CF132D.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.

莎士比亚（Shakespeare）是一种广为人知的深奥编程语言，其程序形如莎士比亚戏剧，而数字则由华丽的修饰语组合来表示。本题中，我们将更细致地考察莎士比亚语言中数字的表示方式。

莎士比亚语言中的每个常量均由 $2$ 的非负整数次幂经算术运算构成。为简化问题，我们仅允许加法与减法，并寻求一种给定数字的表示形式，使其所需运算次数最少。

给定一个整数 $n$。你需要将它表示为 $n = a_1 + a_2 + \dots + a_m$，其中每个 $a_i$ 均为 $2$ 的某个非负整数次幂（即形如 $2^k$，$k \ge 0$），并可乘以 $-1$（即允许取负）。请找出使 $m$ 最小的表示形式。

The only line of input contains a positive integer n, written as its binary notation. The length of the notation is at most 106. The first digit of the notation is guaranteed to be 1.

输入仅包含一行，为一个正整数 $n$ 的二进制表示。该二进制表示的长度至多为 $10^6$，且其首位数字保证为 $1$。

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.

输出所需的最小的 $m$。之后输出 $m$ 行，每行格式为 +2^x 或 -2^x，其中 $x$ 是对应项的幂次系数。各行的顺序无关紧要。