Friend

**Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 2207    Accepted Submission(s): 1108

**

Problem Description

Friend number are defined recursively as follows.

(1) numbers 1 and 2 are friend number;

(2) if a and b are friend numbers, so is ab+a+b;

(3) only the numbers defined in (1) and (2) are friend number.

Now your task is to judge whether an integer is a friend number.

Input

There are several lines in input, each line has a nunnegative integer a, 0<=a<=2^30.

Output

For the number a on each line of the input, if a is a friend number, output “YES!”, otherwise output “NO!”.

Sample Input

3
13121
12131

Sample Output

YES!
YES!
NO!

Source

2007省赛集训队练习赛（2）

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/*刚刚看到这道题的时候一心只想着打表，但是试了几次都超时，没想到有这种规律….
c=ab+b+a=b(a+1)+b=(b+1)(a+1)-1,c+1=(b+1)(a+1),所以输入的数加一之后，它只要是2或者3的倍数就可以*/
#include
#include
int main()
{
int n;
while(scanf("%d",&n)!=EOF)
{
if(n<1)
{
printf("NO!\n");
}
else
{
n=n+1;
while(n%2==0)
n=n/2;
while(n%3==0)
n=n/3;
if(n==1)
printf("YES!\n");
else printf("NO!\n");
}
}
}