You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
#define MAX_N 10000
#define MAX_V 100000000
#define INF 1000000000

int n, A[MAX_N], s, B[MAX_N], T[MAX_V];

int minimum_cost_sort() {
	int ans = 0;
	bool V[MAX_N];
	memset(V, false, sizeof(V));
	for (int i = 0; i < n; i++) { B[i] = A[i]; }
	sort(B, B + n);
	for (int i = 0; i < n; i++) { T[B[i]] = i; }
	for (int i = 0; i < n; i++) {
		if (V[i]) { goto owata; }
		int cur = i;
		int S = 0;
		int m = INF;
		int x = 0;
		while (1) {
			V[cur] = true;
			x++;
			int v = A[cur];
			m = min(m, v);
			S += v;
			cur = T[v];
			if (V[cur]) { break; }
		}
		ans += min(S + (x - 2)*m, m + S + (x + 1)*s);
	owata:;
	}
	return ans;
}

int main() {
	cin >> n;
	s = INF;
	for (int i = 0; i < n; i++){
		cin >> A[i];
		s = min(s, A[i]);
	}
	cout << minimum_cost_sort() << endl;
	return 0;
}