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 PyPy3 (7.3.0) (judge verdict: Accepted)

n=int(input())

if n==0:
    print(0)
    exit(0)

pos=[0]*50
neg=[0]*50

def rec(x):
    if x>0:
        m=1
        while 4**m-1<3*x:
            m+=1
        
        pos[m-1]=1
        rec(x-4**(m-1))
    elif x<0:
        m=1
        while -2*(4**m-1)>3*x:
            m+=1
        
        neg[m-1]=1
        rec(x+2*(4**(m-1)))
    else:
        return

rec(n)

s=''
for i in range(100):
    if i%2==0:
        s=str(pos[i//2])+s
    else:
        s=str(neg[(i-1)//2])+s

i=0
while s[i]=='0':
    i+=1

print(s[i:])