ans += i * 1ll * (j - pr[j]) * (ne[j] - j);
		pr[ne[j]] = pr[j];
		ne[pr[j]] = ne[j];
	}

	cout << ans << endl;
}

### Prompt

Create a solution in CPP for the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int N = 202020;
int a[N], pr[N], ne[N], pos[N];

int main()
{
	int n;
	cin >> n;
	for (int i = 1; i <= n; ++i){
		cin >> a[i];
		pos[a[i]] = i;
	}

	for (int i = 0; i <= n + 1; ++i){
		pr[i] = i - 1;
		ne[i] = i + 1;
	}

	long long ans = 0;
	for (int i = n; i >= 1; i--){
		int j = pos[i];
		ans += i * 1ll * (j - pr[j]) * (ne[j] - j);
		pr[ne[j]] = pr[j];
		ne[pr[j]] = ne[j];
	}

	cout << ans << endl;
}

```