#include <stdio.h>#include <stdlib.h>#include <string.h>#include <ctype.h>#include <math.h>#include <time.h>#include <iostream>#include <algorithm>#include <cstdio>#include <cstdlib>#include <cmath>#include <cstring>#include <cctype>#include <stack>#include <string>#include <list>#include <queue>#include <map>#include <vector>#include <deque>#include <set>using namespace std;#define LOCAL_HOST#define ONLINE_JUDGE#define TIME_OUT_PUT#define INF 0x7F7F7F7F#define eps 1e-8#define PI acos( -1. )#define PI2 asin ( 1. );typedef long long LL;#define MP make_pairtypedef vector<int> VI;typedef vector<int> VS;typedef pair<int , int> PII;#define pb push_back#define mp make_pair#define FOR(a,b,i) for ( i = a ; i < b ; i++ )#define FORE(a,b,i) for ( i = a ; i <= b ; i++ )#define REP(i,n) FOR(0,n,i)#define CL(a,b) memset ( a , b , sizeof ( a ) )#define sqr(a,b) sqrt ( (double)(a)*(a) + (b)*(b) )template < typename T > double DIS ( T va , T vb ) { return sqr ( va.x - vb.x , va.y - vb.y ); }template <class T> inline T INT_LEN( T v ) { int len = 1 ; while ( v /= 10 ) ++len; return len; }#define le 23typedef struct { double x , y;}re;re ar[le] , br[le] , pq[le];int q[le << 1];int N , M;void input (){ int i; scanf ( "%d" , &N ); REP ( i , N ) scanf ( "%lf%lf" , &ar[i].x , &ar[i].y ); scanf ( "%d" , &M ); REP ( i , M ) scanf ( "%lf%lf" , &br[i].x , &br[i].y );}template < typename T >T my_abs ( T num ){ return num >= 0 ? num : -num;}inline int sgn ( double d ) { if ( d > eps ) return 1; if ( d < -eps ) return -1; return 0;}template < typename T >inline int Cmp ( T a , T b , T c ){ if ( my_abs ( b.x - c.x ) > my_abs ( b.y - c.y ) ){ return sgn ( a.x - min ( b.x , c.x ) ) * sgn ( a.x - max ( b.x , c.x ) ); }else { return sgn ( a.y - min ( b.y , c.y ) ) * sgn ( a.y - max ( b.y , c.y ) ); }}template < typename T >inline double det ( T a , T b , T c ){ return ( b.x - a.x ) * ( c.y - a.y ) - ( b.y - a.y ) * ( c.x - a.x );}template < typename T >inline int insec_line ( T a , T b , T c , T d , T &P ){ double s1 , s2; int d1 = sgn ( s1 = det ( a , b , c ) ); int d2 = sgn ( s2 = det ( a , b , d ) ); if ( ( d1 ^ d2 ) == -2 ){ s1 = fabs ( s1 ); s2 = fabs ( s2 ); P.x = ( c.x * s2 + d.x * s1 ) / ( s1 + s2 ); P.y = ( c.y * s2 + d.y * s1 ) / ( s1 + s2 ); }else if ( d1 == 0 ){ P = c; return 1; }else if ( d2 == 0 ){ P = d; return 1; }else { return 0; }}template < typename T >int Melkman ( T p[] , int *q , int &front , int &rear , int n ){ int i; q[n] = 0; FOR ( 2 , n , i ){ q[-~n] = ~-i; if ( det ( p[0] , p[~-i] , p[i] ) ) break; } if ( i >= n ) return 0; front = n , rear = -~n; q[--front] = q[++rear] = i; if ( det ( p[0] , p[ q[-~n] ] , p[ q[n + 2] ] ) < 0 ) swap ( p[0] , p[ q[-~n] ] ); for ( ++i ; i < n ; i++ ){ if ( det ( p[ q[~-rear] ] , p[ q[rear] ] , p[i] ) > 0 && det ( p[ q[front] ] , p[ q[-~front] ] , p[i] ) > 0 ) continue; while ( det ( p[ q[~-rear] ] , p[ q[rear] ] , p[i] ) <= 0 ) rear--; q[++rear] = i; while ( det ( p[ q[front] ] , p[ q[-~front] ] , p[i] ) <= 0 ) front++; q[--front] = i; } return 1;}template < typename T >double convex_cal_min_dis ( T p[] , int *q , int &front , int &rear , int n ){ int i , j; double dis , mn = INF , mx ; FORE ( -~front , rear , i ){ dis = DIS ( p[ q[i] ] , p[ q[~-i] ] ); mx = 0; FOR ( front , rear , j ){ mx = max ( mx , fabs ( det ( p[ q[~-i] ] , p[ q[i] ] , p[ q[j] ] ) ) / dis ); } mn = min ( mn , mx ); } return mn;}template < typename T >double convex_min_dis ( T p[] , int n ){ int front , rear ; if ( Melkman ( p , q , front , rear , n ) ){ return convex_cal_min_dis ( p , q , front , rear , n ); }else return -1;}template < typename T >inline bool inside ( T p[] , T &o , int n ){ int i , num = 0; T va , vb; REP ( i , n ){ if ( !sgn ( det ( o , p[i] , p[-~i] ) ) && Cmp ( o , p[i] , p[-~i] ) <= 0 ) return true; } REP ( i , n ){ va = p[i] , vb = p[-~i]; if ( va.y > vb.y ) swap ( va , vb ); if ( det ( o , va , vb ) < 0 && va.y <= o.y && o.y <= vb.y ) num++; } return num & 1;}bool convex_cmp ( re va , re vb ){ return fabs ( va.x - vb.x ) <= eps ? va.y < vb.y : va.x < vb.x;}template < typename T >inline double hole_cal_max_len ( T &p1 , T &p2 , T p[] , T pq[] , int n ){ int i , k = 0; REP ( i , n ){ if ( insec_line ( p1 , p2 , p[i] , p[-~i] , pq[k] ) ) k++; } sort ( pq , pq + k , convex_cmp ); double len = 0 , mx = 0 ; T mid; k--; REP ( i , k ){ mid.x = ( pq[i].x + pq[-~i].x ) / 2.; mid.y = ( pq[i].y + pq[-~i].y ) / 2.; if ( inside ( p , mid , n ) ){ len += DIS ( pq[i] , pq[-~i] ); mx = max ( mx , len ); }else { len = 0; } } return mx;}template < typename T >double hole_max_len ( T p[] , int n ){ int i , j; double mx = 0 , len; p[n] = p[0]; REP ( i , n ){ FOR ( -~i , n , j ){ len = hole_cal_max_len ( p[i] , p[j] , p , pq , n ); mx = max ( mx , len ); } } return mx;}void solve ( re hole[] , re coin[] , int n , int m ){ double mn = convex_min_dis ( coin , m ); double mx = hole_max_len ( hole , n ); if ( mn <= mx ) puts ( "legal" ); else puts ( "illegal" );}int main (void){ int cas; scanf ( "%d" , &cas ); while ( cas-- ){ input (); solve ( ar , br , N , M ); } return 0;}
