記得檢查會不會超出去
超出去的話只要兩個方向相反走就可以了
//
// GGGGGGGGGGGGG CCCCCCCCCCCCC AAA
// GGG::::::::::::G CCC::::::::::::C A:::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A
// G:::::G GGGGGG C:::::C CCCCCC A:::::::::A
//G:::::G C:::::C A:::::A:::::A
//G:::::G C:::::C A:::::A A:::::A
//G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A
//G:::::G G::::::::GC:::::C A:::::A A:::::A
//G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A
//G:::::G G::::GC:::::C A:::::::::::::::::::::A
// G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A
// GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A
// GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define VAR(a,b) decltype(b) a=(b)
#define debug(...) printf("DEBUG: "),printf(__VA_ARGS__)
#define gettime() end_time=clock();printf("now running time is %.7f\\n",(float)(end_time - start_time)/CLOCKS_PER_SEC);
#else
#define VAR(a,b) __typeof(b) a=(b)
#define debug(...)
#define gettime()
#endif
typedef unsigned int uint;
typedef long long int Int;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I_de(x,n)for(int i=0;i<n;i++)printf("%d ",x[i]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp[htx][hty]);}Pln();}
#define M 30005
#define PII pair<int,int>
#define PB push_back
#define oo INT_MAX
#define Set_oo 0x3f
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)
#define eps 1e-10
clock_t start_time=clock(), end_time;
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
bool xeqy(double x,double y){return fabs(x-y)<eps;}
int min3(int x,int y,int z){
int tmp=min(x,y);
return min(tmp,z);
}
int max3(int x,int y,int z){
int tmp=max(x,y);
return max(tmp,z);
}
double r,x,y,x2,y2;
double dis(double x,double y){
return sqrt(x*x+y*y);
}
void solve(){
double l=y2-y;
double w=x2-x;
double sqr2=sqrt(2);
if(fabs(l)>fabs(w)){
double t=fabs(l)-fabs(w);
if(xcy(l,0)){
double xx=x+w,yy=y-fabs(w);
if(xdy(dis(xx,yy),r)){
if(!xeqy(t,0))printf("south %.10f\\n",t);
if(xdy(w,0))printf("southeast %.10f\\n",w*sqr2);
else if(xcy(w,0)) printf("southwest %.10f\\n",-w*sqr2);
}else{
if(xdy(w,0))printf("southeast %.10f\\n",w*sqr2);
else if(xcy(w,0)) printf("southwest %.10f\\n",-w*sqr2);
if(!xeqy(t,0))printf("south %.10f\\n",t);
}
}else{
double xx=x+w,yy=y+fabs(w);
if(xdy(dis(xx,yy),r)){
if(!xeqy(t,0))printf("north %.10f\\n",t);
if(xdy(w,0))printf("northeast %.10f\\n",w*sqr2);
else if(xcy(w,0)) printf("northwest %.10f\\n",-w*sqr2);
}else{
if(xdy(w,0))printf("northeast %.10f\\n",w*sqr2);
else if(xcy(w,0)) printf("northwest %.10f\\n",-w*sqr2);
if(!xeqy(t,0))printf("north %.10f\\n",t);
}
}
}else{
double t=fabs(w)-fabs(l);
if(xcy(w,0)){
double xx=x-fabs(l),yy=y+l;
if(xdy(dis(xx,yy),r)){
if(!xeqy(t,0))printf("west %.10f\\n",t);
if(xdy(l,0))printf("northwest %.10f\\n",l*sqr2);
else if(xcy(l,0)) printf("southwest %.10f\\n",-l*sqr2);
}else{
if(xdy(l,0))printf("northwest %.10f\\n",l*sqr2);
else if(xcy(l,0)) printf("southwest %.10f\\n",-l*sqr2);
if(!xeqy(t,0))printf("west %.10f\\n",t);
}
}else{
double xx=x+fabs(l),yy=y+l;
if(xdy(dis(xx,yy),r)){
if(!xeqy(t,0))printf("east %.10f\\n",t);
if(xdy(l,0))printf("northeast %.10f\\n",l*sqr2);
else if(xcy(l,0)) printf("southeast %.10f\\n",-l*sqr2);
}else{
if(xdy(l,0))printf("northeast %.10f\\n",l*sqr2);
else if(xcy(l,0)) printf("southeast %.10f\\n",-l*sqr2);
if(!xeqy(t,0))printf("east %.10f\\n",t);
}
}
}
}
int main() {
ios_base::sync_with_stdio(0);
int ff=0;
while(scanf("%lf%lf%lf%lf%lf",&r,&x,&y,&x2,&y2)==5&&r>=0){
if(ff++)Pln();
solve();
}
}