An earthquake takes place in Southeast Asia. The ACM (Asia Cooperated Medical team) have set up a wireless network with the lap computers, but an unexpected aftershock attacked, all computers in the network were all broken. The computers are repaired one by one, and the network gradually began to work again. Because of the hardware restricts, each computer can only directly communicate with the computers that are not farther than d meters from it. But every computer can be regarded as the intermediary of the communication between two other computers, that is to say computer A and computer B can communicate if computer A and computer B can communicate directly or there is a computer C that can communicate with both A and B. 

In the process of repairing the network, workers can take two kinds of operations at every moment, repairing a computer, or testing if two computers can communicate. Your job is to answer all the testing operations. 

Input

The first line contains two integers N and d (1 <= N <= 1001, 0 <= d <= 20000). Here N is the number of computers, which are numbered from 1 to N, and D is the maximum distance two computers can communicate directly. In the next N lines, each contains two integers xi, yi (0 <= xi, yi <= 10000), which is the coordinate of N computers. From the (N+1)-th line to the end of input, there are operations, which are carried out one by one. Each line contains an operation in one of following two formats: 

1. "O p" (1 <= p <= N), which means repairing computer p. 

2. "S p q" (1 <= p, q <= N), which means testing whether computer p and q can communicate. 

The input will not exceed 300000 lines. 

Output

For each Testing operation, print "SUCCESS" if the two computers can communicate, or "FAIL" if not.

Sample Input

4 10 10 20 30 4O 1O 2O 4S 1 4O 3S 1 4

Sample Output

FAILSUCCESS

思路：建立一个数组把之前的信息保留下来，去遍历，然后通过距离的判断是否能进行连接，注意输入既有整数，又有字符，故当成字符串输入

代码：

 

#include
    
     #include
     
      #include
      
       #include
       
        #include
        
         using namespace std;int pre[1005];int s[1005];struct node{	double x,y;}p[1005];double dis(node a,node b){	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}int find(int x){	if(x==pre[x])	{		return x;	}	else	{		return pre[x]=find(pre[x]);	}}void merge(int x,int y){	int fx=find(x);	int fy=find(y);	if(fx!=fy)	{		pre[fx]=fy;	}}int sum=1;int main(){	int N;	double d;		cin>>N>>d;		for(int t=1;t<=N;t++)		{			scanf("%lf %lf",&p[t].x,&p[t].y);		}		for(int t=0;t<=N;t++)		{			pre[t]=t;		}		memset(s,0,sizeof(s));		char c[2];		int p1,q;		while(scanf("%s",c)!=EOF)		{			if(c[0]=='O')			{				scanf("%d",&p1);				for(int t=1;t<=sum;t++)				{					if(dis(p[s[t]],p[p1])<=d+1e-6)					merge(s[t],p1);				}				s[sum++]=p1;			}			if(c[0]=='S')			{				scanf("%d%d",&p1,&q);				if(find(p1)==find(q))				{					printf("SUCCESS\n");				}				else				{					printf("FAIL\n");				}			}		}				return 0;}