topcoder srm 320 div1

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));
	}
}