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 <algorithm>
#include <cstdio>
#include <iostream>

using namespace std;

//?£wi + (n - 2) * min(wi)
//or
//?£wi + min(wi) + (n+1) * x

int main() {
	int MAX = 1000;
	int VMAX = 10000;

	int A[MAX];
	int B[MAX];
	bool V[MAX];
	int T[VMAX];

	int n;
	scanf("%d", &n);

	int s = VMAX;
	for (int i = 0; i < n; ++i) {
		scanf("%d", &A[i]);
		B[i] = A[i];
		V[i] = false;
		s = min(s, A[i]);
	}

	sort(B, B + n);
	for (int i = 0; i < n; ++i) {
		T[B[i]] = i;
	}

	int ans = 0;
	for (int i = 0; i < n; ++i) {
		if (V[i]) {
			continue;
		}
		int cur = i;
		int S = 0;
		int m = VMAX;
		int an = 0;
		while (1) {
			V[cur] = true;
			m = min(m, A[cur]);
			int v = A[cur];
			S += v;
			++an;
			cur = T[v];
			if (V[cur] == true) {
				break;
			}
		}
		ans += min(S + (an - 2) * m, S + m + (an + 1) * s);
	}

	cout << ans << endl;

	return 0;
}