Dream Team

#include <bits/stdc++.h>
using namespace std;

#define cin(vec) for(auto& i : vec) cin >> i
#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout(vec) for(auto& i : vec) cout << i << " "; cout << "\n";
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define cout_map(mp) for(auto& [f, s] : mp) cout << f << "  " << s << "\n";
#define Time cerr << "Time Taken: " << (float)clock() / CLOCKS_PER_SEC << " Secs" << "\n";
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define Num_of_Digits(n) ((int)log10(n)+1)
#define mod_combine(a, b, m) (((a % m) * (b % m)) % m)
#define all(vec) vec.begin(),vec.end()
#define rall(vec) vec.rbegin(),vec.rend()
#define sz(x) int(x.size())
#define TC int t; cin >> t;   while(t--)
#define fi first
#define se second
#define Pair pair < int, int >
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)

void AhMeD_HoSSaM(){
  ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
  #ifndef ONLINE_JUDGE
    //freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
  #endif
  freopen("dream.in", "r", stdin);
}
struct DSU {
    vector < int > parent, Gsize;
    DSU(int MaxNodes){
        parent.resize(MaxNodes + 5);
        for(int i = 0; i <= MaxNodes; i++) parent[i] = i;
    }
    int find_leader(int node){
        return parent[node] = (parent[node] == node ? node : find_leader(parent[node]));
    }
    bool same_set(int u, int v){
        return find_leader(u) == find_leader(v);
    }
    void union_sets(int u, int v){
        int leader_u = find_leader(u), leader_v = find_leader(v);
        if(leader_u ==leader_v) return;
        parent[leader_u] = leader_v;
    }
};

void freq_fact(int n, int idx, vector< vector < int > >& adj){
  for(int i = 1; i < sqrt(n); i++){
    if(n % i == 0) adj[i].push_back(idx), adj[n / i].push_back(idx);
  }
  if(sqrt(n) == (int) sqrt(n)) adj[sqrt(n)].push_back(idx);
}

int main(){
  AhMeD_HoSSaM();
  int test = 1;
  TC {
    int n;
    cin >> n;
    vector < int > nums(n);
    vector < vector < int > > adj(1e5 + 1);
    for(int i = 0; i < n; i++){
        cin >> nums[i];
        freq_fact(nums[i], i, adj);
    }
    ll compatibility = 0;
    DSU dsu(1e5);
    for(int i = 1e5; i >= 0; i--){
      if(sz(adj[i]) < 2) continue;
      int u = adj[i][0];
      for(int j = 1; j < sz(adj[i]); j++){
        int v = adj[i][j];
        if(!dsu.same_set(u, v)) compatibility += i, dsu.union_sets(u, v);
      }
    }
    cout << "Case " << test++ << ": " << compatibility << "\n";
  }
  Time
  return 0;
}