Description

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

思路

题目中定义了一种数，叫做美丽的数，定义是这样的：

一个数的二进制如果有连续的k+1k+1个1和k<script type="math/tex" id="MathJax-Element-139">k</script>个0组成，那么这个数是美丽的数

比如，当：

k=0 :1
k=1 :110
k=2 :11100
k=3 :1111000

题目给出了一个数n，让你从它的因子里面找出一个最大的美丽的数

枚举美丽的数，然后与判断是否可以整除

代码

c++:

#include <bits/stdc++.h>
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
int dec(string s)
{int len=s.length(),ans=0;for(int i=0; i<len; i++)ans+=(s[i]-'0')*(int)pow(2,len-1-i);return ans;
}
int main()
{int n,p=1;string i="110";scanf("%d",&n);while(dec(i)<=n){if(n%dec(i)==0)p=dec(i);i="1"+i+"0";}printf("%d\n",p);return 0;
}

python3:

n=int(input())
i = '110'
p=1
while int(i,2)<=n:if n%int(i,2)==0:p=int(i,2)i='1'+i+'0'
print(p)

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CodeForces - 893B Beautiful Divisors(数学，二进制)

Description

Input

Output

Examples

input

output

input

output

思路

代码

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