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: Accepted)

import bisect

n = int(input())
ps = [0] * (1 << 16)
for i in range(1 << 16):
    temp = 0
    for j in range(16):
        if (i >> j) & 1:
                temp += (-2) ** (2 *j)
    ps[i] = temp

"""
for index, value in enumerate(ps):
    print(bin(index)[2:].zfill(16), value)
"""

pattern1 = None
pattern2 = None

for i in range(1 << 16):
    temp2 = 0
    for j in range(16):
        if (i >> j) & 1:
                temp2 += (-2) ** (2 *j + 1)
    n2 = n - temp2
    pattern1 = bisect.bisect_left(ps, n2)
    if pattern1 != (1 << 16) and ps[pattern1]==n2:
        pattern2 = bin(i)[2:].zfill(16)
        pattern1 = bin(pattern1)[2:].zfill(16)
        break

ans = ""
for i in range(16):
    ans += pattern2[i]
    ans += pattern1[i]
    
true_ans = ""
flag = False
for i in range(len(ans)):
    if ans[i]=="1":
        true_ans += "1"
        flag = True
    elif flag:
        true_ans += "0"

if true_ans == "":
    true_ans = "0"
        
print(true_ans)