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 (3.4.3) (judge verdict: Wrong Answer)

N = int(input())

if N == 0:
    print('0')
    exit(0)

idx = 0
while True:
    idx += 1
    left = sum([(-2)**i for i in range(idx+1) if i%2==1])
    right = sum([(-2)**i for i in range(idx+1) if i%2==0])
    if left <= N <= right:
        break
        
max_idx = idx
coeff = [0 for _ in range(max_idx+1)]
for idx in range(max_idx, 0-1, -1):
    left = sum([(-2)**i for i in range(idx) if i%2==1])
    right = sum([(-2)**i for i in range(idx) if i%2==0])
    print(left, N, right)
    if not left <= N <= right:
        N -= (-2)**(idx)
        coeff[idx] = 1
#     print(N)
# print(reversed(coeff)
print(''.join(map(str, reversed(coeff))))