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 (2.4.0) (judge verdict: Wrong Answer)

N = int(input())
N = 2**30 + N
buf = [0]*35
for i,s in enumerate(bin(N)[2:][::-1]):
    if s == "1":
        buf[i] = 1
#print(buf)

ans = [0]*35

for i in range(33):
    if buf[i]==1:
        if i%2==0:
            ans[i]+=1
        else:
            ans[i]+=1
            ans[i+1]+=1
    while ans[i]>=2:
        ans[i]-=2
        ans[i+1]+=1
        ans[i+2]+=1
    #print(ans)
first = True
a = ""
for i in ans[:30][::-1]:
    if first:
        if i==1:
            first=False
    if not first:
        a += str(i)
if a!="":
    print(a)
else:
    print(0)