class Matrix:

    def __init__(self,body,n_rows,m_columns):   #принимает список ,количество строк и столбцов
        self.body=body
        self.n_r=n_rows
        self.m_c=m_columns

    def __add__(self,matrix):
        g=[]
        if self.n_r==matrix.n_r and self.m_c==matrix.m_c:
            for i in range(len(self.body)):
                g.append(self.body[i]+matrix.body[i])
            return Matrix(g,self.n_r,self.m_c)

    def __mul__(self,arg):
        if type(arg)==int or type(arg)==float:
            new_body=[]
            for i in self.body:
                o=i*arg
                new_body.append(o)
            return Matrix(new_body,self.n_r,self.m_c)

        elif type(arg)==Matrix and self.m_c==arg.n_r:
            o=[]
            m=[]
            f=[]
            j=0
            k=0
            while j!=len(self.body) :
                i=self.body[j:j+self.m_c]
                o.append(i)
                j+=self.m_c
            while k!=arg.m_c :
                s=arg.body[k::arg.m_c]
                m.append(s)
                k+=1
            sum_all=0

            for lm in o:
                d=0

                while d!=len(m):
                    sum_all=0

                    for i in range(0,len(lm)):
                        sum_all+=lm[i]*m[d][i]

                    f.append(sum_all)

                    d+=1
            return Matrix(f,self.n_r,arg.m_c)

    def __sub__(self,arg):

        return Matrix((self+(arg*(-1))).body,self.n_r,self.m_c)

    def trace(self):
        if self.n_r==self.m_c:
            sum_all=0
            for i in range(0,self.m_c):
                sum_all+=(self.body[i*self.m_c+i])

            return sum_all

    def transpose(self):
        m=[]
        k=0
        while k!=self.m_c :
            s=self.body[k::self.m_c]
            m.append(s)
            k+=1
        return Matrix(m,self.m_c,self.n_r)

    def __getitem__(self,key):
        return self.body[self.m_c*(key[0]-1)+key[1]-1]

    def __setitem__(self,key,value):
        self.body[self.m_c*(key[0]-1)+key[1]-1]=value