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 Python (3.8.2) (judge verdict: Runtime Error)

n = int(input())

dp =[0]*40

if n ==0:
    print(0)

elif n >0:
    x = bin(n)
    bx = x[2:]
    lx = len(bx)
    for i in range(lx-1,-1,-1):
        dp[i] = int(bx[lx-1-i])
    for i in range(40):
        if i % 2 ==1 and dp[i]==1:
            dp[i+1] +=1
    while max(dp) >1:
        for i in range(40):
            if dp[i] >=2:
                dp[i] -=2
                if dp[i+1] >0:
                    dp[i+1] -=1
                else:
                    dp[i+1] +=1
                    dp[i+2] +=1
    dpr = list(reversed(dp))
    dprs = list(map(lambda x :str(x),dpr))
    dprj = "".join(dprs)
    print(int(dprj))    

else:
    x = bin(n)
    bx = x[2:]
    lx = len(bx)
    for i in range(lx-1,-1,-1):
        dp[i] = int(bx[lx-1-i])
    for i in range(40):
        if i % 2 ==1 and dp[i]==1:
            dp[i+1] +=1
    while max(dp) >1:
        for i in range(40):
            if dp[i] >=2:
                dp[i] -=2
                if dp[i+1] >0:
                    dp[i+1] -=1
                else:
                    dp[i+1] +=1
                    dp[i+2] +=1
    dpr = list(reversed(dp))
    dprs = list(map(lambda x :str(x),dpr))
    dprj = "".join(dprs)
    print(int(dprj))