import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class ExtraordinarilyLarge {public String compare(String x, String y) {boolean both=false;while(x.endsWith("!")&&y.endsWith("!")) {x=x.substring(0,x.length()-1);y=y.substring(0,y.length()-1);both=true;}boolean bswap=false;if(x.endsWith("!")) {String t=new String(x);x=y;y=t;bswap=true;}long xx=Long.valueOf(x);if(xx==0&&both) {xx=1;}long yy=1;if(y.endsWith("!")) {int id=y.indexOf("!");yy=Long.valueOf(y.substring(0,id));final int num=y.length()-id;for(int i=0;i<num&&yy<=xx;++i) {yy=cal(yy,xx);}}else {yy=Long.valueOf(y);if(yy==0&&both) {yy=1;}}if(xx<yy) {if(bswap) {return "x>y";}return "x<y";}else if(xx==yy) {return "x=y";}else {if(bswap) {return "x<y";}return "x>y";}}long cal(long x,long y) {if(x==0) {return 1;}long result=1;for(int i=2;i<=x;++i) {if(result<=y/i) {result=result*i;}else {return y+1;}}return result;}
}

import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class ContestSchedule {public double expectedWinnings(String[] contests) {final int n=contests.length;int[][] p=new int[n][3];for(int i=0;i<n;++i) {String[] t=contests[i].split("\\W+");assert t.length==3;for(int j=0;j<3;++j) {p[i][j]=Integer.valueOf(t[j]);}}boolean[][] g=new boolean[n][n];for(int i=0;i<n;++i) {for(int j=0;j<n;++j) {if(i==j) {g[i][j]=false;continue;}if(p[i][1]<=p[j][0]) {g[i][j]=true;}else {g[i][j]=false;}}}Queue<Integer> queue=new LinkedList<>();double[] f=new double[n];boolean[] inq=new boolean[n];for(int i=0;i<n;++i) {inq[i]=true;f[i]=p[i][2]/100.0;queue.offer(i);}while(!queue.isEmpty()) {final int u=queue.poll();inq[u]=false;for(int i=0;i<n;++i) {if(g[u][i]) {final double c=p[i][2]/100.0;if(f[u]+c>f[i]) {f[i]=f[u]+c;if(!inq[i]) {inq[i]=true;queue.offer(i);}}}}}double result=0;for(int i=0;i<n;++i) {result=Math.max(result,f[i]);}return result;}
}

import com.sun.org.apache.xpath.internal.operations.Bool;import java.util.*;
import java.math.*;
import static java.lang.Math.*;public class SeatingPlan {public String expectedTrial(int m, int n, int k) {if(n<m) {int x=m;m=n;n=x;}long[][][] f=new long[n+1][1<<m][k+1];int[] num=new int[1<<m];num[0]=0;for(int i=1;i<(1<<m);++i) {num[i]=num[i>>1]+(i&1);}List<List> g=new ArrayList<>();for(int i=0;i<(1<<m);++i) {List<Integer> list=new ArrayList<>();if(((i>>1)&i)!=0) {g.add(list);continue;}for(int j=0;j<(1<<m);++j) {if((i&j)==0&&((j>>1)&j)==0) {list.add(j);}}g.add(list);}f[0][0][0]=1;for(int i=1;i<=n;++i) {for(int j=0;j<(1<<m);++j) {for(int t=0;t<=k;++t) {if(0==f[i-1][j][t]) {continue;}List list=g.get(j);for(int p=0;p<list.size();++p) {int s=(int)list.get(p);if(t+num[s]>k) {continue;}f[i][s][t+num[s]]+=f[i-1][j][t];}}}}long result=0;for(int i=0;i<(1<<m);++i) {result+=f[n][i][k];}if(result==0) {return "Impossible!";}BigInteger sum=BigInteger.ONE;for(int i=1;i<=k;++i) {sum=sum.multiply(int2biginteger(n*m-i+1)).divide(int2biginteger(i));}long s=Long.valueOf(sum.toString());long p=gcd(result,s);result/=p;s/=p;return Long.toString(s)+"/"+Long.toString(result);}static long gcd(long x,long y) {return y==0?x:gcd(y,x%y);}static BigInteger int2biginteger(int x) {return new BigInteger(Integer.toString(x));}
}