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: Runtime Error)

invtwos = [1]
i = 0
while abs(invtwos[i]) <= 10**9:
    invtwos.append(invtwos[i]*(-2))
    i += 1
invtwos.append(invtwos[-1]*(-2))

n = int(input())
ans = []
i = 0
while n != 0:
    if n%abs(invtwos[i+1]) != 0:
        ans.append(1)
        n -= invtwos[i]
    else:
        ans.append(0)
    i += 1
ans.reverse()
for i in range(len(ans)):
    if i != len(ans)-1:
        print(ans[i],end="")
    else:
        print(ans[i])