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
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
const int INF = 100010001;
const ll LINF = (ll)INF*INF*10;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vi a(n), b(n);
    map<int, int> mp;
    int mi = INF;
    rep(i, n) {
        cin >> a[i];
        b[i] = a[i];
        mi = min(mi, a[i]);
    }
    sort(all(b));
    rep(i, n) {
        mp[b[i]] = i;
    }

    int ans = 0;
    vi check(n);
    rep(i, n) {
        if(check[i]) continue;
        int cnt = 0;
        int now = i;
        int sum = 0;
        int nmi = a[i];
        while(true) {
            check[now] = 1;
            nmi = min(nmi, a[now]);
            cnt++;
            sum += a[now];
            now = mp[a[now]];
            if(check[now]) break;
        }
        ans += min(sum+(cnt-2)*nmi, (cnt+1)*mi+sum+nmi);
    }

    cout << ans << endl;
}  
