A Cubic number and A Cubic Number 两数立方差

Problem Description

A cubic number is the result of using a whole number in a multiplication three times. For example,  3×3×3=27  so  27  is a cubic number. The first few cubic numbers are  1,8,27,64  and  125 . Given an prime number  p . Check that if  p  is a difference of two cubic numbers.

 

Input

The first of input contains an integer  T (1≤T≤100)  which is the total number of test cases.
For each test case, a line contains a prime number  p (2≤p≤1012) .

 

Output

For each test case, output 'YES' if given  p  is a difference of two cubic numbers, or 'NO' if not.

Sample Input

   

    10
2
3
5
7
11
13
17
19
23
29
   

 

Sample Output

   

    NO
NO
NO
YES
NO
NO
NO
YES
NO
NO
   

#include <iostream>

#include<cstdio>
#include<algorithm>
using namespace std;


int main()
{
    int T,p,flag,i;
    scanf("%d",&T);
    while(T--)
    {
        flag=0;
        scanf("%d",&p);
        for(i=1;i<=1e6+10;i++)
        {
            if(3*i*i+3*i+1==p)   //(x-y)(x^2+xy+y^2)=p（p是质数）——> x-y=1以及x^2+xy+y^2=p,    将（x-y=1）带入后得到p=3x^2+3x+1。 
            {
                flag=1;
                break;
            }
        }
        if(flag) 
 printf("YES\n");
        else
 printf("NO\n");
    }
    return 0;
}