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: Wrong Answer)

#include <iostream>
#include <bits/stdc++.h>
using namespace std;

pair<int, int> mod(int a, int b){
    int d = a/b;
    int r = a%b;
    if(r<0){
        d++;
        r = a-(d*b);
    }


    return make_pair(d, r);
}
int main(){
    int32_t n;
    int bits[32] = {0};
    scanf("%lu", &n);
    if(n == 0){
        cout << 0 << endl;
        return 0;
    }
    int i=32;
    while(n != 0){
        pair<int, int> div = mod(n, -2);
        n = div.first;
        bits[--i] = div.second;
    }

    int prnt = false;
    for(int i=0; i<32; i++){
        if(!prnt && bits[i]) prnt = true;
        if(prnt) cout << bits[i];
    }
    cout << endl;






}