Help me in solving COSTPERM problem

help
,
1

My issue

i have trid solving this problem but i am not able to find bug in my approach
i am simply just adding the cyles length but i am not able to understandwhy do we need priority queue to store cyccles length and then add min cycles length first,adding in any order would give same answer

My code

#include <bits/stdc++.h>

using namespace std;
int dfs(vector < int > & v, vector < int > & vis, int st) {
    int n = 0;
    while (!vis[st]) {
        vis[st] = 1;
        st = v[st];
        n++;
    }
    return n;
}

void ved() {
    int n;
    cin >> n;
    vector < int > v(n + 1);
    vector < int > vis(n + 1, 0);

    for (int i = 1; i <= n; i++) {
        cin >> v[i];
    }

    int c = 0;

    int nk = 0;
    for (int i = 1; i <= n; i++) {
        if (!vis[i]) {
            int t=dfs(v, vis, i);
            c+=t;
            nk++;

        }
    }
    if (nk == 1) {
        cout << 0 << endl;
        return;

    }

    cout << c << endl;
}


int main() {
    // your code goes here
    int t;
    cin >> t;
    while (t--) {
        ved();
    }

}

Problem Link: Costly Permutations Practice Coding Problem