编写一个Matrix类，实现下列要求：能够输入、输出矩阵，执行矩阵转置，加减法（包括负数）、乘法,将矩阵输出；根据主函数的要求编写；保证数据合法； 备注：（752）

以下是Matrix类的实现：

#include <iostream>
#include <vector>

using namespace std;

class Matrix {
private:
    int rows;
    int cols;
    vector<vector<int>> data;

public:
    // 构造函数
    Matrix(int r, int c) {
        rows = r;
        cols = c;
        data.resize(rows);
        for (int i = 0; i < rows; i++) {
            data[i].resize(cols);
        }
    }

    // 输入矩阵
    void input() {
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                cin >> data[i][j];
            }
        }
    }

    // 输出矩阵
    void output() {
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                cout << data[i][j] << " ";
            }
            cout << endl;
        }
    }

    // 矩阵转置
    void transpose() {
        vector<vector<int>> newData(cols, vector<int>(rows));
        for (int i = 0; i < cols; i++) {
            for (int j = 0; j < rows; j++) {
                newData[i][j] = data[j][i];
            }
        }
        data = newData;
        swap(rows, cols);
    }

    // 矩阵加法
    Matrix operator+(const Matrix& other) const {
        if (rows != other.rows || cols != other.cols) {
            throw invalid_argument("Invalid matrix size for addition!");
        }
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result.data[i][j] = data[i][j] + other.data[i][j];
            }
        }
        return result;
    }

    // 矩阵减法
    Matrix operator-(const Matrix& other) const {
        if (rows != other.rows || cols != other.cols) {
            throw invalid_argument("Invalid matrix size for subtraction!");
        }
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result.data[i][j] = data[i][j] - other.data[i][j];
            }
        }
        return result;
    }

    // 矩阵乘法
    Matrix operator*(const Matrix& other) const {
        if (cols != other.rows) {
            throw invalid_argument("Invalid matrix size for multiplication!");
        }
        Matrix result(rows, other.cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < other.cols; j++) {
                for (int k = 0; k < cols; k++) {
                    result.data[i][j] += data[i][k] * other.data[k][j];
                }
            }
        }
        return result;
    }

    // 取负
    Matrix operator-() const {
        Matrix result(rows, cols);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                result.data[i][j] = -data[i][j];
            }
        }
        return result;
    }
};

下面是一个示例主函数，用于测试Matrix类的各种功能：

int main() {
    int r1, c1;
    cout << "Enter the size of the first matrix (rows columns): ";
    cin >> r1 >> c1;
    Matrix m1(r1, c1);
    cout << "Enter the first matrix:" << endl;
    m1.input();

    int r2, c2;
    cout << "Enter the size of the second matrix (rows columns): ";
    cin >> r2 >> c2;
    Matrix m2(r2, c2);
    cout << "Enter the second matrix:" << endl;
    m2.input();

    cout << "The first matrix is:" << endl;
    m1.output();
    cout << "The second matrix is:" << endl;
    m2.output();

    cout << "The transpose of the first matrix is:" << endl;
    m1.transpose().output();

    try {
        Matrix m3 = m1 + m2;
        cout << "The sum of the two matrices is:" << endl;
        m3.output();
    } catch (const invalid_argument& e) {
        cout << e.what() << endl;
    }

    try {
        Matrix m4 = m1 - m2;
        cout << "The difference of the two matrices is:" << endl;
        m4.output();
    } catch (const invalid_argument& e) {
        cout << e.what() << endl;
    }

    try {
        Matrix m5 = m1 * m2;
        cout << "The product of the two matrices is:" << endl;
        m5.output();
    } catch (const invalid_argument& e) {
        cout << e.what() << endl;
    }

    cout << "The negative of the first matrix is:" << endl;
    (-m1).output();

    return 0;
}