A8304 | Constants in the language of Shakespeare

Shakespeare is a widely known esoteric programming language in which programs look like plays by Shakespeare, and numbers are given by combinations of ornate epithets. In this problem we will have a closer look at the way the numbers are described in Shakespeare.

Each constant in Shakespeare is created from non-negative powers of 2 using arithmetic operations. For simplicity we'll allow only addition and subtraction and will look for a representation of the given number which requires a minimal number of operations.

You are given an integer $n$ . You have to represent it as $n=a_{1}+a_{2}+...+a_{m}$ , where each of $a_{i}$ is a non-negative power of 2, possibly multiplied by -1. Find a representation which minimizes the value of $m$ .

The only line of input contains a positive integer $n$ , written as its binary notation. The length of the notation is at most $10^{6}$ . The first digit of the notation is guaranteed to be 1.

Output the required minimal $m$ . After it output $m$ lines. Each line has to be formatted as "+2^x" or "-2^x", where $x$ is the power coefficient of the corresponding term. The order of the lines doesn't matter.