(LightOJ) 1242 – Similar Trees (II)

0

/***********Template Starts Here***********/
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <functional>
#include <string>
#include <iostream>
#include <cctype>
#include <set>
#include <climits>
#include <iomanip>
#include <cassert>
//#include <unordered_map>

#define pb push_back
#define nl puts ("")
#define sp printf ( " " )
#define phl printf ( "hello\n" )
#define ff first
#define ss second
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define MP make_pair
#define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1)
#define SQ(x) ((x)*(x))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define ALL(x) (x).begin(),(x).end()
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define SZ(x) ((int)(x).size())
#define NORM(x) if(x>=mod)x-=mod;

using namespace std;

typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<pii> vii;
typedef vector<int> vi;

const vlong inf = 2147383647;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-9;

#ifdef forthright48
     #include <ctime>
     clock_t tStart = clock();
     #define debug(args...) {dbg,args; cerr<<endl;}
     #define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC)
#else
    #define debug(args...)  // Just strip off all debug tokens
    #define timeStamp
#endif

struct debugger{
    template<typename T> debugger& operator , (const T& v){
        cerr<<v<<" ";
        return *this;
    }
}dbg;

//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};

inline vlong gcd ( vlong a, vlong b ) {
    a = ABS ( a ); b = ABS ( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;
}

vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
    vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
    x2 = 1; y2 = 0;
    x1 = 0; y1 = 1;
    for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
        q = r2 / r1;
        r = r2 % r1;
        x = x2 - (q * x1);
        y = y2 - (q * y1);
    }
    *X = x2; *Y = y2;
    return r2;
}

inline vlong modInv ( vlong a, vlong m ) {
    vlong x, y;
    ext_gcd( a, m, &x, &y );
    if ( x < 0 ) x += m; //modInv is never negative
    return x;
}

inline vlong power ( vlong a, vlong p ) {
    vlong res = 1, x = a;
    while ( p ) {
        if ( p & 1 ) res = ( res * x );
        x = ( x * x ); p >>= 1;
    }
    return res;
}

inline vlong bigmod ( vlong a, vlong p, vlong m ) {
    vlong res = 1 % m, x = a % m;
    while ( p ) {
        if ( p & 1 ) res = ( res * x ) % m;
        x = ( x * x ) % m; p >>= 1;
    }
    return res;
}

/***********Template Ends Here***********/

/*********** Hasib Templates Starts Here**********/

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

#define loop(i, n) for(int i=0; i<(n); i++)
#define sf scanf
#define pf printf
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) (v).begin(), (v).end()
#define PI acos(-1.0)
#define mem(ara, val) memset(ara, val, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define vdump(x) cerr<<#x<<" = "<<x<<endl;
#define dump(args...) cerr,args; cerr<<endl

template<typename T>
ostream& operator<<(ostream& out, vector<T> v)
{
    out<<"[ ";

    loop(i, SZ(v))
    {
        if(i) out<<", ";
        out<<v[i];
    }

    out<<" ]";
    return out;
}

template<typename T1, typename T2>
ostream& operator<<(ostream &out, pair<T1, T2> p)
{
    out<<"( "<<p.fr<<", "<<p.sc<<")";
    return out;
}

template<typename T>
ostream& operator,(ostream &out, T x)
{
    out<<x<<" ";
    return out;
}


/**********Hasib Templates Ends Here**************/

/**
 *  WARTNING for me:
 *     Never use    FOR
 *     Never use    pii, pll, vi, vi
 *     Never use    ff, ss, phl, sp, nl
 */



#define NODE 107

struct KUHN{
        int left[NODE], right[NODE], vis[NODE], cc;
        vector<int> adj[NODE];

        KUHN() : cc(1) {

        }

        void clear(int n)
        {
                FOR(i, 0, n) adj[i].clear();
        }

        bool tryK(int v)
        {
                if(vis[v] == cc) return false;

                vis[v] = cc;

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if(right[t] == -1)
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if( tryK(right[t]))
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                return false;
        }


        int match(int n)
        {
                int res = 0;
                bool done;
                CLR(left, -1); CLR(right, -1);
                do{
                        done = true; cc++;
                        FOR(i, 0, n)
                        {
                                if(left[i] == -1 && tryK(i))
                                {
                                        done = false;
                                }
                        }
                }while(!done);

                FOR(i, 0, n) res += (left[i] != -1);

                return res;
        }
};



vector<int>original[NODE], modified[NODE];
int orgN, modN;

bool orgVisited[NODE], modVisited[NODE];
bool isMatch[NODE][NODE];

bool match(int u, int v)
{
        orgVisited[u] = modVisited[v] = true;

        int uu, vv;

        KUHN kuhn;


        /// !wow! Got WA because I took kuhn as local variable, and didn't clear visited!
        mem(kuhn.vis, 0);

        kuhn.clear(NODE-1);

        loop(i, SZ(original[u]))
        {
                uu = original[u][i];

                if(orgVisited[uu]) continue;

                loop(j, SZ(modified[v]))
                {
                        vv = modified[v][j];

                        if(modVisited[vv]) continue;

                        if(match(uu, vv))
                        {
                                kuhn.adj[i].pb(j);
                        }
                }
        }

        orgVisited[u] = modVisited[v] = false;

        int m = kuhn.match( SZ(original[u]) + 2 );
        int child = SZ(original[u]) - 1;
        if(u == 1) child++;

        bool ret = (m == child);

        return ret;
}


void solve()
{
        //mem(orgVisited, 0); ///
        //mem(modVisited, 0); ///

        bool ret = match(1, 1);

        if(ret)
        {
                pf("Yes\n");
        }
        else
        {
                pf("No\n");
        }

}

int main ()
{
    #ifdef hasibpc
        read("input.txt");
        //write("output.txt");
    #endif // hasibpc

    int kases, kaseno = 0;
    int u, v;

    sf("%d", &kases);

    while(kases--)
    {
            sf("%d", &modN);

            FOR(i, 0, modN) modified[i].clear();

            for(int i=1; i<modN; i++)
            {
                    sf("%d %d", &u, &v);

                    //debug(u, v);

                    modified[u].pb(v);
                    modified[v].pb(u);
            }

            //vdump(endl);


            sf("%d", &orgN);

            FOR(i, 0, orgN) original[i].clear();

            for(int i=1; i<orgN; i++)
            {
                    sf("%d %d", &u, &v);

                    //debug(u, v);

                    original[u].pb(v);
                    original[v].pb(u);
            }


            pf("Case %d: ", ++kaseno);

            solve();

    }


    return 0;
}

(LightOJ) 1304 – The Best Contest Site Ever

0

/***********Template Starts Here***********/
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <functional>
#include <string>
#include <iostream>
#include <cctype>
#include <set>
#include <climits>
#include <iomanip>
#include <cassert>
//#include <unordered_map>

#define pb push_back
#define nl puts ("")
#define sp printf ( " " )
#define phl printf ( "hello\n" )
#define ff first
#define ss second
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define MP make_pair
#define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1)
#define SQ(x) ((x)*(x))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define ALL(x) (x).begin(),(x).end()
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define SZ(x) ((int)(x).size())
#define NORM(x) if(x>=mod)x-=mod;

using namespace std;

typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<pii> vii;
typedef vector<int> vi;

const vlong inf = 2147383647;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-9;

#ifdef forthright48
     #include <ctime>
     clock_t tStart = clock();
     #define debug(args...) {dbg,args; cerr<<endl;}
     #define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC)
#else
    #define debug(args...)  // Just strip off all debug tokens
    #define timeStamp
#endif

struct debugger{
    template<typename T> debugger& operator , (const T& v){
        cerr<<v<<" ";
        return *this;
    }
}dbg;

//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};

inline vlong gcd ( vlong a, vlong b ) {
    a = ABS ( a ); b = ABS ( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;
}

vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
    vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
    x2 = 1; y2 = 0;
    x1 = 0; y1 = 1;
    for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
        q = r2 / r1;
        r = r2 % r1;
        x = x2 - (q * x1);
        y = y2 - (q * y1);
    }
    *X = x2; *Y = y2;
    return r2;
}

inline vlong modInv ( vlong a, vlong m ) {
    vlong x, y;
    ext_gcd( a, m, &x, &y );
    if ( x < 0 ) x += m; //modInv is never negative
    return x;
}

inline vlong power ( vlong a, vlong p ) {
    vlong res = 1, x = a;
    while ( p ) {
        if ( p & 1 ) res = ( res * x );
        x = ( x * x ); p >>= 1;
    }
    return res;
}

inline vlong bigmod ( vlong a, vlong p, vlong m ) {
    vlong res = 1 % m, x = a % m;
    while ( p ) {
        if ( p & 1 ) res = ( res * x ) % m;
        x = ( x * x ) % m; p >>= 1;
    }
    return res;
}

/***********Template Ends Here***********/

/*********** Hasib Templates Starts Here**********/

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

#define loop(i, n) for(int i=0; i<(n); i++)
#define sf scanf
#define pf printf
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) (v).begin(), (v).end()
#define PI acos(-1.0)
#define mem(ara, val) memset(ara, val, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define vdump(x) cerr<<#x<<" = "<<x<<endl;
#define dump(args...) cerr,args; cerr<<endl

template<typename T>
ostream& operator<<(ostream& out, vector<T> v)
{
    out<<"[ ";

    loop(i, SZ(v))
    {
        if(i) out<<", ";
        out<<v[i];
    }

    out<<" ]";
    return out;
}

template<typename T1, typename T2>
ostream& operator<<(ostream &out, pair<T1, T2> p)
{
    out<<"( "<<p.fr<<", "<<p.sc<<")";
    return out;
}

template<typename T>
ostream& operator,(ostream &out, T x)
{
    out<<x<<" ";
    return out;
}


/**********Hasib Templates Ends Here**************/

/**
 *  WARTNING for me:
 *     Never use    FOR
 *     Never use    pii, pll, vi, vi
 *     Never use    ff, ss, phl, sp, nl
 */



#define NODE 5100
#define MAXX 107

struct KUHN{
        int left[NODE], right[NODE], vis[NODE], cc;
        vector<int> adj[NODE];

        KUHN() : cc(1) {

        }

        void clear(int n)
        {
                FOR(i, 0, n) adj[i].clear();
        }

        bool tryK(int v)
        {
                if(vis[v] == cc) return false;

                vis[v] = cc;

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if(right[t] == -1)
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if( tryK(right[t]))
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                return false;
        }


        int match(int n)
        {
                int res = 0;
                bool done;
                CLR(left, -1); CLR(right, -1);
                do{
                        done = true; cc++;
                        FOR(i, 0, n)
                        {
                                if(left[i] == -1 && tryK(i))
                                {
                                        done = false;
                                }
                        }
                }while(!done);

                FOR(i, 0, n) res += (left[i] != -1);

                return res;
        }
}kuhn;

char grid[MAXX][MAXX];
int N, M;


#define index sflajfsa

paii index[MAXX][MAXX];



void solve()
{
        int r = 0, c = 0;

        loop(i, N)
        {
                loop(j, M)
                {
                        if(j == 0)
                        {
                                r++;

                                if(grid[i][j] == '.')
                                {
                                        index[i][j].fr = r;
                                }
                        }
                        else
                        {
                                if(grid[i][j] == '.')
                                {
                                        index[i][j].fr = r;
                                }
                                else
                                {
                                        index[i][j].fr = -1;

                                        if(grid[i][j] == 'W' && grid[i][j-1] != 'W' )
                                        {
                                                r++;
                                        }
                                }
                        }
                }
        }


        loop(j, M)
        {
                loop(i, N)
                {
                        if(i == 0)
                        {
                                c++;
                                if(grid[i][j] == '.')
                                {
                                        index[i][j].sc = c;
                                }
                        }
                        else
                        {
                                if(grid[i][j] == '.')
                                {
                                        index[i][j].sc = c;
                                }
                                else
                                {
                                        index[i][j].sc = -1;

                                        if(grid[i-1][j] != 'W' && grid[i][j] == 'W')
                                        {
                                                c++;
                                        }
                                }
                        }

                }
        }


        kuhn.clear(r+2);


        loop(i, N)
        {
                loop(j, M)
                {
                        if(grid[i][j] == '.')
                        {
                                kuhn.adj[ index[i][j].fr ].pb( index[i][j].sc );

                        }
                }
        }


        int m = kuhn.match(r + 2);

        pf("%d\n", m);

        int u, v;

        loop(i, N)
        {
                loop(j, M)
                {
                        if(grid[i][j] == '.')
                        {
                                u = index[i][j].fr;
                                v = index[i][j].sc;

                                if(kuhn.left[u] == v)
                                {
                                        pf("T");
                                }
                                else
                                {
                                        pf(".");
                                }
                        }
                        else
                        {
                                pf("%c", grid[i][j]);
                        }
                }

                pf("\n");
        }





}

int main()
{
#ifdef hasibpc
        read("input.txt");
        //write("output.txt");
#endif

        int kases, kaseno = 0;

        sf("%d", &kases);

        while(kases--)
        {
                sf("%d %d", &N, &M);


                loop(i, N)
                {
                        sf("%s", grid[i]);
                }

                pf("Case %d: ", ++kaseno);

                solve();
        }

}

(LightOJ) 1218 – Multiple Free Subset

0

Step 1. Sort the array.
Step 2. Remove duplicates.
Step 3. Make a bipartite graph. There should be a connection from i to j iff i divides j.
Step 4. Start from the smallest number, and follow the next steps repeatedly.

– Remove all the multiples of this number from the graph. Remove from both sides of bipartite graph.
– Now check, if we can create exactly same size of maximum independent set as before.
– If possible, parmanently delete those multiples and push the current number into result array. If not possible, restore the previous graph.


/***********Template Starts Here***********/
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include
<map>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <functional>
#include <string>
#include <iostream>
#include <cctype>
#include <set>
#include <climits>
#include <iomanip>
#include <cassert>
//#include <unordered_map>

#define pb push_back
#define nl puts ("")
#define sp printf ( " " )
#define phl printf ( "hello\n" )
#define ff first
#define ss second
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define MP make_pair
#define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i) #define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b)) #define MAX(a,b) ((a)>(b)?(a):(b))
#define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1)
#define SQ(x) ((x)*(x))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x)) #define ALL(x) (x).begin(),(x).end() #define LCM(x,y) (((x)/gcd((x),(y)))*(y)) #define SZ(x) ((int)(x).size()) #define NORM(x) if(x>=mod)x-=mod;

using namespace std;

typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<pii> vii;
typedef vector<int> vi;

const vlong inf = 2147383647;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-9;

#ifdef forthright48
     #include <ctime>
     clock_t tStart = clock();
     #define debug(args...) {dbg,args; cerr<<endl;}
     #define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC)
#else
    #define debug(args...)  // Just strip off all debug tokens
    #define timeStamp
#endif

struct debugger{
    template<typename T> debugger& operator , (const T& v){
        cerr<<v<<" ";
        return *this;
    }
}dbg;

//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};

inline vlong gcd ( vlong a, vlong b ) {
    a = ABS ( a ); b = ABS ( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;
}

vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
    vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
    x2 = 1; y2 = 0;
    x1 = 0; y1 = 1;
    for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
        q = r2 / r1;
        r = r2 % r1;
        x = x2 - (q * x1);
        y = y2 - (q * y1);
    }
    *X = x2; *Y = y2;
    return r2;
}

inline vlong modInv ( vlong a, vlong m ) {
    vlong x, y;
    ext_gcd( a, m, &x, &y );
    if ( x < 0 ) x += m; //modInv is never negative     return x; } inline vlong power ( vlong a, vlong p ) {     vlong res = 1, x = a;     while ( p ) {         if ( p & 1 ) res = ( res * x );         x = ( x * x ); p >>= 1;
    }
    return res;
}

inline vlong bigmod ( vlong a, vlong p, vlong m ) {
    vlong res = 1 % m, x = a % m;
    while ( p ) {
        if ( p & 1 ) res = ( res * x ) % m;
        x = ( x * x ) % m; p >>= 1;
    }
    return res;
}

/***********Template Ends Here***********/

/*********** Hasib Templates Starts Here**********/

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

#define loop(i, n) for(int i=0; i<(n); i++)
#define sf scanf
#define pf printf
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) (v).begin(), (v).end()
#define PI acos(-1.0)
#define mem(ara, val) memset(ara, val, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define vdump(x) cerr<<#x<<" = "<<x<<endl;
#define dump(args...) cerr,args; cerr<<endl

template<typename T>
ostream& operator<<(ostream& out, vector<T> v)
{
    out<<"[ ";

    loop(i, SZ(v))
    {
        if(i) out<<", ";
        out<<v[i];
    }

    out<<" ]";
    return out;
}

template<typename T1, typename T2>
ostream& operator<<(ostream &out, pair<T1, T2> p)
{
    out<<"( "<<p.fr<<", "<<p.sc<<")";
    return out;
}

template<typename T>
ostream& operator,(ostream &out, T x)
{
    out<<x<<" ";
    return out;
}

/**********Hasib Templates Ends Here**************/

/**
 *  WARTNING for me:
 *     Never use    FOR
 *     Never use    pii, pll, vi, vi
 *     Never use    ff, ss, phl, sp, nl
 */

int N;

vector<int>v;
#define NODE 107

int mark[NODE];

struct KUHN{
        int left[NODE], right[NODE], vis[NODE], cc;
        vector<int>adj[NODE];

        KUHN() : cc(1) {}

        void clear(int n)
        {
                FOR(i, 0, n) adj[i].clear();
        }

        bool tryK(int v)
        {
                if (vis[v] == cc) return false;
                vis[v] = cc;

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if(mark[t]) continue;

                        if(right[t] == -1)
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                loop(i, SZ(adj[v]))
                {
                        int t = adj[v][i];

                        if(mark[t]) continue;

                        if(tryK(right[t]))
                        {
                                right[t] = v; left[v] = t;
                                return true;
                        }
                }

                return false;

        }

        int match(int n)
        {
                int res = 0;
                bool done;

                CLR(left, -1); CLR(right, -1);

                do{
                        done = true;
                        cc++;
                        FOR(i, 0, n)
                        {
                                if(mark[i]) continue;

                                if(left[i] == -1 && tryK(i))
                                {
                                        done = false;
                                }
                        }
                }while(!done);

                FOR(i, 0, n)
                {
                        if(mark[i]) continue;

                        res += (left[i] != -1);
                }
                return res;
        }
}kuhn;

void solve()
{
        sort(all(v));
        UNIQUE(v);

        N = SZ(v);

        kuhn.clear(N + 2);

        loop(i, N)
        {
                for(int j=i+1; j<N; j++)
                {
                        if( (v[j] % v[i]) == 0 )
                        {
                                //vdump(MP(i,j));
                                kuhn.adj[i].pb(j);
                        }
                }
        }

        mem(mark, 0);

        int M = N - kuhn.match(N+2);

        vector<int>result;

        int m;
        int prevMarked = 0;

        loop(i, N)
        {
                if(mark[i]) continue;

                m = 0;

                for(int j=i+1; j<N; j++)
                {
                        if( (mark[j] == 0) && (v[j] % v[i] == 0) )
                        {
                                mark[j] = 2;
                                m++;
                        }
                }

                int tmp = (N - m - prevMarked - kuhn.match(N+2));

                if(tmp == M )
                {
                        result.pb(i);
                        prevMarked += m;
                        m = 1;
                }
                else
                {
                        m = 0;
                }

                loop(i, N)
                {
                        if(mark[i] == 2)
                        {
                                mark[i] = m;
                        }
                }
        }

        loop(i, M)
        {
                pf(" %d", v[result[i]]);
        }

        pf("\n");
}

int main ()
{
    #ifdef hasibpc
        read("input.txt");
        //write("output.txt");
    #endif // hasibpc

    int kases, kaseno = 0;

    sf("%d", &kases);

    while(kases--)
    {
            sf("%d", &N);

            v.resize(N);

            loop(i, N)
            {
                    sf("%d", &v[i]);
            }

            pf("Case %d:", ++kaseno);

            solve();
    }

    return 0;
}