Educational Codeforces Round 33 (Rated for Div. 2) B. Beautiful Divisors【进制思维/打表】

B. Beautiful Divisors

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 (2k - 1) * (2k - 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

【题意】：beautiful数定义：如果该数在二进制下表示由k+1个连续的1个，接着k个连续的0组成，则该数字称为beautiful的。比如：

 

换句话说，当且仅当存在一些正整数k使得这个 number =  ( 2k - 1 ) * ( 2^(k - 1) ) ,这个number就是beautiful的。现在给你一个number，求它最大beautiful因子。

【分析】：打表得到K为最大9。求最大因子数可以逆向枚举。

【代码】：beautiful numbers表：

void init(){
    num[1] = 1 ; 
    num[2] = 6 ; 
    num[3] = 28 ; 
    num[4] = 120 ; 
    num[5] = 496 ;
    num[6] = 2016 ; 
    num[7] = 8128 ; 
    num[8] = 32640 ; 
    num[9] = 130816 ; 
    
}

#include <bits/stdc++.h>

using namespace std;
const int N = 15;
int n;
int a[N];
int main()
{
    for(int i=1;i<=10;i++) a[i]=(pow(2,i)-1)*pow(2,i-1);
    scanf("%d",&n);
    for(int i=10;i>=1;i--) if(n%a[i]==0) {printf("%d\n",a[i]);break;}
    return 0;
}