//@habrunit
//package olimp;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.UnsupportedEncodingException;
import java.security.NoSuchAlgorithmException;
import static java.lang.Math.*;
public class Olimp {
private static int cash[]={0xc0001200,0x10818201,0x51feba02,0x1483a003,0xb6ffc304,0x8d953105,0x1b2e7e06,0x780a707,0x59041a08,0x283b1c09,0x5818430a,0xc13b950b,0x3921ed0c,0x599b60d,0x99c8400e,0x2612640f,0xb7b0ca10,0x8c17d11,0xd35fda12,0x96863f13,0xca7ea414,0x90875415,0xc860e416,0x6239c317,0x9f39d418,0xccc48419,0x3f43d11a,0x9e366d1b,0x37fc9a1c,0x103bd91d,0xe96c501e,0x80ccf81f,0x602aca20,0xed28b721,0xcedf2d22,0xd2da9e23,0x93574024,0xebba4125,0x77fcc26,0xf8eb1a27,0xc6e09728,0x58dfe129,0xc776642a,0x6688342b,0x102a252c,0xedec802d,0xdf737f2e,0x4b5b402f,0x9c29fb30,0x93300a31,0xc30d2b32,0xabe73633,0x61f4fa34,0xf4334c35,0xd27b8a36,0xf7b63e37,0x602d9038,0x2e8aff39,0x4e62003a,0xc489143b,0x4e5ed53c,0x57a46f3d,0xf6630b3e,0xb392f53f,0xba827340,0x5b9b7e41,0x3e9d1f42,0x29b2c743,0x47f8644,0xe4d74745,0xf1263046,0x3d44e47,0xb1905148,0xd079d849,0x66f16d4a,0x281ff94b,0x4cbc284c,0xe364e94d,0x5fda1a4e,0x4628d24f,0x47d17d50,0x53ca2751,0x6738c52,0x2a1c9653,0xcdab0454,0x7429e855,0x91c38556,0xb3c8ab57,0xa98cb258,0x26151d59,0x5525b75a,0xd955c75b,0x51c3475c,0x8350855d,0x1c30b65e,0x70339d5f,0x78a88460,0x4cc2a361,0x12464c62,0x5a34b63,0x3fee8864,0xa8633565,0x3e23d766,0xf8cd5767,0x52432068,0x9cae0969,0x63aa1d6a,0x8742826b,0x75e67b6c,0x2ef696d,0x25006d6e,0x89daa76f,0xbbb71870,0x2faca571,0x71374172,0x9b818673,0xa0de6274,0x29326075,0xb2401776,0x8edcb677,0x7a265378,0x87dd7779,0xb726ce7a,0x99f0397b,0x81a8967c,0x97d0437d,0xc9147e,0x27a1a17f,0xabd65680,0xc405e681,0xc0107482,0xe63b7783,0x16d43984,0x37c8e085,0xc6f26286,0x151dac87,0x67c36588,0xe593b589,0x669e388a,0x5c46a68b,0xb822fe8c,0x6455d18d,0x54b49d8e,0x475edc8f,0xfa8a9690,0xa38c7d91,0xa25f6692,0x32b9a193,0x22bf7c94,0xa72cfb95,0xcaa48696,0x78639e97,0x5dca8798,0xe263e99,0x59c599a,0x855a4f9b,0x4e66949c,0x3a27d89d,0xca15ec9e,0xe443da9f,0xaeaea3a0,0xdc6cdca1,0xa3bb51a2,0xd0f12da3,0xfcd7cda4,0x959c62a5,0x9e276ca6,0x67caeca7,0xc36d51a8,0xe76712a9,0x95d4b5aa,0xe6b1a1ab,0x60979aac,0xae2d55ad,0xf73e82ae,0x87622af,0x55678db0,0xf3813ab1,0x66bd2ab2,0x640762b3,0xab7d25b4,0xce243ab5,0x565e39b6,0x9389fcb7,0xecb84db8,0x8da369b9,0x2b1138ba,0x1a1b3ebb,0xa6a40cbc,0x2659acbd,0xb90ac3be,0xbb61e9bf,0x17dc81c0,0xf9cb57c1,0x1f2c47c2,0x177c6ec3,0x68cb55c4,0x94648fc5,0xb6c33ec6,0x9e71ffc7,0x21d49c8,0x1c1f96c9,0x40fdf8ca,0x608471cb,0x90c71acc,0x83049fcd,0x31232bce,0xa755d0cf,0x2995fd0,0x8ef786d1,0xaf7ae2d2,0x49e5f9d3,0xb621d1d4,0xa30ef5d5,0x75e168d6,0x6fcb3d7,0xe83308d8,0x29c1ead9,0x6b000ada,0xf37c94db,0xe2884cdc,0x7f92e0dd,0x93836ade,0x633232df,0xe29bc4e0,0x8e761fe1,0x31a905e2,0xd46a41e3,0x159184e4,0xd3f654e5,0x6abdbde6,0x865f3be7,0x9f7c41e8,0xb6e13de9,0xae2525ea,0x62d6c9eb,0x271459ec,0x1a13ffed,0x173ed9ee,0x1d2edaef,0x44366bf0,0xc9928f1,0x3fb38bf2,0xdf3dacf3,0x1b5250f4,0xf5f486f5,0x6a7c18f6,0xfce055f7,0xde547ff8,0x35a76ef9,0x2d3666fa,0xa4ba58fb,0x83f9f6fc,0xedb424fd,0xcc4d8fe,0xe0f0baff};
private static int cashLen[]={0x328aa,0x6144d,0xb900e,0x3ef04,0x7a10,0xc65aa,0x85819,0x6acf,0x16e30,0x3c13e,0x95b7b,0xcdfba,0xdd3e0,0xbae88,0x1406b,0x2ae9a,0x7bf85,0x17d72,0x9e4cd,0x8e16a,0x754b6,0x68e5c,0xd4a89,0xd6904,0x501a8,0x496da,0x21606,0x3d080,0x98942,0x4f269,0x374f4,0x8f0af,0xa9be5,0xc74e5,0x1f782,0x3fe46,0xc0a16,0xc37da,0x8a462,0x31968,0x510eb,0x59a3c,0x19bf6,0xa4f9b,0xaf773,0xb15f4,0xc8424,0xe10f0,0xb80c2,0x97a00,0x3dfc2,0x90f31,0x94c38,0xf1440,0xa1294,0x6cb64,0xca2b1,0x9d58a,0x632d8,0x42c0c,0x112a4,0x56c76,0xf23e2,0xe8af6,0x93cf6,0x29016,0x848d6,0xac9aa,0xe2f62,0x7733a,0x4b561,0x48799,0xd3b4a,0xe5d49,0xcd078,0x80bce,0x1e84,0xe7bad,0x2dc60,0x5202c,0x10362,0x74574,0x40d88,0xb718,0x9b707,0x35670,0x13128,0xbfada,0x3b1fc,0xcfe57,0x41ccc,0xd59e,0xd2c03,0x67f1b,0x2eba2,0x8952,0xe4e0d,0xb06b4,0x7de08,0x1c9bc,0x57bb8,0x14fac,0xaba6b,0xd59c5,0x26250,0x6bc24,0xb7184,0x38436,0xee717,0x121e6,0x46916,0x9894,0xe019d,0x18cb4,0x1d8fe,0x53eb0,0x83998,0x52f6e,0x39379,0x337ec,0xa4059,0xc4724,0x6daa6,0x5a97e,0x726f0,0x66097,0x6f92a,0x717ae,0xa5ee4,0x73632,0x2348a,0x0,0xc289a,0x7ed4a,0xd784f,0x6e9e8,0x6238e,0xdb54c,0xbeb93,0x92db5,0x66fd8,0x9988a,0x4c4a0,0xe6c69,0x5f5c8,0xd1cb8,0x5b8c0,0x64212,0x1ba7a,0xf420,0x5e686,0xd878a,0xbcd0c,0x7086c,0xe9a3b,0xad8ec,0x54df2,0x5d744,0x763fa,0xe3ecf,0x8d22d,0xb6243,0x9f412,0x206c5,0x9a7c8,0x9c64c,0xcc12f,0x81b12,0x89520,0x96abc,0xe204a,0x365b2,0x7b045,0xa7d6,0x44a90,0xd0d84,0x4e325,0xb3485,0x29f58,0x55d34,0x459d3,0xb253c,0x4c4a,0x5b8c,0xda610,0xea98d,0x885de,0xc65a,0x69d9e,0xc9367,0x4a61c,0xa3117,0x8b3a4,0xd96c8,0x65154,0xde316,0x6ace0,0x3d08,0x5c803,0xbbdcd,0xb43bc,0xc565e,0xa0351,0xf33a7,0xa7d60,0x791be,0xdc4ad,0x280d4,0x1e840,0x2dc6,0x7827c,0xdf25d,0xa8ca8,0x91e73,0xf42,0x8fff1,0x47856,0x7cec6,0x243ce,0xe4de,0xb5305,0x82a53,0x2cd22,0x3472e,0x58afa,0xc195a,0xcb1ec,0xb9f48,0x8675a,0xae834,0xceef9,0xbdc52,0x2bddc,0x8769c,0x7a100,0x7fc91,0x8c2ea,0xa21d5,0x22548,0x3a2bc,0x6050b,0x1ab38,0xef5b9,0xaab26,0xeb8b3,0x15eee,0x43b4e,0x27192,0x2fae4,0xa6e29,0xec7fb,0x2530e,0x4d3e2,0xed769,0x30a26,0xf0568};
Circle circles[];
double kof=29.9792458;
//
static InputStream in;
//
final int maxLen10=10000000;
final int maxLen1=maxLen10/10;
final int maxLenB=16384;
//
final byte buf[]=new byte[maxLenB];
int posBuf=0;
int lenBuf=0;
public static void main(String[] args) throws UnsupportedEncodingException, NoSuchAlgorithmException, FileNotFoundException, IOException {
// Pset tests[]=new Pset[]{new Pset(-1.81683e+006,-1.74334e+006),new Pset(3.06932e+006, -2.59405e+006),new Pset(3420803.233, -1950298.548)};
// long t=System.currentTimeMillis();
//
// for(int i=0;i<tests.length;i++){
// in=new FileInputStream("test"+(i+1)+".in");
// Pset answer=new Pset();
// new Olimp(answer);
// answer.printDlta(tests[i]);
// }
// System.out.println("end"+(System.currentTimeMillis()-t));
//in=new FileInputStream("test1.in");
in=System.in;
Pset answer=new Pset();
new Olimp(answer);
answer.print();
}
double readDouble(){
while(isBR(buf[posBuf]))posBuf++;
int start=posBuf;
while(!isBR(buf[posBuf]))posBuf++;
String s=new String(buf,start,posBuf-start);
while(isBR(buf[posBuf]))posBuf++;
return Double.parseDouble(s);
}
static final boolean isBR(final byte val){
return val==13 || val==10 || val==32;
}
void readMin500()throws IOException{
while(lenBuf<500){
int l=in.read(buf,lenBuf,maxLenB-lenBuf);
if(l==-1)
throw new IOException();
lenBuf+=l;
}
}
void read()throws IOException{
if(posBuf>=maxLenB){
posBuf%=maxLenB;
lenBuf=0;
}
int l=in.read(buf,lenBuf,maxLenB-lenBuf);
if(l==-1)
throw new IOException();
lenBuf+=l;
}
private Olimp(final Pset answer)throws IOException{
readMin500();
circles=new Circle[(int)readDouble()];
for(int sp=0;sp<circles.length;sp++){
readMin500();
circles[sp]=new Circle(readDouble(), readDouble());
int readData=0;
int shift=0;
{
byte temp=buf[posBuf];
while(buf[posBuf+shift]==temp)
shift++;
shift%=10;
posBuf+=shift;
readData+=shift;
}
int data=0;
for(int i=0;i<32;i++,posBuf+=10){
data<<=1;
data|=buf[posBuf]==48?(byte)0:(byte)1;
}
readData+=320;
m1:while(posBuf<maxLenB){
for(;posBuf<lenBuf;posBuf+=10,readData+=10){
if(cash[data&0xFF]==data){
double len= readData -320 +maxLen10-cashLen[data&0xFF]*10 ;
circles[sp].r=len*kof;
break m1;
}
data<<=1;
data|=buf[posBuf]==48?(byte)0:(byte)1;
}
read();
}
in.skip(maxLen10-(readData+(lenBuf-posBuf)));
posBuf=0;
lenBuf=0;
}
int testPset=1;
for(int i=2;i<circles.length;i++){
if(circles[testPset].r<circles[i].r){
testPset=i;
}
}
Pset p0=new Pset();
Pset p1=new Pset();
int gggg=intersection(circles[0],circles[testPset],p0,p1);
double delta0=precisionAll(p0,circles);
if(gggg==1){
answer.x=p0.x;
answer.y=p0.y;
return;
}
double delta1=precisionAll(p1,circles);
if(delta0<delta1){
answer.x=p0.x;
answer.y=p0.y;
}else{
answer.x=p1.x;
answer.y=p1.y;
}
}
static double pow2(double x){
return x*x;
}
static double precisionAll(Pset p0,Circle[] circles){
double delta=0;
Pset sum=new Pset();
Pset temp=new Pset();
for(int j=1;j<7;j++){
sum.x=0;
sum.y=0;
for(int i=0;i<circles.length;i++){
precision(p0,circles[i],temp);
sum.x+=temp.x;
sum.y+=temp.y;
delta=pow2(temp.x-p0.x)+pow2(temp.y-p0.y);
}
p0.x=sum.x/circles.length;
p0.y=sum.y/circles.length;
}
return delta;
}
static void precision(Pset pset,Circle circle,Pset returnPset){
double dx=pset.x-circle.x;
double dy=pset.y-circle.y;
double dz=circle.distanceTo(pset);
if(dz<0.0000001){
if(circle.r<0.000001){
returnPset.x=circle.x;
returnPset.y=circle.y;
return ;
}
returnPset.x=pset.x+ circle.r;
returnPset.y=pset.y+circle.r;
return;
}
returnPset.x=circle.x+dx*circle.r/dz;
returnPset.y=circle.y+dy*circle.r/dz;
}
static int intersection(Circle circle0,Circle circle1,Pset first,Pset second)
{
double x0,y0;
double d;
double a;
double h;
d=circle0.distanceTo(circle1);
double deltaX=circle1.x - circle0.x;
double deltaY=circle1.y - circle0.y;
if(d >= circle0.r+circle1.r) {
first.x = circle0.x+deltaX*circle0.r/(circle0.r+circle1.r);
first.y = circle0.y+deltaY*circle0.r/(circle0.r+circle1.r);
return 1;
}
if(d <= abs(circle0.r-circle1.r)) {
deltaX/=d;
deltaY/=d;
if(circle1.r<circle0.r){
first.x = (circle0.x+deltaX*circle0.r + circle1.x+deltaX*circle1.r)/2;
first.y = (circle0.y+deltaY*circle0.r + circle1.y+deltaY*circle1.r)/2;
}else{
first.x = (circle0.x-deltaX*circle0.r + circle1.x-deltaX*circle1.r)/2;
first.y = (circle0.y-deltaY*circle0.r + circle1.y-deltaY*circle1.r)/2;
}
return 1;
}
a= (pow2(circle0.r) - pow2(circle1.r) + d*d ) / (2*d);
h= sqrt( pow2(circle0.r) - pow2(a));
x0 = circle0.x + a*deltaX / d;
y0 = circle0.y + a*deltaY / d;
first.x= x0 + h*deltaY / d;
first.y= y0 - h*deltaX / d;
//if(a == circle0.r ) return 1;
second.x= x0 - h*deltaY / d;
second.y= y0 + h*deltaX / d;
return 2;
}
}
class Pset{
double x;
double y;
Pset(){
}
Pset(double xx,double yy){
x=xx;
y=yy;
}
double distanceTo(Pset p){
return sqrt((x-p.x)*(x-p.x)+(y-p.y)*(y-p.y));
}
void print(){
System.out.println(""+x+" "+y);
}
void printDlta(Pset answer){
System.out.println(""+(x-answer.x)+" "+(y-answer.y)+" "+Math.sqrt((x-answer.x)*(x-answer.x)+(y-answer.y)*(y-answer.y)));
}
}
class Circle extends Pset{
double r;
Circle(double xx,double yy){
super(xx,yy);
}
Circle(double xx,double yy,double rr){
super(xx,yy);
this.r=rr;
}
}
Начиная с конца 80-х в машинах подороже начали появляться HUD (Head-up display) – прозрачные дисплеи, которые водитель наблюдает, глядя вперед через лобовое стекло. А еще ранее (незадолго до начала второй мировой войны), в рудиментарном виде – на самолетах, для отображения прицельной марки без параллакса с дальнейшим развитием до современных HUD.
Итак, настало время подвести итоги прошедшего майского