#include using namespace std; #if __has_include() #include using namespace atcoder; templateistream &operator>>(istream &is,static_modint &a){long long b;is>>b;a=b;return is;} istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;} #endif #ifdef LOCAL #include "debug.h" #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) #define esper(...) static_cast(0) templateostream &operator<<(ostream &os,const pair&p){os<; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define reps(i,a,n) for(int i=(a);i<(n);i++) #define rep(i,n) reps(i,0,n) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcountll(x) #define fin(x) return cout<(0) ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } void SOLVE(); int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout<>testcase; for(int i=0;i>n; vectora(n); cin>>a; if(a==vector(n,1))fin(n*2); int mx=*max_element(all(a)); vectorp(mx+1,-1); reps(i,2,mx+1)if(p[i]==-1)for(int j=1;i*j<=mx;j++)p[i*j]=i; vectorprime; rep(i,mx+1)if(p[i]==i)prime.push_back(i); dsu uf(n+prime.size()); debug(prime); rep(i,n){ vectorz; int c=a[i]; while(c!=1){ z.push_back(p[c]); c/=p[c]; } for(auto j:z)uf.merge(i,lower_bound(all(prime),j)-prime.begin()+n); } vectormust; int one=0; for(auto g:uf.groups()){ if(g.size()==1){ if(g[0]=n)chmin(mn,prime[i-n]); must.push_back(mn); } } debug(must,one); assert(!must.empty()); ll ans=0; sort(all(must)); ans+=ll(must[0])*(one+must.size()-1); chmin(ans,2*(one+must.size())); cout<