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: Accepted)

n = int(input())

a = []

if n > 0:
    while n > 0:
        a.append(n % 2)
        n //= 2

    a.append(0)
    a.append(0)
    for i in range(len(a) - 1):
        if i % 2 == 1:
            if a[i] == 1:
                a[i + 1] += 1
            elif a[i] == 2:
                a[i + 1] += 1
                a[i] = 0
        else:
            if a[i] == 2:
                a[i + 1] += 1
                a[i] = 0

    for i in range(len(a)):
        a[i] = str(a[i])
    for i in range(len(a) - 1, -1, -1):
        if a[i] == '0':
            a[i] = ''
        else:
            break
    print(''.join(reversed(a)))
elif n == 0:
    print('0')
else:
    n = 0 - n
    while n > 0:
        a.append(n % 2)
        n //= 2

    a.append(0)
    a.append(0)
    for i in range(len(a) - 1):
        if i % 2 != 1:
            if a[i] == 1:
                a[i + 1] += 1
            elif a[i] == 2:
                a[i + 1] += 1
                a[i] = 0
        else:
            if a[i] == 2:
                a[i + 1] += 1
                a[i] = 0

    for i in range(len(a)):
        a[i] = str(a[i])
    for i in range(len(a) - 1, -1, -1):
        if a[i] == '0':
            a[i] = ''
        else:
            break
    print(''.join(reversed(a)))