E. Mahmoud and Ehab and the xor-MST(神仙规律题)

http://codeforces.com/problemset/problem/959/E

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n - 1. For all 0 ≤ u < v < n, vertex u and vertex v are connected with an undirected edge that has weight  (where  is the bitwise-xor operation). Can you find the weight of the minimum spanning tree of that graph?

You can read about complete graphs in https://en.wikipedia.org/wiki/Complete_graph

You can read about the minimum spanning tree in https://en.wikipedia.org/wiki/Minimum_spanning_tree

The weight of the minimum spanning tree is the sum of the weights on the edges included in it.

Input

The only line contains an integer n (2 ≤ n ≤ 1012), the number of vertices in the graph.

Output

The only line contains an integer x, the weight of the graph's minimum spanning tree.

Example

input

Copy

4

output

Copy

4

Note

In the first sample:The weight of the minimum spanning tree is 1+2+1=4.

我经历千辛万苦找的规律居然不能这样做。

A[n]=A[n-1]+pow(2,j)j是n-1数 二进制中最低位为1的位置。

但是n是1e12的，j又是变得无法用矩阵快速幂。

百度了一波题解，没太看懂，就先放着，感觉这类题还是比较难的对于我来说

来自：https://blog.csdn.net/elijahqi/article/details/79839261

#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
ll n,ans,base=1;
int main(){
    freopen("cf959e.in","r",stdin);
    scanf("%lld",&n);
    while(n>1){
        ans+=base*(n>>1);base<<=1;n-=n>>1;
    }printf("%lld\n",ans);
    return 0;
}