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

output

input

output

【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 = ;

int n;

int a[N];

int main()

{

    for(int i=;i<=;i++) a[i]=(pow(,i)-)*pow(,i-);

    scanf("%d",&n);

    for(int i=;i>=;i--) if(n%a[i]==) {printf("%d\n",a[i]);break;}

    return ;

}

巴特西

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

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