import java.math.BigInteger;
 
public class Problem020
{
	private static int sumDigits(String s)
	{
		int sum = 0;
 
		for (int i = 0; i < s.length(); i++)
		{
			int j = Integer.parseInt(s.substring(i,i+1));
			sum += j;
		}
 
		return sum;
	}
 
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
		BigInteger fact = BigInteger.valueOf(1);
 
		for (int i = 1; i <= 100; i++)
			fact = fact.multiply(BigInteger.valueOf(i));
 
		long end = System.currentTimeMillis();
 
		System.out.println(sumDigits(fact.toString()));
		System.out.println(end-begin + "ms");
	}
}

import java.math.BigInteger;
 
public class Problem016
{
	private static int calcDigits(String s)
	{
		int sum = 0;
 
		for (int i = 0; i < s.length(); i++)
		{
			Character c = new Character(s.charAt(i));
			String z = c.toString();
			int j = Integer.parseInt(z);
			sum += j;
		}
 
		return sum;
	}
 
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
 
		BigInteger n = BigInteger.valueOf(2);
		n = n.pow(1000);
		System.out.println(calcDigits(n.toString()));
 
		long end = System.currentTimeMillis();
		System.out.println(end - begin + "ms");
	}
}

public class Problem015
{
	public static long binomialCoefficient(int n, int k)
	{
		/* N-choose-k combinatorics: (n! / (k! * (n-k)!)
		 * Where:
		 * 		n is the number of moves,
		 * 		k is the number of down and right moves required (20 each) */
 
		if (k > (n-k))
			k = n - k;
 
		long c = 1;
 
		for (int i = 0; i < k; i++)
		{
			c = c * (n-i);
			c = c / (i+1);			
		}
 
		return c;
	}
 
	public static void main (String[] args)
	{
		long begin = System.currentTimeMillis();
 
		System.out.println(binomialCoefficient(40,20));
 
		long end = System.currentTimeMillis();
		System.out.println(end-begin + "ms");		
	}
}

import java.util.*;
 
public class Problem014
{
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
 
		LinkedList<Long> list = new LinkedList<Long>();
 
		long length = 0;
		int res = 0;
 
		for(int j = 10; j < 1000000; j++)
		{
			long i = j;
 
			while (i != 1)
			{
				if (i % 2 == 0)
				{
					i /= 2;
					list.add(i);
				}
				else
				{
					i = (3 * i) + 1;
					list.add(i);
				}
			}
 
			if(list.size() > length)
			{
				length = list.size();
				res = j;
			}
			list.clear();
		}
		long end = System.currentTimeMillis();
 
		System.out.println(res+" with chain size: "+ length);
		System.out.println(end-begin + "ms");
	}
}

import java.math.*;
 
public class Problem013
{
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
		String data[] = { "37107287533902102798797998220837590246510135740250",
		"46376937677490009712648124896970078050417018260538",
		"74324986199524741059474233309513058123726617309629",
		"91942213363574161572522430563301811072406154908250",
		"23067588207539346171171980310421047513778063246676",
		"89261670696623633820136378418383684178734361726757",
		"28112879812849979408065481931592621691275889832738",
		"44274228917432520321923589422876796487670272189318",
		"47451445736001306439091167216856844588711603153276",
		"70386486105843025439939619828917593665686757934951",
		"62176457141856560629502157223196586755079324193331",
		"64906352462741904929101432445813822663347944758178",
		"92575867718337217661963751590579239728245598838407",
		"58203565325359399008402633568948830189458628227828",
		"80181199384826282014278194139940567587151170094390",
		"35398664372827112653829987240784473053190104293586",
		"86515506006295864861532075273371959191420517255829",
		"71693888707715466499115593487603532921714970056938",
		"54370070576826684624621495650076471787294438377604",
		"53282654108756828443191190634694037855217779295145",
		"36123272525000296071075082563815656710885258350721",
		"45876576172410976447339110607218265236877223636045",
		"17423706905851860660448207621209813287860733969412",
		"81142660418086830619328460811191061556940512689692",
		"51934325451728388641918047049293215058642563049483",
		"62467221648435076201727918039944693004732956340691",
		"15732444386908125794514089057706229429197107928209",
		"55037687525678773091862540744969844508330393682126",
		"18336384825330154686196124348767681297534375946515",
		"80386287592878490201521685554828717201219257766954",
		"78182833757993103614740356856449095527097864797581",
		"16726320100436897842553539920931837441497806860984",
		"48403098129077791799088218795327364475675590848030",
		"87086987551392711854517078544161852424320693150332",
		"59959406895756536782107074926966537676326235447210",
		"69793950679652694742597709739166693763042633987085",
		"41052684708299085211399427365734116182760315001271",
		"65378607361501080857009149939512557028198746004375",
		"35829035317434717326932123578154982629742552737307",
		"94953759765105305946966067683156574377167401875275",
		"88902802571733229619176668713819931811048770190271",
		"25267680276078003013678680992525463401061632866526",
		"36270218540497705585629946580636237993140746255962",
		"24074486908231174977792365466257246923322810917141",
		"91430288197103288597806669760892938638285025333403",
		"34413065578016127815921815005561868836468420090470",
		"23053081172816430487623791969842487255036638784583",
		"11487696932154902810424020138335124462181441773470",
		"63783299490636259666498587618221225225512486764533",
		"67720186971698544312419572409913959008952310058822",
		"95548255300263520781532296796249481641953868218774",
		"76085327132285723110424803456124867697064507995236",
		"37774242535411291684276865538926205024910326572967",
		"23701913275725675285653248258265463092207058596522",
		"29798860272258331913126375147341994889534765745501",
		"18495701454879288984856827726077713721403798879715",
		"38298203783031473527721580348144513491373226651381",
		"34829543829199918180278916522431027392251122869539",
		"40957953066405232632538044100059654939159879593635",
		"29746152185502371307642255121183693803580388584903",
		"41698116222072977186158236678424689157993532961922",
		"62467957194401269043877107275048102390895523597457",
		"23189706772547915061505504953922979530901129967519",
		"86188088225875314529584099251203829009407770775672",
		"11306739708304724483816533873502340845647058077308",
		"82959174767140363198008187129011875491310547126581",
		"97623331044818386269515456334926366572897563400500",
		"42846280183517070527831839425882145521227251250327",
		"55121603546981200581762165212827652751691296897789",
		"32238195734329339946437501907836945765883352399886",
		"75506164965184775180738168837861091527357929701337",
		"62177842752192623401942399639168044983993173312731",
		"32924185707147349566916674687634660915035914677504",
		"99518671430235219628894890102423325116913619626622",
		"73267460800591547471830798392868535206946944540724",
		"76841822524674417161514036427982273348055556214818",
		"97142617910342598647204516893989422179826088076852",
		"87783646182799346313767754307809363333018982642090",
		"10848802521674670883215120185883543223812876952786",
		"71329612474782464538636993009049310363619763878039",
		"62184073572399794223406235393808339651327408011116",
		"66627891981488087797941876876144230030984490851411",
		"60661826293682836764744779239180335110989069790714",
		"85786944089552990653640447425576083659976645795096",
		"66024396409905389607120198219976047599490197230297",
		"64913982680032973156037120041377903785566085089252",
		"16730939319872750275468906903707539413042652315011",
		"94809377245048795150954100921645863754710598436791",
		"78639167021187492431995700641917969777599028300699",
		"15368713711936614952811305876380278410754449733078",
		"40789923115535562561142322423255033685442488917353",
		"44889911501440648020369068063960672322193204149535",
		"41503128880339536053299340368006977710650566631954",
		"81234880673210146739058568557934581403627822703280",
		"82616570773948327592232845941706525094512325230608",
		"22918802058777319719839450180888072429661980811197",
		"77158542502016545090413245809786882778948721859617",
		"72107838435069186155435662884062257473692284509516",
		"20849603980134001723930671666823555245252804609722",
		"53503534226472524250874054075591789781264330331690" };
 
		BigInteger sum = BigInteger.ZERO;
		for (int i = 0; i < data.length; i++)
		{
			BigInteger b = new BigInteger(data[i]);
			sum = sum.add(b);
		}
		long end = System.currentTimeMillis();
 
		System.out.println(sum);
		System.out.println(end-begin + "ms");
	}
}

public class Problem012
{
	private static int countFactors(int f)
	{
		int factors = 0;
 
		for (int i = 1; i <= Math.sqrt(f); i++)
		{
			if (f % i == 0)
				factors += 2;
		}
 
		return factors;
	}
 
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
		int iter = 1;
		int size = 1;
		int NumFactors = 0;
 
		while (NumFactors <= 500)
		{
			NumFactors = countFactors(size);
			iter++;
			size += iter;
		}
 
		System.out.println(size-iter);
		long end = System.currentTimeMillis();
		System.out.println(end-begin + "ms");
	}
}

public class Problem008
{
	public static int checkInt(String s)
	{
		int product = 1;
 
		for (int i = 0; i < 5; i++)
		{
			Character c = new Character(s.charAt(i));
			String tmp = c.toString();
			int temp = Integer.parseInt(tmp);
			product *= temp;
		}
		return product;
	}
 
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
		String BigNum = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
		String snip;
		int largest = 0;
 
		for (int i = 0; i <= (BigNum.length()-5); i++)
		{
			snip = "";
 
			for (int j = 0; j < 5; j++)
			{
				char c = BigNum.charAt(i+j);
				snip += c;
			}
 
			if (checkInt(snip) > largest)
				largest = checkInt(snip);
		}
		long end = System.currentTimeMillis();
		System.out.println(largest);
		System.out.println(end-begin + "ms");
	}
}

public class Problem007
{
	private static boolean isPrime(long n)
	{
		//returns 0 if not prime, 1 if prime
		if ((n % 2 == 0)&&(n != 2))
			return false;		// is even, therefore not prime
		for (long i = 3; i <= (n^(1/2)+1); i += 2)	// Skip all the even numbers
		{
			if (n % i == 0)
				return false;	//not prime
		}
		return true;
	}
 
	public static void main(String[] args)
	{
		long begin = System.currentTimeMillis();
		int NumPrimes = 1;
		long i = 2;
		while(NumPrimes <= 10001)
		{
			if (isPrime(i))
			{
				i++;
				NumPrimes++;
			}
			else i++;
		}
		long end = System.currentTimeMillis();
		System.out.println(i);
		System.out.println(end-begin + "ms");
	}	
}

public class Problem006
{
	private static long sum_squares(int n)
	{
		int total = 0;
		for (int i = 1; i <= n; i++)
			total += (i*i);
		System.out.println("sum_squares() = " + total);
		return total;
	}
 
	private static long squares_sum(int n)
	{
		long total = 0;
		for (int i = 1; i <= n; i++)
			total += i;
		total *= total;
		System.out.println("squares_sum() = " + total);
		return total;
	}
 
	public static void main(String args[])
	{
		long begin = System.currentTimeMillis();
		long omg_zombies = squares_sum(100) - sum_squares(100);
		long end = System.currentTimeMillis();
		System.out.println(omg_zombies);
		System.out.println(end-begin + "ms");
	}	
}