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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>


int s[40];


int main(void){
    //入力
    int n;
    int xxxx;
    int xxx;
    xxx = 0;
    xxxx = 1;
    scanf("%d", &n);
    if(n == 0){
        xxxx = 0;
        xxx = 1;
    }
    //sの初期化
    int i;
    for(i = 0 ; i < 40 ; i++){
        s[i] = 0;
    }
    //計算
    int n_, n_n;
    while(n != 0){
        i = 0;
        if(n > 0){
            n_ = 1;
            n_n = 1;
            while(n > n_){
                i++;
                n_n *= 4;
                n_ += n_n;
            }
            s[39 - 2 * i] = 1;
        }
        if(n < 0){
            i++;
            n_ = -2;
            n_n = -2;
            while(n < n_){
                i++;
                n_n *= 4;
                n_ += n_n;
            }
            s[39 - (2 * i - 1)] = 1;
        }
        n -= n_n;
    }
    //表示
    i = -1;
    while(xxx == 0){
        i++;
        if(s[i] == 1){
            xxx = 1;
        }
    }
    for( ; i < 40 ; i++){
        printf("%d", s[i]);
    }
    if(xxxx == 0){
        printf("0");
    }
    printf("\n");

    return 0;
}