Supernatural

 Problem:-

You are given a number n.

A supernatural number is a number whose product of digits is equal to n, and in this number there is no digit 1.

Count the number of supernatural numbers for a given n.

Input

Contains a single integer n, 1 <= n <= 100.

Output

Print the number of supernatural numbers.

Sample Input

4

Sample Output

2

Time Limit: 1

Memory Limit: 256

Source Limit:

Explanation

There are only two natural numbers, the product of the digits of which is 4 - 4, 22.

Logic:-

Here constrains for n is :-  n<=100   so multiplication of digits of a number should be less than 100;

and 1 should not in supernatural number (according to question) so the minimum number is 2.

and when we multiply 2

2=2

2*2=4

2*2*2=8

2*2*2*2=16

2*2*2*2*2=32

2*2*2*2*2*2=64

2*2*2*2*2*2*2=128  (which is greater then 100)

So the maximum length of the number is 6.

and we have to check from 2 to 1000000 (maximum number) for all the number . 

Code:-

#include<bits/stdc++.h>

using namespace std;

int main()

{

int n;

cin>>n;

int count=0;

for(int i=2;i<=1000000;i++)

{

int j=i;

int mul=1;

int flag=0;

while(j)

{

int r=j%10;

// if r<2 i.e r is 1

// or 0 which is not

// allowed in supernatural

if(r<2)

{

flag=1;

break;

}

else

mul=mul*r;

j=j/10;

}

if(mul==n && flag==0)

count++;

}

cout<<count;

return 0;

}

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