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<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;
const int MAX = 5000;
const int maxnum = 10010;
bool V[MAX];

int n, A[MAX], s;
int B[MAX], T[maxnum];
int solve() {
	int ans = 0;

	// T??°???????????????????´????????????????????????????????????\??¨??????????????¢???
	for (int i = 0; i < n; i++)
		T[B[i]] = i;
	for (int i = 0; i < n; i++) {
		// ????????¨???????????¢????????¨??????
		if (V[i])
			continue;

		int cur = i;
		int S = 0, m = maxnum, an = 0;
		// ?????¢?????????
		while (!V[cur]) {
			V[cur] = true;
			// ?????¢?????°????´????
			an++;
			int v = A[cur];
			// ??????????????¢??????????°????
			m = min(m, v);
			S += v;
			// ?????¢??????????????????
			cur = T[v];
		}
		ans += min(S + (an - 2) * m, m + S + (an + 1) * s);
	}
	return ans;

}
int main() {

	scanf("%d", &n);
	s = maxnum;
	for (int i = 0; i < n; i++) {
		scanf("%d", &A[i]);
		s = min(s, A[i]);
		B[i] = A[i];
		V[i] = false;
	}
	sort(B, B + n);
	printf("%d\n", solve());
	return 0;
}