Fibonacci number system
Consider the Fibonacci sequence: F[1] = 1, F[2] = 1, F[n] = F[n-1] + F[n-2] if n > 2.
Any positive integer can be represented as the sum of several members of the Fibonacci sequence. Such a representation will be ambiguous, but if we impose an additional condition that there are no two neighboring members of the Fibonacci sequence in the representation, then the representation becomes unique.
We shall say that A can be represented in the Fibonacci number system in the form a[k]a[k-1]...a[2], where a[i] equals to 0 or 1, if A = a[k]F[k] + ... + a[2]F[2] and in the notation a[k]a[k-1]...a[2] there is no two ones in a row.
Here is how small numbers are written in the Fibonacci number system:
Number n is given. Find its representation in the Fibonacci number system.
Input
One integer n (0 ≤ n ≤ 2 * 10^9).
Output
Print the representation of the number n in the Fibonacci number system without leading zeros.