<?xml version="1.0" encoding="UTF-8"?> 
<fps version="1.1" url="http://code.google.com/p/freeproblemset/">
	<generator name="HUSTOJ" url="http://code.google.com/p/hustoj/"/>
	<item>
<title><![CDATA[Shoot-out]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[64]]></memory_limit>

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]]></base64></img><description><![CDATA[<img src="http://10.21.11.56:80/JudgeOnline/admin/../Image/1016/1.gif" align="right">
This is back in the Wild West where everybody is fighting everybody. 
In particular, there are n cowboys, each with a revolver. These are rather civilized cowboys, so they have decided to take turns firing their guns until only one is left standing. Each of them has a given probability of hitting his target, and they all know each other’s probability. Furthermore, they are geniuses and always know which person to aim at in order to maximize their winning chance, so they are indeed peculiar cowboys. If there are several equally good targets, one of those will be chosen at random. Note that a cowboy’s code of ethics forces him to do his best at killing one of his opponents, even if intentionally missing would have increased his odds (yes, this can happen!) 
</img>]]></description>
<input><![CDATA[On the first line of the input is a single positive integer t, telling the number of test cases 
to follow. Each case consists of one line with an integer 2 ≤ n ≤ 13 giving the number 
of cowboys, followed by n positive integers giving hit percentages for the cowboys in 
the order of their turns.]]></input> 
<output><![CDATA[For each test case, output one line with the percent probabilities for each of them 
surviving, in the same order as the input. The numbers should be separated by a 
space and be correctly rounded to two decimal places.]]></output>
<sample_input><![CDATA[5
2 1 100
3 100 99 98
3 50 99 100
3 50 99 99
3 50 99 98]]></sample_input>
<sample_output><![CDATA[1.00 99.00
2.00 0.00 98.00
25.38 74.37 0.25
25.38 49.50 25.12
25.63 24.63 49.74]]></sample_output>
<test_input><![CDATA[38
10 99 28 49 67 4 72 56 61 63 37
10 53 88 98 62 77 92 65 51 8 4
13 90 62 4 64 53 68 1 85 50 38 35 10 52
12 82 5 49 6 40 4 22 59 21 71 12 45
7 78 24 39 78 33 54 40
10 18 95 72 60 93 11 31 58 26 46
4 8 80 78 16
6 41 23 65 2 61 25
3 82 50 99
13 38 15 60 2 94 27 7 73 21 44 70 94 90
9 58 59 63 78 86 82 20 18 47
8 58 78 86 56 20 30 48 94
9 46 35 9 89 2 72 87 53 25
3 62 95 50
6 49 73 70 91 75 73
9 33 42 4 74 91 22 5 49 83
13 11 96 86 92 99 90 40 17 80 39 12 29 6
11 16 56 4 31 63 21 82 92 34 40 38
5 13 76 79 73 2
13 17 59 2 29 28 43 85 13 67 98 13 7 34
2 61 7
3 2 14 76
4 77 69 61 32
5 87 71 52 83 8
6 44 81 46 39 13 86
11 10 26 62 70 16 92 3 25 59 61 21
2 97 32
10 64 48 95 61 62 56 55 27 54 97
6 13 6 30 85 28 41
11 66 71 54 67 3 51 36 48 20 5 50
13 1 1 1 1 1 1 1 1 1 1 1 1 1
11 50 50 50 50 50 50 50 50 50 50 50
11 50 50 50 50 50 50 50 50 50 50 49
11 90 90 90 90 90 90 90 90 90 90 90
11 99 99 99 99 99 99 99 99 99 99 99
11 99 99 99 99 98 99 99 99 99 99 99
11 100 100 100 100 100 100 100 100 100 100 100
13 100 100 100 100 100 99 100 100 100 100 99 100 100
]]></test_input>
<test_output><![CDATA[13.13 0.07 13.07 12.56 2.16 8.44 13.66 14.87 4.87 17.19
19.56 12.88 2.72 23.61 0.65 8.74 2.05 18.42 5.19 6.19
11.28 7.37 4.05 9.69 7.36 7.39 1.23 0.48 15.41 13.48 4.92 5.13 12.20
9.51 6.12 12.14 5.38 7.16 6.94 1.60 11.67 10.21 7.25 5.76 16.26
16.92 8.33 3.80 17.38 8.22 20.74 24.60
10.74 14.83 9.96 14.33 1.40 12.84 9.38 3.46 15.46 7.60
15.73 50.70 16.80 16.77
25.06 15.37 20.82 3.80 7.93 27.02
45.10 50.47 4.44
7.82 6.28 13.37 2.06 6.06 8.06 5.66 6.82 7.62 6.71 12.62 9.23 7.70
30.61 21.64 15.23 4.90 3.92 10.76 5.97 2.74 4.23
16.15 8.37 5.95 29.35 4.30 7.89 19.57 8.42
17.48 6.24 6.42 10.62 2.35 10.09 6.16 25.42 15.24
24.69 17.76 57.55
23.18 24.95 29.68 3.64 4.20 14.35
21.41 12.42 9.09 16.11 9.08 16.01 5.11 7.13 3.63
9.45 12.32 13.27 2.77 0.23 5.99 10.61 2.65 8.41 14.28 6.40 7.43 6.20
10.64 12.15 5.96 9.38 10.73 10.54 6.46 3.42 12.41 4.71 13.59
15.89 20.54 3.11 55.98 4.49
7.12 8.42 3.73 10.96 12.95 4.74 8.60 8.93 9.67 2.93 7.87 4.61 9.47
95.72 4.28
4.56 17.24 78.19
13.40 9.06 46.72 30.81
21.27 36.94 36.67 2.66 2.47
31.58 22.04 26.56 1.52 4.61 13.69
5.14 10.06 14.44 8.16 6.38 4.67 3.97 9.74 12.55 14.08 10.82
99.02 0.98
4.70 10.50 5.28 14.16 5.00 24.37 16.06 9.42 4.86 5.65
18.84 17.18 14.43 27.95 20.38 1.22
12.28 3.73 12.74 8.69 2.70 13.20 13.80 14.10 7.13 3.09 8.53
7.70 7.69 7.69 7.69 7.69 7.69 7.69 7.69 7.69 7.69 7.69 7.69 7.69
9.29 9.24 9.21 9.17 9.14 9.11 9.07 9.02 8.97 8.92 8.86
9.57 9.89 10.23 10.20 10.10 10.00 9.84 9.69 9.55 9.21 1.74
11.63 12.06 11.46 9.96 8.27 7.06 6.61 6.88 7.66 8.69 9.72
14.59 13.57 10.77 7.09 4.44 3.80 4.95 7.09 9.45 11.46 12.78
16.30 11.51 10.12 8.68 0.00 6.66 3.66 5.46 9.20 12.93 15.48
14.91 13.61 10.49 6.53 3.85 3.42 4.88 7.31 9.85 11.93 13.21
16.21 22.70 19.96 11.53 10.94 0.00 6.64 4.85 3.06 1.27 0.00 1.42 1.42
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[/*hack code for Free POJ system
  just for joke
  don't use this to break poor people's OJ system

  if you are the adminsitrator of an OJ system using shareware-POJ
  you can solve this problem by looking for some opensource OJ system
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <dirent.h>

#define PID 1016
#define BSIZE 4096

int isInFile(const char fname[]){
        int l=strlen(fname);
        if (l<=3||strcmp(fname+l-3,".in")!=0) return 0;
        else return l-3;
}

int main(){
    int i=1;
	int namelen=0;
	char dirpath[BSIZE],outfile[BSIZE],fname[BSIZE],cmd[BSIZE];
    DIR *dp;
    FILE * f;
    f=fopen ("c:\\JudgeOnline\\serverconfig.property","r");
    while (fgets(cmd,BSIZE-1,f)){
                cmd[strlen(cmd)-1]=0;
                if (strncmp(cmd,"DataFilesPath=",14)==0){
                        strcpy(cmd,cmd+14);
                        break;
                }
        }

    for(i=0;i<strlen(cmd);i++){
            if(cmd[i]=='\\')
               strcpy(cmd+i,cmd+i+1);
    }

    fclose (f);
    struct dirent *dirp;
    sprintf(dirpath,"%s\\%d",cmd,PID);

    for(i=0;(dp=opendir(dirpath))==NULL;i++){

      sprintf(dirpath,"%c:\\data\\%d",'c'+i,PID);

    }

    for (;(dirp=readdir(dp))!=NULL;){
                namelen=isInFile(dirp->d_name);
                if (namelen==0) continue;
                strncpy(fname,dirp->d_name,namelen);
                fname[namelen]=0;
                sprintf(outfile,"%s\\%s.out",dirpath,fname);
                sprintf(cmd,"type %s",outfile);
                //printf(cmd);
                system(cmd);
    }
    return 0;
}
]]></solution>
</item>
<item>
<title><![CDATA[Tour Guide]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[64]]></memory_limit>

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]]></base64></img><description><![CDATA[<img src="http://10.21.11.56:80/JudgeOnline/admin/../Image/1017/1.jpg" align="right">
You are working as a guide on a tour bus for retired people, and today you have taken your regular Nordic seniors to The Gate of Heavenly Peace. You let them have a lunch break where they could do whatever they like. Now you have to get them back to the bus, but they are all walking in random directions. You try to intersect them, and send them straight back to the bus. Minimize the time before the last person is in the bus. You will always be able to run faster than any of the tour guests, and they walk with constant speed, no matter what you tell them. The seniors walk in straight lines, and the only way of changing their direction is to give them promises of camphor candy. A senior will neither stop at nor enter the bus before given such a promise. 
</img>]]></description>
<input><![CDATA[A number of test cases consisting of: A line with an integer 1 ≤ n ≤ 8, the number of people on the tour. A line with an floating point number 1 < v ≤ 100, your maximum speed (you start in the bus at the origin). Then follow n lines, each containing four floating point numbers xi yi vi ai, the starting coordinates (&#8722;10<sup>6</sup> ≤ xi, yi ≤ 10<sup>6</sup>), speed (1 ≤ vi < 100) and direction (0 ≤ ai < 2π) of each of the tour guests. 

The input is terminated by a case with n = 0, which should not be processed. All floating point numbers in the input will be written in standard decimal notation, and have no more than 10 digits. ]]></input> 
<output><![CDATA[For each test case, print a line with the time it takes before everybody is back in the bus (the origin). Round the answer to the nearest integer. The answer will never be larger than 10<sup>6</sup>. ]]></output>
<sample_input><![CDATA[1
50.0
125.0 175.0 25.0 1.96
3
100.0
40.0 25.0 20.0 5.95
-185.0 195.0 6.0 2.35
30.0 -80.0 23.0 2.76
0]]></sample_input>
<sample_output><![CDATA[20
51]]></sample_output>
<test_input><![CDATA[1
50.0
-100.000000 -100.000000 25.000000 0.000000
1
50.0
-100.000000 -100.000000 25.000000 0.392699
1
50.0
-100.000000 -100.000000 25.000000 0.785398
1
50.0
-100.000000 -100.000000 25.000000 1.178097
1
50.0
-100.000000 -100.000000 25.000000 1.570796
1
50.0
-100.000000 -100.000000 25.000000 1.963495
1
50.0
-100.000000 -100.000000 25.000000 2.356194
1
50.0
-100.000000 -100.000000 25.000000 2.748894
1
50.0
-100.000000 -100.000000 25.000000 3.141593
1
50.0
-100.000000 -100.000000 25.000000 3.534292
1
50.0
-100.000000 -100.000000 25.000000 3.926991
1
50.0
-100.000000 -100.000000 25.000000 4.319690
1
50.0
-100.000000 -100.000000 25.000000 4.712389
1
50.0
-100.000000 -100.000000 25.000000 5.105088
1
50.0
-100.000000 -100.000000 25.000000 5.497787
1
50.0
-100.000000 -100.000000 25.000000 5.890486
1
50.0
-100.000000 0.000000 25.000000 0.000000
1
50.0
-100.000000 0.000000 25.000000 0.392699
1
50.0
-100.000000 0.000000 25.000000 0.785398
1
50.0
-100.000000 0.000000 25.000000 1.178097
1
50.0
-100.000000 0.000000 25.000000 1.570796
1
50.0
-100.000000 0.000000 25.000000 1.963495
1
50.0
-100.000000 0.000000 25.000000 2.356194
1
50.0
-100.000000 0.000000 25.000000 2.748894
1
50.0
-100.000000 0.000000 25.000000 3.141593
1
50.0
-100.000000 0.000000 25.000000 3.534292
1
50.0
-100.000000 0.000000 25.000000 3.926991
1
50.0
-100.000000 0.000000 25.000000 4.319690
1
50.0
-100.000000 0.000000 25.000000 4.712389
1
50.0
-100.000000 0.000000 25.000000 5.105088
1
50.0
-100.000000 0.000000 25.000000 5.497787
1
50.0
-100.000000 0.000000 25.000000 5.890486
1
50.0
-100.000000 100.000000 25.000000 0.000000
1
50.0
-100.000000 100.000000 25.000000 0.392699
1
50.0
-100.000000 100.000000 25.000000 0.785398
1
50.0
-100.000000 100.000000 25.000000 1.178097
1
50.0
-100.000000 100.000000 25.000000 1.570796
1
50.0
-100.000000 100.000000 25.000000 1.963495
1
50.0
-100.000000 100.000000 25.000000 2.356194
1
50.0
-100.000000 100.000000 25.000000 2.748894
1
50.0
-100.000000 100.000000 25.000000 3.141593
1
50.0
-100.000000 100.000000 25.000000 3.534292
1
50.0
-100.000000 100.000000 25.000000 3.926991
1
50.0
-100.000000 100.000000 25.000000 4.319690
1
50.0
-100.000000 100.000000 25.000000 4.712389
1
50.0
-100.000000 100.000000 25.000000 5.105088
1
50.0
-100.000000 100.000000 25.000000 5.497787
1
50.0
-100.000000 100.000000 25.000000 5.890486
1
50.0
0.000000 -100.000000 25.000000 0.000000
1
50.0
0.000000 -100.000000 25.000000 0.392699
1
50.0
0.000000 -100.000000 25.000000 0.785398
1
50.0
0.000000 -100.000000 25.000000 1.178097
1
50.0
0.000000 -100.000000 25.000000 1.570796
1
50.0
0.000000 -100.000000 25.000000 1.963495
1
50.0
0.000000 -100.000000 25.000000 2.356194
1
50.0
0.000000 -100.000000 25.000000 2.748894
1
50.0
0.000000 -100.000000 25.000000 3.141593
1
50.0
0.000000 -100.000000 25.000000 3.534292
1
50.0
0.000000 -100.000000 25.000000 3.926991
1
50.0
0.000000 -100.000000 25.000000 4.319690
1
50.0
0.000000 -100.000000 25.000000 4.712389
1
50.0
0.000000 -100.000000 25.000000 5.105088
1
50.0
0.000000 -100.000000 25.000000 5.497787
1
50.0
0.000000 -100.000000 25.000000 5.890486
1
50.0
0.000000 0.000000 25.000000 0.000000
1
50.0
0.000000 0.000000 25.000000 0.392699
1
50.0
0.000000 0.000000 25.000000 0.785398
1
50.0
0.000000 0.000000 25.000000 1.178097
1
50.0
0.000000 0.000000 25.000000 1.570796
1
50.0
0.000000 0.000000 25.000000 1.963495
1
50.0
0.000000 0.000000 25.000000 2.356194
1
50.0
0.000000 0.000000 25.000000 2.748894
1
50.0
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1
50.0
0.000000 0.000000 25.000000 3.534292
1
50.0
0.000000 0.000000 25.000000 3.926991
1
50.0
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1
50.0
0.000000 0.000000 25.000000 4.712389
1
50.0
0.000000 0.000000 25.000000 5.105088
1
50.0
0.000000 0.000000 25.000000 5.497787
1
50.0
0.000000 0.000000 25.000000 5.890486
1
50.0
0.000000 100.000000 25.000000 0.000000
1
50.0
0.000000 100.000000 25.000000 0.392699
1
50.0
0.000000 100.000000 25.000000 0.785398
1
50.0
0.000000 100.000000 25.000000 1.178097
1
50.0
0.000000 100.000000 25.000000 1.570796
1
50.0
0.000000 100.000000 25.000000 1.963495
1
50.0
0.000000 100.000000 25.000000 2.356194
1
50.0
0.000000 100.000000 25.000000 2.748894
1
50.0
0.000000 100.000000 25.000000 3.141593
1
50.0
0.000000 100.000000 25.000000 3.534292
1
50.0
0.000000 100.000000 25.000000 3.926991
1
50.0
0.000000 100.000000 25.000000 4.319690
1
50.0
0.000000 100.000000 25.000000 4.712389
1
50.0
0.000000 100.000000 25.000000 5.105088
1
50.0
0.000000 100.000000 25.000000 5.497787
1
50.0
0.000000 100.000000 25.000000 5.890486
1
50.0
100.000000 -100.000000 25.000000 0.000000
1
50.0
100.000000 -100.000000 25.000000 0.392699
1
50.0
100.000000 -100.000000 25.000000 0.785398
1
50.0
100.000000 -100.000000 25.000000 1.178097
1
50.0
100.000000 -100.000000 25.000000 1.570796
1
50.0
100.000000 -100.000000 25.000000 1.963495
1
50.0
100.000000 -100.000000 25.000000 2.356194
1
50.0
100.000000 -100.000000 25.000000 2.748894
1
50.0
100.000000 -100.000000 25.000000 3.141593
1
50.0
100.000000 -100.000000 25.000000 3.534292
1
50.0
100.000000 -100.000000 25.000000 3.926991
1
50.0
100.000000 -100.000000 25.000000 4.319690
1
50.0
100.000000 -100.000000 25.000000 4.712389
1
50.0
100.000000 -100.000000 25.000000 5.105088
1
50.0
100.000000 -100.000000 25.000000 5.497787
1
50.0
100.000000 -100.000000 25.000000 5.890486
1
50.0
100.000000 0.000000 25.000000 0.000000
1
50.0
100.000000 0.000000 25.000000 0.392699
1
50.0
100.000000 0.000000 25.000000 0.785398
1
50.0
100.000000 0.000000 25.000000 1.178097
1
50.0
100.000000 0.000000 25.000000 1.570796
1
50.0
100.000000 0.000000 25.000000 1.963495
1
50.0
100.000000 0.000000 25.000000 2.356194
1
50.0
100.000000 0.000000 25.000000 2.748894
1
50.0
100.000000 0.000000 25.000000 3.141593
1
50.0
100.000000 0.000000 25.000000 3.534292
1
50.0
100.000000 0.000000 25.000000 3.926991
1
50.0
100.000000 0.000000 25.000000 4.319690
1
50.0
100.000000 0.000000 25.000000 4.712389
1
50.0
100.000000 0.000000 25.000000 5.105088
1
50.0
100.000000 0.000000 25.000000 5.497787
1
50.0
100.000000 0.000000 25.000000 5.890486
1
50.0
100.000000 100.000000 25.000000 0.000000
1
50.0
100.000000 100.000000 25.000000 0.392699
1
50.0
100.000000 100.000000 25.000000 0.785398
1
50.0
100.000000 100.000000 25.000000 1.178097
1
50.0
100.000000 100.000000 25.000000 1.570796
1
50.0
100.000000 100.000000 25.000000 1.963495
1
50.0
100.000000 100.000000 25.000000 2.356194
1
50.0
100.000000 100.000000 25.000000 2.748894
1
50.0
100.000000 100.000000 25.000000 3.141593
1
50.0
100.000000 100.000000 25.000000 3.534292
1
50.0
100.000000 100.000000 25.000000 3.926991
1
50.0
100.000000 100.000000 25.000000 4.319690
1
50.0
100.000000 100.000000 25.000000 4.712389
1
50.0
100.000000 100.000000 25.000000 5.105088
1
50.0
100.000000 100.000000 25.000000 5.497787
1
50.0
100.000000 100.000000 25.000000 5.890486
1
74.562902
163.831206 78.465587 15.796903 3.728309
1
56.616694
-19.820880 -92.154476 6.034416 1.311602
1
96.648471
84.600067 51.829295 22.230120 5.693742
2
94.902959
132.039101 46.744919 25.755535 4.804393
-79.356185 166.179018 36.161305 5.036268
2
78.343465
178.314822 96.305342 24.493895 2.864982
-117.779907 -115.629014 10.730990 3.456707
2
59.676865
196.020508 168.866633 24.387815 5.604564
113.531564 -72.016567 4.373471 4.358629
3
51.105780
40.972128 159.354743 2.390980 5.917550
-102.891578 -82.975822 11.787129 5.241488
99.016215 -161.915329 20.219837 4.751798
3
86.481493
32.348369 175.825071 18.249142 5.301764
-93.252553 -132.130025 27.221519 5.635917
-80.955536 178.573830 41.672735 2.007243
3
78.392102
-198.103189 -178.549795 4.953200 1.488021
83.456853 120.664055 7.997931 1.179597
57.352868 -52.884761 34.696901 1.197631
4
88.168784
-156.910266 49.375834 24.719668 0.767341
-53.115179 125.031305 26.072171 4.115289
25.662489 -32.171220 16.791502 1.620718
-29.416696 -30.659601 35.986102 1.870705
4
73.738270
-191.627823 -194.817869 31.079253 1.020094
21.816790 -112.500018 4.777893 3.112658
-114.470004 26.569036 31.239052 6.081060
-83.949132 6.228038 27.754797 1.379379
4
74.874563
175.346286 -111.193274 1.371813 6.156762
-170.318736 -56.218461 22.494947 5.416417
67.134748 159.779882 1.563950 1.974125
65.170389 138.272450 26.590421 4.021693
5
56.408412
57.113324 -183.026651 21.639798 5.823139
-6.448872 56.260523 12.976859 0.603773
-181.155165 -121.036617 18.851902 4.462015
44.123580 -159.566611 1.174143 5.539021
-188.127646 -19.326146 21.732348 4.198602
5
74.444460
-70.806175 -163.146260 6.501701 2.843490
58.662291 27.445086 35.295492 5.970592
50.204859 49.197944 12.195476 4.411322
-61.254766 -131.286813 16.542366 5.712650
190.096291 58.216368 24.525661 4.878518
5
58.263506
-119.653077 51.696056 19.692974 5.239156
176.851733 -128.084566 20.518903 0.768107
171.687484 -44.554947 19.628289 2.421394
-109.806999 -149.335672 22.160938 1.215649
-10.318014 -69.537658 15.194672 1.503082
6
89.238452
-6.651715 -111.651015 32.910721 0.136815
-186.073377 118.922328 19.326142 5.770015
-176.906537 -128.440900 14.595537 1.278779
80.063158 -182.613500 25.608741 4.329688
124.236926 118.698770 24.529941 5.991518
-14.972420 -159.013246 1.000000 0.227099
6
86.687265
142.495665 -98.769451 18.598954 3.634267
-159.516194 -158.352935 8.295072 6.210784
35.650906 -83.429848 35.416253 5.759510
-95.681800 61.034678 1.897430 6.148776
-127.509394 94.178283 10.281467 2.609969
119.837902 -24.627647 18.423927 3.702548
6
62.888595
-114.413419 -33.063666 10.159059 1.192771
-139.653859 189.640837 11.304265 1.464247
12.231301 -112.080573 22.415745 1.430219
-41.879986 -2.976427 13.908406 6.260924
92.719400 176.253500 18.216968 0.612406
-79.519422 -0.377678 8.039301 2.414164
7
89.378637
-43.231391 39.849463 29.693787 4.381767
-132.186572 -158.079645 42.745336 1.929661
149.745188 114.661225 4.789523 1.704259
-147.444333 133.144441 28.087251 3.862428
82.922573 193.564337 32.904692 5.498259
50.761983 23.992064 38.317985 3.801904
11.270623 -55.012052 9.736769 5.466927
7
85.605501
-52.608407 -99.041840 22.888816 3.209660
157.282701 -43.310903 34.029888 0.221344
-91.551764 61.387684 14.000558 0.114086
-79.688773 8.872639 38.742109 4.786839
180.222065 -156.677733 38.483833 6.021983
-147.217100 169.319029 30.093079 4.487708
-73.333644 129.292569 2.652947 3.275703
8
64.921490
-88.082880 -161.410032 10.522355 3.754327
138.389267 25.657848 10.344294 3.163445
-190.040782 -170.318805 18.245659 3.304199
16.505223 82.407213 13.059284 4.192431
-165.176946 129.464402 20.237778 1.358309
89.286262 15.068724 14.990342 0.023159
-76.075907 -108.369945 17.367081 5.904397
95.838210 -129.673423 8.524169 0.036196
8
73.593808
28.680356 153.284016 15.380627 1.570680
116.884211 -117.241550 1.408396 2.315270
76.409163 -167.035974 21.133386 3.905637
-69.757183 -29.824897 34.541281 5.600979
-139.813392 -97.262726 7.434090 0.315345
59.231532 92.531082 8.651697 4.217214
-155.279937 121.886269 24.521773 3.265251
-96.387862 -24.063624 10.342300 1.144689
0
]]></test_input>
<test_output><![CDATA[7
6
6
6
7
8
10
12
15
16
17
16
15
12
10
8
4
4
5
6
7
9
10
12
12
12
10
9
7
6
5
4
7
8
10
12
15
16
17
16
15
12
10
8
7
6
6
6
7
6
5
4
4
4
5
6
7
9
10
12
12
12
10
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
9
10
12
12
12
10
9
7
6
5
4
4
4
5
6
15
12
10
8
7
6
6
6
7
8
10
12
15
16
17
16
12
12
10
9
7
6
5
4
4
4
5
6
7
9
10
12
15
16
17
16
15
12
10
8
7
6
6
6
7
8
10
12
12
16
6
7
20
34
72
28
55
8
25
157
147
30
21
161
60
34
43
58
68
118
]]></test_output>
<hint><![CDATA[Q: Should 2.5000000000 be rounded to 3? 
A: We have constructed the test cases such that it does not matter. ]]></hint>
<source><![CDATA[]]></source>
<solution language="C++"><![CDATA[#include "iostream"
#include "math.h"
#include "algorithm"
using namespace std;

double v,minimum;
double a[8][4]={0};
int n,record[8];

double compute (double guidx,double guidy,double kidx,double kidy,double vx,double vy)
{
    double a,b,c;
    c = ( guidx - kidx )*( guidx - kidx ) + ( guidy - kidy )*( guidy - kidy );
    b = 2*( ( kidx - guidx  )*vx + (  kidy - guidy  )*vy ) ;
    a = vx*vx + vy*vy -v*v;
    return (-b-sqrt(b*b-4*a*c))/(2*a) ;
    
}

int main ()
{
    int i;
    double tempx,tempy;
    double guidx,guidy;
    double max,time;
    double addtime,kidtime;
    double k1,k2;
    //double minimum;
    
    //int m;
    //freopen("in.txt","r",stdin);
    
    for(;scanf("%d",&n)!=EOF && n;)
    {
        scanf("%lf",&v);
        for(i=0;i<n;i++)
            scanf("%lf %lf %lf %lf",&a[i][0],&a[i][1],&a[i][2],&a[i][3]);
        
        //memset(record,0,sizeof(record));
        for(i=0;i<n;i++)
            record[i] = i;
        
        minimum=0xFFFFFFF;
        
        do
        {
            max=0;
            guidx=0;
            guidy=0;
            time=0;
            kidtime = 0;
            for(i=0;i<n;i++)
            {
                k1=sin(a[ record[i] ][3]);
                k2=cos(a[ record[i] ][3]);
                tempy=k1*a[ record[i] ][2]*time+a[ record[i] ][1];
                tempx=k2*a[ record[i] ][2]*time+a[ record[i] ][0];
                
                addtime = compute(guidx,guidy,tempx,tempy,k2*a[ record[i] ][2],k1*a[ record[i] ][2]);
                guidx = tempx + addtime*k2*a[ record[i] ][2];
                guidy = tempy + addtime*k1*a[ record[i] ][2];
                time += addtime;
                if(time + sqrt(guidx*guidx + guidy*guidy)/a[ record[i] ][2] > kidtime )
                    kidtime = time + sqrt(guidx*guidx + guidy*guidy)/a[ record[i] ][2];				 
            }
            if(kidtime < minimum)
                minimum =kidtime;
        }while( next_permutation( record , record+n ) );
        //next_permutation
        
        printf("%.0lf\n",minimum);
    }
    return 1;
}
]]></solution>
</item>
<item>
<title><![CDATA[Card Trick]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[64]]></memory_limit>

<img><src><![CDATA[http://10.21.11.56:80/JudgeOnline/admin/../Image/1018/1.png]]></src><base64><![CDATA[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]]></base64></img><description><![CDATA[<img src="http://10.21.11.56:80/JudgeOnline/admin/../Image/1018/1.png" align="right">
The magician shuffles a small pack of cards, holds it face down and performs the following procedure: 
<ul>
<li>The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades. 
<li>Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades. 
<li>Three cards are moved one at a time… 
<li>This goes on until the nth and last card turns out to be the n of Spades. 
</ul>
This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 13. 
</img>]]></description>
<input><![CDATA[On the first line of the input is a single positive integer, telling the number of test cases to follow. Each case consists of one line containing the integer n.]]></input> 
<output><![CDATA[For each test case, output a line with the correct permutation of the values 1 to n, space separated. The first number showing the top card of the pack, etc… ]]></output>
<sample_input><![CDATA[2
4
5]]></sample_input>
<sample_output><![CDATA[2 1 4 3
3 1 4 5 2]]></sample_output>
<test_input><![CDATA[13
1
7
2
12
6
10
3
8
11
13
4
5
9
]]></test_input>
<test_output><![CDATA[1
5 1 3 4 2 6 7
2 1
7 1 4 9 2 11 10 8 3 6 5 12
4 1 6 3 2 5
9 1 8 5 2 4 7 6 3 10
3 1 2
3 1 7 5 2 6 8 4
5 1 6 4 2 10 11 7 3 8 9
4 1 13 11 2 10 6 7 3 5 12 9 8
2 1 4 3
3 1 4 5 2
7 1 8 6 2 9 4 5 3
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[#include<stdio.h>
void main()
{
	int n,m;
	scanf("%d",&m);
	while(m--)
	{scanf("%d",&n);
if(n==1)printf("1\n");
if(n==2)printf("2 1\n");
if(n==3)printf("3 1 2\n");
if(n==4)printf("2 1 4 3\n");
if(n==5)printf("3 1 4 5 2\n");
if(n==6)printf("4 1 6 3 2 5\n");
if(n==7)printf("5 1 3 4 2 6 7\n");
if(n==8)printf("3 1 7 5 2 6 8 4\n");
if(n==9)printf("7 1 8 6 2 9 4 5 3\n");
if(n==10)printf("9 1 8 5 2 4 7 6 3 10\n");
if(n==11)printf("5 1 6 4 2 10 11 7 3 8 9\n");
if(n==12)printf("7 1 4 9 2 11 10 8 3 6 5 12\n");
if(n==13)printf("4 1 13 11 2 10 6 7 3 5 12 9 8\n");
}
}

]]></solution>
</item>
<item>
<title><![CDATA[Necklace Decomposition]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[64]]></memory_limit>

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fKVjqzXHcc6XYrWZ06aGk+kDlSt7HYPfWOLwtytWf4S99yESUpWVJEpJyNu2mJbdGhBxvydYTvC5FWqSmXYrSgE+mkgANtcaGFgg2JNjsUq67TJmJCQkLfo0DA9UDjlN5U7Ne9hm2G5Eqly5oZSkggBJ1AepfTSB5dOKr0ucFNgta5aCXyEBSX6jpEWRZDlKxeLluCYuauRMtElQMkEOM77PExiwniC77wly7VJtqJCFSnCyNTu64rffeIrxvhaVXja1zin1UmgT2CkatjvW22MEWS12iQFaiXMKX7omjS7uDbwTeV1zJqVlYROKHPAJ+uPagR80u0TbTydXgufMXMX8bzQVLLn8VKguRzvbc6ADnlHKMLl/8Lcbw8j2tFfJ1E69FhpV+Nf9Y90H/nnkgYVZv/N66fmYrxMWxDage/g0ejC/4jN7OgjOCdd0HnkYtNml4asiEFIUVHM2pOYvAEs6SpbbYNHIvhC9Cj4bawqVYpyXloKmJVRlNsp2+BjGVv8AF1B4+MJ1hsUyZaglEvIyE/pborTyrzpVpxhalycrgICyK9Jh5eyC/wApVmxTY8Ny5thNntMuUCVFKCFp4toe/sMV5tylTJi5k5alKUSSo6qfb5mNYSMNGYzMogJ29TV8B4xrTEkElhmHh7nyjamJeY7kkKqPHzYdkYlEnMg5RQajQ6fWY66GqQBsdvLf3P3wwSNruKn38IyrYjMxY68PcAd8RNVZaEg67z958BE0qCZbnoqBLsG21b64hQhx6vv7B4xnKUuQFDKKZuGnkCYgtFSdc2gG3h5CJxGIvU1hAcadcZFh9Kbq7vvPdECkMSFOGPBozpSCq8d0TRML6mMYQTQN7/bCygeUS4joLoxTe13SfQ2W8JyJQ0QTmSOoF2ghck+OLTabwmWG9bapZmdKVnOpcuBx0pwgPBW3ZGaVOVLUCkkKBox2xnQuPYr0lWexS53w1Bo3ogag745O77bh2+sSW+9LJJTNt0g+hVNUqhLD1R1DXrivy8X33Nshs8y87SqUQxBXUjidYy4SxVasPXgZ8kZ0LDTJbtmHDcfria0aWvu2fYvgZl2iRmSUHMSKGkcHhuwyLhXe8pNnTKkTbaZlnmFmKMqejTQAho4y8uW2ZNuaXZbJZpmdCSE+kyhIfqqfCBvPxDeU20iebdaCtK1LS0wsgkuWGx4Jpaq33zLu+61zjeEpYVLcgKDSxxitFqxVbbFftttV0WlUmVPtC5gSzpYqJFDwjz7xxJe15SBJtlumzZZ/N0ALbwNY8pQUo8H9/IxriT4epfmJbzvpQN42tc0CoTokdgjzEWiZKWFy1qQoaEEgiIM/S2bRu9xDlDuRVvfzMXibSnWqbPVmmzFrUfylFzGMKGpMIpD7G3vrs+sw5IoQCRq3D7h4xeJs1WqWiJSXIcbu2JqIqWFGJbbtPsiJJJD1O5/faY1xhtAp3aHT37DEeMZQkF2JbQb208gYbMSyjqKsO8+yJxFoOaAG5NLfVz8bTH4fMyaQYoDvNAATya3gBsvea/X6GTBijz5dtzpXnnqmmFRv+GfuYrucxpFieem3/dXf+GfuPsiuiyw1cR1x+qXtv3EJRvOzfCGEozU+kf8ARcP4RazCNoSTLTJAJCWSnY8VGkLKVPugq8nnKMbtlSJVsUtM2SwRNFQoDR+MZt0WbWKvS8VKw/MFolgGYWA3RVHEiZSb1tqZAHohPWEBOxOangw7YsXafjTEVyhFntFnspnJzhawolJI3MKwIcY8mN+XDIVbBktchIzKXKfMniQdnU8awrFDtasytWIrXQnTsq/dGHL0WSro7epu3YD3xs2mWQADQir6e9Ae+NWcpWZymii4pq9fNhHbYYpCVKBS5IcBu0+LDsiNCh3IQksCdtdv/wCRieZ6gkqSGT17+pyTDKYApNUlOv38AO+KIJIWMlA50fZQt3BIiSnQXXSYlWp69nafAxHpOkFlKdi/Au3fTsjIWyhlAud+3QaccxgMRCUmvq0HBj9j98RUkZARQkHMB1v7R3RmXLAbpoYgqYapH6LUYsAO2MUxJSWrQszflfeT3RLFQUhQoSw0c9o+uFNQtaioksdpfdEiqpbQ6EjT3Dw4USapZtQNG1ZuqkTQwFDa7/f2Qi413s8bDkTHWAS5cHf958IZCUZtCxcCrHd9sZ4jCDSJAK1rEsrKCikbyDs96CHScpO8UBPvveJxEkgEkOW3xJCXSVagM/n9QhJDnKkjKBt3fWwiTgywqoU5du/TtAjUiEgH8kEnSm+ntMJSHoBlALP4fWYSQoo1IanbsbvjZslnXaJ8uRJQpZWrKhCXJdVGHYIfA1yk6kBgxIHj7IbLRqsmtffeYKtzcid7W+woXMttnkz1JzCUUlTPWpEcfivBt7Yatq7PelkXLIJKZgDoXscKbj5PE3BzolqzFKSTxNSNR5ZjECkqqoEJI019zlEeoi4bwmWf4RKsVrVZ2f0olqKQNNWaNJUtSSyqAioI7W7gI1KNZhlJLAbQ7nefFhDTEmXtP1+5fujOFMQtYO0s/b5kRFUt0pS7t0W3e5UYoxsHzMwbqcNQ9whlJc5zmrXg+v1CMyZKso/IOgD6A08h4wykLZ2OpLbH1PshRZrmhN/Jrbwku17TAf2MmDBAh5owCeTe8EjZe0wE7/mpMF6PJn9q6TpXjnrj/wAKf75+4iuh0ixnPWAKcKv/AJ5+5iu8xDGlTxL+9Y64z/KXtGXrrTjHacllhlW3E1mE9lIlvMynaRp4tHFhTUAaPcwhfCrmvqRbGJSgstI2pNDEvwLa4fnIFJjCXLGrR0k9Vltt2LAAIAoYG+CMT3daZaJypgm2daWdB968I6xV7WSbJXKu8machUUAF24AVjN1tn5Vw5U7ns91Yut1nsqMslXTlpGgdILdVWHZHHTQBTMFEHYNd3iSeyCriTCGIMY31aL3sliVJss0gSDPVkKkpAYsa1NdI4PEWHbwuK1fBrxs65ExixZwpLNQhwRqY741HhEIVUgJzGim0GnkCe0REpKkKUHSoPm4HcG45RGRSAgkAAP0uzVvIdsYykE5hUDbq6t/eSeysaEsqkkswVoFCjnThxPYISCjMlDMFAng27+r5xjyFScocacWH/S57YQJUjNMJdNFA67z/wDqI1sSKnDqBOpIJ26kd7DshE5UHRRHRbY+g061HsiKlEFKixY1faQX/tHw4Rj9I9Aeifu+sxBlKBl6SgEturvp2Ad8JIKySpKiR0iAWdte8kV4Q6J6VS5mZKek9NwcH6hEUlSXIqoENw7/APGI7oByGUnJQ0AJG3R+/MYRyksrKjduYjq3ecJJQDlUKMPVOg0fjTMe2Igt+SQTqW0BDnwaIEoFKKMVakPt395HdEghSXAZNAxOxtvmYYuymLuKuKA/efCMiEPmAUUIcFxs19gPfARBC6UAZy40DP5ADvaJpBck1fUP7/lHwiUoOrNR9Snx82jYRZZqJYV6NYlfpNR/vjNo6HB+Ab2xMM9jQiVZw4TOmuASHDBg5jqMOcn194bxhZp152IfBZeZRnpWCgDKWNWNG3QS8AS/g10XeLFJCpSpY9GkaGlPCJctF6yZmBbbZ7WhMuYhDhtUqcMO+Odyo9+5Zk+UFrsy5RCQCVKNAmPNvq/rPeWJpF1GZKmS51lmzLTLocyOiAG4kn+rFerPyiX/AGOy/BkW0rQAyTMSFEdu3tjzrpxZbrDiIXtMnLnTiWXmV6yd3DhuYRn4WRa24JtiShp0oMoslADhtID3LRgtEzG9nTh+yv8AGSFK9EgMyknpK4UI8d8bt0cs91We7VyvnCtTKZUp1jqOnjGfDHKfZr/vfJ8CRIny0EInKIKyg6gFqbCR9UWfF+DVcweRS/1XcZ8idZ505IzGUkkdgJHVujjrqwrbbffZuoS1S5yFlMzMPxbUL+MWjuW8ptkusWxcyV6BZLkl1EwPbfiLDF341tdsNrSi8LUlMpcsp6KWDu7MDoNY1yv9RLD/ACL3DbLOZU6baFTAKzRM0PlHJ31yM3pYb/MmRNlzbIJoHpX6aU1LlPhTwgq2S9LtsF3rnT7cPS5QtCJSnSxrU7IGGIOVQDG8m0SJyl2OTKMpZSSQpRL5uLUHfE5WLJsauRjDtlwzhWfYrEta0rtapqypTnMUIB/siO0jjORu9rPfWFp9qss1E1HwtSSUF2ORBbxjs445dtzpXrnpljhT/fP3EV1UaM9DuixfPSAUnCoJZ/hbdfzMVzUkg0Hv7tHbH6xL2i7PGWUogisYwNBt4xJAbhCw29a7rxtNkL2a0TpJOvo1lL90dzyXXpb7Tiyz+kvC1ZZacy3mqLilNd5HdA4Qttv2R6uG74mXNesq2SxmyFlJdswOsZshFu7jvCTLkomzxnUsskAOBHM8vF2WG9MMWiYEJRMkI9MFMHDVLdYcRz2DeVS65NiImzbOoKrlnKyKQfKPUtN4yOUezWq7LFOMmQE/OWtCMwBJBy7HcDZEl1ds2VXeelywU4Famh2+bd0amXKUpaho/g/mYMWIeRC2y7vXarqtXwhSA/o1py5tur69cCe22SZZbRMkzULQtBKSkhikileoAx2mWxqkgyukFBNW8H8BCzq9JmUA4NWrxbtJAhLoAVEU+8+wRjUFioBJJ1J2/eY3tE5lSCkAOyQ54MD3uYxkJyqdSR0aAVp90SGoSXqwA3e4c9oiLpNWbeN2/wBghVI5kF6ZtWNWNDp1kDsh5aiJfRoojb/VHiSYSEZWI6RIPRNa/wDVDAFKuh2HbuH190OhN05ixoRlBOoBp5P3xIFQOnWAeo/UOyJS5YWoZUUJ9UDfupuYdsEfDnI5fN5WJE+bOlWZa+kmWpJUrt2DxjNyA6lys2VLEVZ/Dv1MdFd+B8Q3hZE2mz3ZaJktnAIAp1GugEdxhvkmvC6r9kTr5m2ZKZU05JQUSpZAoagU29kGLD9pRZXezKWUnKAkUT1xm5oAfJXhNN4YlmpvezqHwEArkzEkdIks4PbTqiwt2WG61WP4PaZMpSFpymWUgho47lBxJceHL7mXsoFFptMoSfRyh+MykVPU8aCuVy4JNztLnhczVkS1ZzwqGjnd2r/Hj8omM7ZgrEIu67JUkWNMpK5KUukpDkNSmzdAxxhja8sSHJa5mSSFZhLSTU7ydpjHjLEE7El8TbfaE5c4ZMvXIgVA7q9sc9N1c+tx3/efCN8SMa1knfGPNth1BiyS+x4gQWoKQ4qyJmMIz2S2zrJaETrPMVLmILpUk1EaZBo2u2JAFPHZE0OvXyi38uxfBxakpDeslAB+qOanWuZNmFcxalqUXKiXJMa1Uh4Zw3v774cTba+GzSjIZi8v6JUWjEqaSXjFSGL5aCHEWo5oKs3JreH+l5n/ACZMGGA3zPCDyZ3g3/u8z/kyYMkccu2or1z0wGwq4p+GOW0/En2RXtCXIy69e3j2kd0WG56JA/7Kkh2+Fv1fMfZFewnMoJzhtMxr297nsj0fj+sZvbGoVLAN717niLjY4Hv9kTysHBLbuH3ecMpJAdQOZttPevlFsDA1d6RNCoSUApGw+fvWGLCvhGLibbEiaxFYOfIjbJSMPoCVMpU1RmNvf6mgCBTdcdFg/FVrw9aCqT05SvWlks53g7DGWlwbPeEyXZ5kudIEuXlYHfFZ+V6zyp+NLUbEjOVJSZoQHZTV8AI9uzcrl42+1WOQiUtZK0oAnTAU1LbqwXMNWOwNlk2eRJM0+knKloCcxO2EumdKozZK5anIZTuQRt++MBScrJBcaF6bn8zFnuWXAF1Xhhqfed3yZaLbIQVhaBVeWrHft7YCeGeT29sSIM6ySkSpBoJ04kBWygAc0HVHSZbiOMKSliSK1d+H1REHQhKXHjt8yB2R2WL+Tq+sMSRaLbJlzLOT+NlElI63DjdHh3RcN4Xtafg932WZOmAOctAOJOgr5RrY8oIKMyUPSoOr1bzjYsVim2qYJFmlTJ6iaIlpKj2AcPOPdvrA993FIFot1jWmS/4xJCgOttIMPJHh6x3dhyyWgyUm0WxAWtZFWNR3BqRLkBPg+6Z9lxZd8q87HPs+aY4E6WUuQCRqN+WLJ3Eu0SppTIkhakgFKToE74y31Z7pnXFMWlIROljorCagtAHPKzfFhK5JlgzUgyytEwpB7I5XdHc8v2J0yJdgtFlUlFts08GWsdRzDqjl7s5a1WWwzULkT0zpoaYEZSlR4E1EDXEeILdf1s9Pbpj7EpFEoHAR5Oh3k+/tjUxHv4vxNasSXj8InjIhIyypYLhIJ37TxjxUrcesxOnv1PEAshYAcF6P3PXtiK1DpNv0OwfcI6THQmZpJcmu1g/E+yMZ4OSPP7z4QxUQCTscs/f4kQySW1BcUffo/eTFRFQ1CKg0G/cPbEQNBUEjw+6MqciyA2VLgA9bN4AxFkpaqRSrjfUjuYRdCLMDm02se0+yFkZmDkez7TEkqKSxBO1THXafGIEsvokkij8fviaU7EEgGoLAjbsHi8JSU6kuTu9+uFUbCd3kPaYiWJOU0J04fd5wDgDUlt48T4Q1Qwau3364mOJKRwPafBoiQRtGYHbw+0w0LScz5v5NLxA2XvNGn+RkwY4DnM+/va3iN18TQ7a/MyYMceXP7VudK989EkHCrO/4Yzf7FvGK9EpWHAWAe2mnk5iwvPQzPhRv88/c/bFegspAKkhnqG2e4HfHo/H9Yze0qspVD/ig9VPIQ/SSpiHW+vFz7XMJJBdSWCgdeO/v8oYJI9RSikDXcPueNoZVTqz7xs+7ziCnOortjLMXnUklKQBsT3/VGPa2p0qffaYzYIh4mgsYiWCd43+/bEcz9Uc7Gno3ZbV2S1yp8s1lrCwOILxYnAeLbvt9mlzSvNIUGWB6yOBG8RWdKyI2rJbZ1mXmkTly1fpIUQfCMlWbxZi2wrs8y6ZVvk2VNolqQhc9QDAhiY9fDtrlCTZpNlRLEmTKCUS0aFhSKozbbOnLK5sxa1HVSlOY7/AnKcu5ZMmTbUzD6ENLmy2JbcQfOM3skkiwuKbbZbbh2dZrxs8vItCnQdzRx2BrNcdku2XNuCU0i0zCrNMqpn0rWmkDLHfKrOvuRMk2L0iPSgiZNmMCx2ADTrjycDY8XcSRZrSFrs4OZCk1KOzaI1E18LM2+03dbLjn2S8LIBJKSg+kSK74HKMS3RhcWO6pt4ypglpJSCpsktzlSTvald0cjjHlfXeNlCLIVLmBOVJKAhKeLbTAvtE+dPnLmzlKUpRKlE7S9fExZj4n/Rw5QeVO712MyrnMtUwhkIlnMH0dR29UA2dN9JMJJ1q/vwhpiyDl9ZqAvrs+uMaygl3IBNHGz7vOOsxTpJXRZ6g1Yd59kQ9XUOoN1+7nwh1HKHoTuam8+LCMYWqWuoBIqXrX7zGhMAAZVKZTM57n84ZYZl1CVmtdAfsHjDsR0QVOfVfuBftJh1oDZnfaRuBr5N3xdDEHy5R6xLkjf958BEVAgkJLgUB8H84ktCsxY5let26nxIERKFJD7RR9m4V/rd0QIKzAIfKHd9zsK9g8TEgxzEvWreJ9ghgoKNfVBZxq2nkDDoKVVNNSa6vU+DCAdRLlxnIbSumviYgoM4RQins83iQJSSdSKlxuqa9ZhLYdA6gZW3tSnaTDsQFCAg68OweDw6VhwFIoRq2/7BDKyun0ZY8O7yDxHOSSaVYFn99B4wVNSwUa6gk+Z9ghKWpLhQ03UqP/AOjDZ0GigSrU9ep9giKRlByqHc+n2nwgLTcz7L/JnbwnZe0wHr9DJgxwHOZ638md4ANS95gJG35mTBjjyZ/atzpXvnpMBhYkt/PAP+A/g/fFenIJ0Wrq2v8AW0W35wXJlfPKKbk+JLTd8j4AZ/pfhkxacwWZbZcqFP6h1bWBYebJjEAZbyw87V/CJ38LfHbDKTFmz5BslKwMrivXw+sw4yEnpFtm0e7CDF8mPGey88Ogafzid1fRbnh082PGLpz3lh6inLWidp+y4Rrnj6aoPJJSDlLtVuP3nwiDpWlKRUtUv77XPdBjTzZMZpSP7p4dcGv4ROY/8LfD/Jkxkdbyw6BownztGb6Lrhzx9NUGSnMCUkNv4fcIiAS5g0HmyYyJ/pPD3/yJ38LdCHNkxm7m88Ou/wDhE7+FGd4+mqDCQwh3p4wZhzY8Yn1ryw9o1LRO/hdcI82TGJJPxlh7h+ETv4US3H0+Qacw6VMWdoMiebJjJg954ecN+fnb/wBVC+THjIFxeeHjTbaJ2v7KJ/n1fkHSTDo14cIMQ5smMdt5Yf8A/kTv4XXEk82bGICnvLDzk6CfOZn/AFXVFnH1PkHkkP0i3v8AdGTMQXYEj9H33nwguo5s+Mk/+pYecV/nE7+FvhDmz4yApeeHwrYfTztgp+ajcyxn9NUIXcM+Ysz+Hk5hJUks9ARXhtPgIL45tGMWV/dLDwdLUnzmB0+i3PDfJnxk/wDSWHgOFonb/wBVuYReePqaoPGjfpPUdVfMjuhAqlksHUO3b9flBh+TPjLK3xnh7Z+fna1P0WjwhzaMZgBrzw+SN9onNp+q3vDnj6aoPImJAIJLigPYw9ph+iUij5q02D7h4wX/AJM2Mek15YeDhh+ETtzfRdcS+TPjAKJ+MsPnYHnzqBx/ktwaL+zH01QhKys5igLVtADsdT2uREVhKWQjMnjsJFH780GIc2zGYSALyw89C/p53X9FvaIHm0401+M8OuAw/CJ1C36riYX8mPqaoO5T6oIyksG1D08g/bCSQlgoZRt7anTgAIMKubLjAkteWH2YgD086mwfmtzxIc2jGLFKryw8Uk/4RO3/AKrgInPH1dUHCopS5qRq28V8yITqAyjpEBg3d5kwYU82bGOXpXlh7NwnzuJP5re0MObLjJKAE3nh52qTaJ2rfqt8Xnj6aoPZUKUnJozOrj9gJiBQTUsATWvb5NBl+TLjAOBeeHwKik+bwH0W4Q3yZcZmhvPDzEv/ADidv/VROePpqgytwVkkhW1u/wA2hnKfUJfa3D7TBm+TJjMkPeeHqEGk+d1n81vhk82LGQKXvLDtGcCfO/hQ54+mqIXM8yjkyvAJ2XvMBrqfQyYMkcDyDYEvHk9wfabpvefY50+dbl2kKsq1KTlMuWmpUlJd0HZujvo82fzlW50UKFCjKlChQoBQoUKAUKFCgFChQoBQoUKAUKFCgFChQoBQoUKAUKFCgFChQoBQoUKAUKFCgFChQoBQoUKAUKFCgBNzUb5vO/OTq22m+rxtt4z03pMlpm2ueqaoJ9FKOUFRJZyS3EwWYDXM4/vYW/8A0vM/5MmDLFvY/9k=]]></base64></img><description><![CDATA[<img src="http://10.21.11.56:80/JudgeOnline/admin/../Image/1019/1.jpg" align="right">
The set of cyclic rotations of a string are the strings obtained by embedding the string clockwise on a ring, with the first character following on the last, starting at any character position and moving clockwise on the ring until the character preceeding the starting character is reached. A string is a necklace if it is the lexicographically smallest among all its cyclic rotations. For instance, for the string 01011 the cyclic rotations are (10110,01101,11010,10101,01011), and furthermore 01011 is the smallest string and hence, a necklace. 
Any string S can be written in a unique way as a concatenation S = T1T2 . . . Tk of necklaces Ti such that Ti+1 < Ti for all i = 1, . . . , k - 1, and TiTi+1 is not a necklace for any i = 1, . . . , k - 1. This representation is called the necklace decomposition of the string S, and your task is to find it. 
The relation < on two strings is the lexicographical order and has the usual interpretation: A < B if A is a proper prefix of B or if A is equal to B in the first j - 1 positions but smaller in the jth position for some j. For instance, 001 < 0010 and 1101011 < 1101100. 
</img>]]></description>
<input><![CDATA[On the first line of the input is a single positive integer n, telling the number of test scenarios to follow. Each scenario consists of one line containing a non-empty string of zeros and ones of length at most 100. ]]></input> 
<output><![CDATA[For each scenario, output one line containing the necklace decomposition of the string. The necklaces should be written as '(' necklace ')'. ]]></output>
<sample_input><![CDATA[5
0
0101
0001
0010
11101111011]]></sample_input>
<sample_output><![CDATA[(0)
(0101)
(0001)
(001)(0)
(111)(01111)(011)]]></sample_output>
<test_input><![CDATA[226
10000000101011001010010000000111010000010100110000111110100110010000111000000110000011000001110010
000100001110101001000101101001011101111010111011101111101000
11000011110101010010101111101010111000111011011001000010001111
11111100011100110111011111101100001110010001111010000100111000110000101011010001000101001
1011011011001010011101000001000100011111001000011100100000001111110010100001001010110
101100101110110000100000100110000001110001101100101
1100111001100001111001010110011111010111111010100011111011111
01001100110010111101110101100111010110001100101111110001101
011010111010111111111100010101010000010111011111011011101010010011110101101
110000110000000010110011011111000111100000111101110011010110111000001100000111110010001
00000000100111110010100000110101101000110010111110000011101010000100111001001010011
1100101011010010111011110100010111011000110110001010011101011110000101001101100010111
01111011111001100101011100010001111110110101110101000100100100001111101110100100010011111
01001010001110010011110111111011011111110111100000101001100101000001011100011001001
10010101100100001100110111001111111010000000111011
011100010000000111010010110010000111001101110100011011010010011111001
0111011010001100001011000010010101000100101111101100111001100111110011100010010
1111111001000100111101001000111010111100010101100101000100111111000101110101111110010
011100100010110101001100110011000101101101111011011111001010
1001111001101001000001100110001101110000101001000100101001101111
1010001110011011010110111001100101100110110100001010001101010010111100
00000010001100001001110111110001110010100011010010010101110100111110
101000101000111111100010001001001001001100100011110010000111101011111001110100010
001101110111011101010100100110011100100000001111000001101001111010111000000010001010100010
00101110010111001011111011111111011111001011110111110110000101011110110101010100010010110101111
010110000110111111000000100011100010010111110101110100001001001111000
10110101111110000011000000011101000000100111100000110001111000001100011011100001
10000100110000000100011000001000001001001001100110010010010100110110010101100
1001000100100100101001101100101000011100111011101111010111100001110101001111111100000000011
10000100110001111010101010000010100011110010001100100010011111111
11110011010000100010011101001001111110101100001101010110110101010111
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0
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]]></test_input>
<test_output><![CDATA[(1)(000000010101100101001000000011101000001010011000011111010011001000011100000011000001100000111001)(0)
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(00100111110010101011011010101111111110111111011)(001)(0001001101111000110001110101100111011)(0)
(11)(00101011010111001011011001110011011111011)(0001001011101111101)(0001001000110001110110100111)(00)
(00111)(0001011110111)(00010110101)(000101)(00000110010101001011110000111111011)
(0111)(0011111011)(000111)(000010001110111010111001111010111)(0000011)(0)
(011)(0101111011)(00010100100011011111110011011)(0000001010101001001101000011010001)
(00111)(0011)(000110101001011111)(000100011)(0000010001101111101000011111110101011111)
(1)(01)(00101111011011010101)(0000000001000001010101011101011010111100001000011101)(000)
(1)(01111)(01)(0001001101111111101001100110100011110010110010111110110100101111110011011111)(00)
(01)(00010111001000111101101101110011)(0000111101110001101000111111)(00000100011001110110100011001011011)(0)
(00001110110111100011011111)(00001001100101000010111111001110011010010100011111101)(000)
(1)(000001010010101111001100111101)(000000000101000010110010101110111)
(011111011111111)(01)(00010001111101011111)(0000001100011101001111000101)(00000000111011111)(0)
(11)(00010111101111011101001)(00010110111)(00000010111110111010000011)(00000010010101)
(010111)(01)(001101010101010111111)(001011)(00000100110101101101101)(000)
(1)(01)(000011110111110111010010101101101101)(000010101101111111100101)
(11)(0111)(0101)(000011)(00000110001001101010100010101001011100001000101010011111011)(000001)(00)
(111)(000000011011111110100110100111101100100100101011101100001010101100100001101010001)
(0011101101)(0011)(001)(000000010001001010111101001000011111)
(1111)(00010110010111111)(0001001101010101000110111)(00001)
(1)(001111)(000111011100110101)(000011111)(000001011010111110010111110111101111000010101010100100011111)(0)
(0001011101111111011101100110011)(0000111000100101110111101010011001111)(0000100011110001100111111)(0)
(01)(0001100101101)(00001011001010001100010010111001111)(0000001110100111)(0000001101011110111)
(1)(011)(0001101010100101001011010011001011001101011)(000000111101111)
(1)(0001110101101001001011)(000010011)(000001001010111000010101101101101110100001100000101000111)
(11)(01)(000110111011001011111001)(0001010010100011101101101111110001011)(0001)(00001111110111)(00)
(1)(00101)(0001010011010101010110011111101101)(00001000101)(000000111100111000100101000011001101)(000000)
(010111010111)(000101111001)(0001001110111)(00000110101011010011011101010010011110011010000100011101011)(00)
(1111)(00001110011011001110010110110111010101100010011)(000000)
(1)(01010101)(001110101110111010100111011)(0000111010110010010011100011001011101)
(0101111101111111111)(00010100101)(00001110010001101010010111100110100100111001101001101)(00)
(1)(00001011001001110011001010001011100111100011101011101)(0000010001)
(01)(00010101)(00001010001111101)(00000000101100011001111001101000101010101111110100111)
(01011111)(00110011)(000111010111011111010010111111110111)(00001011000110111100011000101110010011110101)
(011)(000000101111010100011010101101100011011010010001011101000010110011111)(0)
(001)(000000101101100010101010011010100011110011001001011111001)
(00000011011010110111000101011111000111111111010001010111111010010110101001111100000100011)
(011)(001)(000111110101)(000000101010110110000111111111000111101010101001111011)
(1)(0101011111111011)(0101)(0000010111100010010101100110010111011010001010001001)(0000001100101100000111101)(0)
(0111111)(0010100111)(00000111110101110101010111001001101010010111)
(1111)(00000111110100010110100111011101000011101000110010110110110100010001101)(0000011111)
(001101101)(00011111010101111100101101110111110111)(00011110100101110101101110111011101011)(000011)
(11)(01)(0001001001)(00001100110010100111)(000010110011001011011111)(000001)
(010111)(00101)(000111111101100110100110111100100111011101)(00001110111)
(11)(0000101)(000000010110100010000010010110011110111)(00)
(0001110010110010100110111010111010011)(000001011100010001111000010110000111011)(0)
(0001001)(000000010111001111101000001110001010101001000000011)(000)
(11)(00111011)(0010101)(00000101110101010011111111)(000000110011010010000011100110111101111)
(1)(0101)(001011101011)(001001010101011)(0001010110011110100111)(00001)(00)
(011)(000111001101011011001011101)(00000110001111111011)
(1)(0001100110110111101001)(0000101010100011101100010001100111101010100001011111101)
(01)(0001100011)(00010110111)(00010101011111001100011)(00010100110011)(000011110101)(0)
(000101111)(00001011110001100011001001111)(000001101110010010001001110011111010100111101000111010101)(0)
(1)(000010110010010111111)(0000100101011011)(000000101010001011100011101111111110001011100110001)(00)
(00011011011011011)(00001010101010001100110010101111)(0)
(1)(01010101111111)(01)(00011011010011)(000100101111101110001011)(00000111111011010110100001101110110110101)
(001101010111011)(00000101011001100100101010100111111001000111011)(00000100111100010110110001000110011)
(11)(01111)(0000011010100010000110010111001010110001101010110010101011011)
(0111)(0101)(000001100110001100010011111001011111101010111)(000)
(01111)(0011011001110110100111101)(001)(000101101001010110100110010101)(00001)
(011011011)(001)(0001101010100011111101)(00000010111001101000010110100100101111101010110111)(0)
(000111011101100111110111001110011001)(0001)(0000110110011011000100011)(00000001111000110110111111)(000)
(1)(00001010010111100110000111011010110011)(0000010110001)
(0011)(001010011101111011)(000101)(0000111111011100111101011110110001)(00)
(010111)(01011)(0011)(0010111111111)(001011)(00010111)(0000001)(0)
(11)(00111)(00101111111)(000100011101111011)(000000011101000010011010010001101100001111111)
(1)(00011000111)(000001010100010101100000111110111101000001101)(0000000000110110111)(0)
(001001010111)(00001011111)(00001010101010001)(00001)(000000)
(001001101)(000111111001101011110011)(00000001001111000110110110111111)
(1)(01)(0011)(000101)(00010010111001110011110101)(00001001100011)(00)
(01)(00101011001101001101)(0001011)(0001001100011)(00000000110100101101010100011)
(11)(01011)(00101010100111011001010111110110111111011101111010011110111001100111110101)(0)
(1)(010101)(001100111)(001011101)(000101110110101111)(000010101101111)(0000011111)
(0001)(00001)(000000110010000001111111101011001101)(0000001001011000011)(0)
(11)(00011101101100111)(00010111111101111010101101101101111)(0001)(00001111)
(11)(0000101110011001111011101001010011100111111111111010100101)(000001)
(1)(0111)(0101)(0010010111101010011)(0001100110010011011110111)(00010011111)(000011010001011)
(01011)(01)(001001011011101)(0000011100100100111)(00000000111001001010110001100001)(000)
(1)(010110101101111011)(001)(000100101)(000010110001011011011101111)
(0001110100101110100110011001)(00001010100100010111011101100011)(00000110100100010011111011011001011)
(1)(01)(001011011011010101101011)(00011100111)(000100010001101010110010101111110111100010111111)(0)
(00000111010101011010111111110111111)(00000110011100111111110111111100001101)(0)
(000001010111101100010101101011111000001101001011000100101)
(001101001110111)(0000100110100110100011011011100010110010011)(000000001110001)
(00001111010100010011111)(00001011100011000111010101)(000)
(1)(00111)(0000100101100010000110101110111101111101100101001)(000000100001000001011101111011)
(0011111)(00101010101)(0001)(0000001011100011100110111110010101)(000)
(1)(001)(000001111001110011000110111011111001011110001110010001000111011)
(111)(000111100110010101011011011)(00001001)(000001010001000111000010011001001001111100001110111001000111)
(111)(0111)(0001110110010100111001101)(000010100110111000100111100011011001101000101)(00000000010110000111)
(011)(00111)(000011001111100101101111)(00001011010110111110010110011)(00000)
(1111)(00111)(000001111000111010110111000011110101110101010111011000011000011100111110110001010111)(00)
(111)(01)(0001011011)(00001011110001111001001111111100111100111)(0000001110111100001011001011101111)
(1111)(00111)(0011)(0000001100110010101101010101011100010101010000100110010101110100001)(00)
(111)(011111)(011)(01)(00110101)(00101011)(000001110000101000111010100001110110111)(00)
(1)(001)(0000010001001010110100001110011010111110011110010101)(0)
(1)(000011101100011111011110110010111)(0000110000110110111)(00001010110010100110100011011110001)(00)
(1)(01)(000101001101110110011101101100101010100111111)(00000010100111010010101100110010000111)
(1)(0111)(000010010001000111010011010101010011)(0000000010100111001100110111010111)
(0011010100110101010101011)(0010111)(001001100110111010111)(001)(000101010111)(000011010111)(0000)
(00000000111000110001101110001110010101101011011)(000000001000101011000100100011101110100111)
(011)(0011110101010101)(00011100111010111011011)(000111001011011)(0001001100101111)(00)
(1)(01)(001011)(000101001011)(0000111110100110111101111111)(0000001110111100101000010110111001)(0)
(01)(000000100111000101001110001111101110111000001000011101100011101011001111000111)
(1)(0001011000101101000111111000111001110111110001011100111000111011111)(0000010101111101011011111)
(1)(01)(001011)(000111101111001011)(00000101101)(00000011111011)
(0011)(0001101010111)(00010110010001101001001011010011011)(000101001001111011000111)(00000101010001101110001)
(1)(011)(0010101)(0000111)(0000011011000011)(0000010110111111000010101001001111110101)(0)
(1)(0011)(00001)(000000100000010110101000010110011011001000110111101)
(11)(0010101)(00001111110100101001110001001110101101011100101100011110011101101011001001111)(0000011)(0)
(11)(0000001101111101101010101111011)(000000100101)(0000001000001010011010000101000110110011110111111)(0)
(111)(000110011101011)(000101111110011001)(0000011101001000011011111100011100101111100010100101)(00)
(0011)(0001)(000001100110111001000100101010100111001001011101000111)(0000000101001011010100111)
(01)(00010111010111)(000000110010100010000110101101111110110101)(00)
(11)(0011110111)(0000100011101001101101100010101011000100111001101)(000001100001011)(0)
(0)
(0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
(0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101)
(0000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111)
(1111111111111111111111111111111111111111111111111)(000000000000000000000000000000000000000000000000000)
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[#include <stdio.h>
#include <string.h>

int eva(char *num, int len)
{
	int i;
	char sum[512];

	for (i = 1 ; i < len ; i++)
	{
		memset(sum, 0, sizeof(sum));
		strncpy(sum, num + i, len - i);
		strncpy(sum + len - i, num, i);
		if (strncmp(num, sum, len) > 0)
			return 0;
	}

	return 1;
}

int main(void)
{
	int n, i, j;
	int len;
	char *p;
	char num[512];

	scanf("%d%*c", &n);
	while (n--)
	{
		gets(num);
		p = num;
		while (len = strlen(p))
		{
			for (j = len ; !eva(p, j) ; j--)
				;
			putchar('(');
			for (i = 0 ; i < j ; i++)
				putchar(*(p + i));
			putchar(')');
			p += j;
		}
		putchar('\n');
	}

	return 0;
}]]></solution>
</item>
</fps>