CodeForces - 893B Beautiful Divisors

Posted 2021-02-13 pinefrost

题目链接 CodeForces - 893B

time limit per test:2 seconds

memory limit per test:256 megabytes

input:standard input

output:standard output

 

Recently Luba learned about a special kind of numbers that she calls beautiful numbers. The number is called beautiful iff its binary representation consists of k + 1 consecutive ones, and then k consecutive zeroes.

Some examples of beautiful numbers:

• 1₂ (1₁₀);
• 110₂ (6₁₀);
• 1111000₂ (120₁₀);
• 111110000₂ (496₁₀).

More formally, the number is beautiful iff there exists some positive integer k such that the number is equal to (2^k - 1) * (2^k - 1).

Luba has got an integer number n, and she wants to find its greatest beautiful divisor. Help her to find it!

Input

The only line of input contains one number n (1 ≤ n ≤ 10⁵) — the number Luba has got.

Output

Output one number — the greatest beautiful divisor of Luba‘s number. It is obvious that the answer always exists.

Examples

Input

3

Output

1

Input

992

Output

496

 

Tutorial:

Let‘s notice that there are only 8 beautiful numbers less than 10⁵. Generate them all and select the greatest one which is also divisor of n.

Overall complexity: O(1).

#include<iostream>
using namespace std;
int main()
{
    int a[8]={1,6,28,120,496,2016,8128,32640};
    int n;
    cin>>n;
    for (int i=7;i>=0;i--)
    {
        if (n%a[i]==0)
        {
            cout<<a[i]<<endl;
            break;
        }
    }
    return 0;
}