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 <cstdio>
#include <set>
#define N 200005
using namespace std;

typedef long long ll;
ll n, a, l, r, ans, d[N];
set<ll> v;
int main()
{
	ll i;
	cin >> n;
	for (i = 1; i <= n; i++) {
		scanf ("%lld", &a);
		d[a] = i;
	}
	v.insert(0);
	v.insert(n + 1);
	for (i = 1; i <= n; i++) {
		l = *(--v.lower_bound(d[i]));
		r = *v.lower_bound(d[i]);
		ans += (d[i] - l) * (r - d[i]) * i;
		v.insert(d[i]);
	}
	cout << ans;
    return 0;
}