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 <sstream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cctype>
#include <algorithm>
#include <functional>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <stack>
#include <queue>
#include <list>
#include <set>
#include <map>

using namespace std;
typedef long long ll;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const ll mod = 1000000007;
const int maxn = 1005;
const int maxw = 10005;

int a[maxn], b[maxn];
int Index[maxw];
bool vis[maxw];


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

	int min_w = inf;
	for (int i = 0; i < n; ++i) {
		scanf("%d", &a[i]);
		b[i] = a[i];
		min_w = min(min_w, a[i]);
	}
	sort(b, b + n);

	for (int i = 0; i < n; ++i) Index[b[i]] = i;

	int res = 0;
	for (int i = 0; i < n; ++i) {
		if (vis[i]) continue;

		int cnt = 0, sum = 0;
		int cur = i;
		int minm = inf;

		while (true) {
			if (vis[cur]) break;
			int x = a[cur];
			++cnt; sum += x;
			minm = min(minm, x);
			vis[cur] = true;
			cur = Index[x];
		}

		res += min(sum + (cnt - 2) * minm, sum + minm + (cnt + 1) * min_w);
	}
	printf("%d\n", res);
	return 0;
}
