# Xor on Figures

## 题目描述

There is given an integer $k$ and a grid $2^k \times 2^k$ with some numbers written in its cells, cell $(i, j)$ initially contains number $a_{ij}$ . Grid is considered to be a torus, that is, the cell to the right of $(i, 2^k)$ is $(i, 1)$ , the cell below the $(2^k, i)$ is $(1, i)$ There is also given a lattice figure $F$ , consisting of $t$ cells, where $t$ is odd. $F$ doesn't have to be connected. We can perform the following operation: place $F$ at some position on the grid. (Only translations are allowed, rotations and reflections are prohibited). Now choose any nonnegative integer $x$ . After that, for each cell $(i, j)$ , covered by $F$ , replace $a_{ij}$ by $a_{ij}\oplus x$ , where $\oplus$ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). More formally, let $F$ be given by cells $(x_1, y_1), (x_2, y_2), \dots, (x_t, y_t)$ . Then you can do the following operation: choose any $x, y$ with $1\le x, y \le 2^k$ , any nonnegative integer $x$ , and for every $i$ from $1$ to $n$ replace number in the cell $(((x + x_i - 1)\bmod 2^k) + 1, ((y + y_i - 1)\bmod 2^k) + 1)$ with $a_{((x + x_i - 1)\bmod 2^k) + 1, ((y + y_i - 1)\bmod 2^k) + 1}\oplus x$ . Our goal is to make all the numbers equal to $0$ . Can we achieve it? If we can, find the smallest number of operations in which it is possible to do this.

## 输入输出格式

### 输入格式

The first line contains a single integer $k$ ( $1 \le k \le 9$ ). The $i$ -th of the next $2^k$ lines contains $2^k$ integers $a_{i1}, a_{i2}, \dots, a_{i2^k}$ ( $0 \le a_{ij} < 2^{60}$ ) — initial values in the $i$ -th row of the grid. The next line contains a single integer $t$ ( $1\le t \le \min(99, 4^k)$ , $t$ is odd) — number of cells of figure. $i$ -th of next $t$ lines contains two integers $x_i$ and $y_i$ ( $1 \le x_i, y_i \le 2^k$ ), describing the position of the $i$ -th cell of the figure. It is guaranteed that all cells are different, but it is not guaranteed that the figure is connected.

### 输出格式

If it is impossible to make all numbers in the grid equal to $0$ with these operations, output $-1$ . Otherwise, output a single integer — the minimal number of operations needed to do this. It can be shown that if it is possible to make all numbers equal $0$ , it is possible to do so in less than $10^{18}$ operations.

## 输入输出样例

### 输入样例 #1

2
5 5 5 5
2 6 2 3
0 0 2 0
0 0 0 0
5
1 1
1 2
1 3
1 4
2 4


### 输出样例 #1

3

## 说明

The figure and the operations for the example are shown above: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1270I/511777d098f2351e14f6ca9e9eca0ce62e603850.png)