CF515C Drazil and Factorial

Drazil is playing a math game with Varda.

Let’s define for positive integer x as a product of factorials of its digits. For example, .

First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:

1. x doesn’t contain neither digit 0 nor digit 1.

2. F(x) = F(a)

Help friends find such number.

Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.

The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.

Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.

Examples
Input
4
1234
Output
33222
Input
3
555
Output
555

题目地址

思路：
对于每一个数字，如6

我们把它分成几个阶乘相乘的形式

让能分的阶乘数尽量地多，最后构成的数必然最大

你可用10分钟手算

1!=1!1!=1!

2!=2!2!=2!

3!=3!3!=3!

4!=3!*2!*2!4!=3!∗2!∗2!

5!=5!5!=5!

6!=5!*3!6!=5!∗3!

7!=7!7!=7!

8!=7!*2!*2!*2!8!=7!∗2!∗2!∗2!

9!=7!*3!*3!*2!9!=7!∗3!∗3!∗2!

把这些数放入一个数组，再从大到小排序，输出答案

import java.util.Scanner;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        String s = sc.next();
        int[] a = new int[20];
        for(int i=0;i<n;i++){
            int t = s.charAt(i)-'0';
            if(t==2)a[2]++;
            if(t==3){
                a[3]++;
            }
            if(t==4){
                a[2]+=2;
                a[3]++;
            }
            if(t==5){
                a[5]++;
            }
            if(t==6){
                a[3]++;
                a[5]++;
            }
            if(t==7){
                a[7]++;
            }
            if(t==8){
                a[2]+=3;
                a[7]++;
            }
            if(t==9){
                a[2]++;
                a[3]+=2;
                a[7]++;
            }
        }
        for(int i=9;i>1;i--){
            for(int j=0;j<a[i];j++){
                System.out.print(i);
            }
        }
    }
}