Problem:
Score : 300 points

Problem Statement

Given an integer N, find the base -2 representation of N.

Here, S is the base -2 representation of N when the following are all satisfied:

S is a string consisting of 0 and 1.

Unless S = 0, the initial character of S is 1.

Let S = S_k S_{k-1} ... S_0, then S_0 \times (-2)^0 + S_1 \times (-2)^1 + ... + S_k \times (-2)^k = N.

It can be proved that, for any integer M, the base -2 representation of M is uniquely determined.

Constraints

Every value in input is integer.

-10^9 \leq N \leq 10^9

Input

Input is given from Standard Input in the following format:

N

Output

Print the base -2 representation of N.

Sample Input 1

-9

Sample Output 1

1011

As (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9, 1011 is the base -2 representation of -9.

Sample Input 2

123456789

Sample Output 2

11000101011001101110100010101

Sample Input 3

0

Sample Output 3

0

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,a,b) for(int i=a;i<b;i++)
#define REP(i,a,b) for(int i=a;i<=b;i++)
#define rev(i,n) for(int i=n-1;i>=0;i--)
#define vi vector<int>
#define pb push_back
#define pi pair<int,int>
#define vp vector<pair<int,int> >
#define mp make_pair
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define inf 1000000000000000000

using namespace std;

void run(){
    int n;
    cin>>n;
    if(!n){
        cout<<0<<endl;
        return;
    }
    string s;
    while(n){
        int a=abs(n%2);
        if(a)n--;
        n/=-2;
        s+=a+'0';
    }
    reverse(all(s));
    cout<<s<<endl;
}

signed main(){
    cout<<fixed;
    run();
    return 0;
}