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ural 1049. Brave Balloonists math

2017-06-25 19:01 330 查看


1049. Brave Balloonists

Time limit: 2.0 second

Memory limit: 64 MB

Ten mathematicians are flying on a balloon over the Pacific ocean. When they are crossing the equator they decide to celebrate this event and open a bottle of champagne. Unfortunately, the cork makes
a hole in the balloon. Hydrogen is leaking out and the balloon is descending now. Soon it will fall into the ocean and all the balloonists will be eaten by hungry sharks.

But not everything is lost yet. One of the balloonists can sacrifice himself jumping out, so that his friends would live a little longer. Only one problem still exists: who is the one to get out. There
is a fair way to solve this problem. First, each of them writes an integer ai not less than 1 and not more than 10000. Then they calculate the magic number N that
is the number of positive divisors of the product a1*a2*…*a10.
For example, the number of positive integer divisors of 6 is 4 (they are 1,2,3,6). The hero (a mathematician who will be thrown out) is determined according to the last digit of N. Your task is to find this digit.

Input

Input contains ten integer numbers (each number is in separate line).

Output

Output a single digit from 0 to 9 — the last digit of N.

Sample

inputoutput
1
2
6
1
3
1
1
1
1
1

9

Problem Author: Stanislav Vasilyev
Problem Source: Ural State University collegiate programming contest (25.03.2000)
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {
public static void main(String[] args) {
new Task().solve();
}
}

class Task{

InputReader in = new InputReader(System.in) ;
PrintWriter out = new PrintWriter(System.out) ;

void add(Map<Integer, Integer> factor , int fac , int cnt){
Integer c = factor.get(fac) ;
factor.put(fac, c == null ? cnt : cnt + c) ;
}

void gao(int n , Map<Integer, Integer> factor){
for(int i = 2 ; i * i <= n ; i++){
if(n % i == 0){
int cnt = 0 ;
while(n % i == 0){
cnt++ ;
n /= i ;
}
add(factor, i, cnt) ;
}
}
if(n != 1){
add(factor, n, 1) ;
}
}

void solve(){
Map<Integer , Integer> factor = new HashMap<Integer, Integer>() ;
for(int i = 0 ; i < 10 ; i++){
gao(in.nextInt() , factor) ;
}
int sum = 1 ;
for(int cnt : factor.values()){
sum *= (cnt+1) ;
sum %= 10 ;
}
out.println(sum) ;
out.flush();
}

}

class InputReader {
public BufferedReader reader;
public StringTokenizer tokenizer;

public InputReader(InputStream stream) {
reader = new BufferedReader(new InputStreamReader(stream), 32768);
tokenizer = new StringTokenizer("");
}

private void eat(String s) {
tokenizer = new StringTokenizer(s);
}

public String nextLine() {
try {
return reader.readLine();
} catch (Exception e) {
return null;
}
}

public boolean hasNext() {
while (!tokenizer.hasMoreTokens()) {
String s = nextLine();
if (s == null)
return false;
eat(s);
}
return true;
}

public String next() {
hasNext();
return tokenizer.nextToken();
}

public int nextInt() {
return Integer.parseInt(next());
}

public long nextLong() {
return Long.parseLong(next());
}

public double nextDouble() {
return Double.parseDouble(next());
}

public BigInteger nextBigInteger() {
return new BigInteger(next());
}

}
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