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>
using namespace std;

static const long MAX = 1000;
static const long VMAX = 10000;

long n, A[MAX], s;
long B[MAX], T[VMAX + 1];

long solve(){
	long ans = 0;
	bool V[MAX];
	for (long i = 0; i < n; i++){ // ?????????
		B[i] = A[i];
		V[i] = false;
	}
	sort(B, B + n);
	for (long i = 0; i < n; i++) T[B[i]] = i; // ??????????????????
	for (long i = 0; i < n; i++){
		if (V[i]) continue; // True?????¨??????????£???°???
		long cur = i, S = 0, m = VMAX, an = 0;
		while (1){
			V[cur] = true; // ???????????????????????\??£?????????
			an++; // ?????????????????¨??????1?????°???
			long v = A[cur]; // ???????????????????´?
			m = min(m, v); // ???????????????????°????????¨????
			S += v; // ?????????????????°?????????????¨????
			cur = T[v]; // ??????index??????????????¢??????
			if (V[cur]) break; // ?????£??????????????????
		}
		ans += min(S + (an - 2) * m, m + S + (an + 1) * s); // ?°???????????????????
	}
	return ans;
}

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