Sandy is developing a new computer as part of the ambitious System for Binary Compression (SBC) project. This project is part of a major technological challenge known as the Interface for Compact Pattern Coding (ICPC), whose goal is to achieve maximum efficiency in writing large volumes of data.

The SBC proposal is bold: choose a base pattern $$$B$$$, consisting of 8 bits $$$b_0,\dots,b_7$$$, and from it generate any other pattern by applying only simple, fast operations.

Sandy wants to write a sequence of $$$N$$$ bits to memory, with $$$N \geq 8$$$, denoted by $$$C = c_0,\dots,c_{N-1}$$$. Initially, memory contains only zeros. She may then repeat the following operation any number of times:

• Choose an integer $$$i$$$ between $$$-7$$$ and $$$N-1$$$, the position at which $$$B$$$ will be applied;
• For each position of $$$B$$$ that overlaps the sequence, that is, for every $$$j$$$ from $$$0$$$ to $$$7$$$ such that $$$0 \leq i+j \leq N-1$$$, replace $$$c_{i+j}$$$ with $$$b_j \oplus c_{i+j}$$$, where $$$\oplus$$$ denotes the XOR (exclusive OR) operation.

Since the data we want to write to memory is usually not random, Sandy believes that, with a good choice of base pattern $$$B$$$, it will be possible to produce the desired content with few operations.

To test this hypothesis, she needs your help: given the content $$$C$$$ that must be written to memory, determine the base pattern $$$B$$$ that minimizes the number of operations needed to generate $$$C$$$ as described, and also the number $$$Q$$$ of operations required.

It can be proven that it is always possible to write any content using this procedure. However, for the SBC project to be successful and earn the ICPC seal of excellence, your solution needs to be fast and efficient!