/**
  *矩阵计算类
  */
 class Matrix{
     
     /*
      * 根据字符串解析密钥矩阵
      * param key 密钥
      * param rank 密钥矩阵的阶
      * return 返回密钥矩阵
 */
     public static int[][] getKeyMatrix(String key,int rank){
         key=key.trim();
         String[] akey=key.split(" ");
         int key_len=akey.length;
         int[][] pk=new int[rank][rank];            //密钥矩阵
     
         for(int i=0;i<key_len;i++){
             String num=akey[i];          
             int row=i/rank,col=i%rank;
             pk[row][col]=num.charAt(0)-'0';     //初始化第一位
             for(int j=1;j<num.length();j++){
                 pk[row][col]=pk[row][col]*10+num.charAt(j)-'0';
             }
         }
         return pk;
     }
     
     /* 矩阵a、b相乘，返回矩阵c */
     public static int[][] Multi(int[][] a,int[][] b){
         int row=a.length,
             col=b[0].length,
             rank=b.length;
         int[][] c=new int[row][col];
     
         for(int i=0;i<row;i++){
             for(int j=0;j<col;j++){
                 c[i][j]=0;
                 for(int k=0;k<rank;k++){
                     c[i][j]+=a[i][k]*b[k][j];
                 }
                 c[i][j]%=modular;
             }
         }
         return c;
     }
     
     /* 
      * 计算行列式的值
      * param n 矩阵的阶 
      * param N 矩阵
 */
     public static int Det(int n,int[][] matrix) {
         if (n == 1) {
             return matrix[0][0];
         }
         int[][] matrix2 = new int[n - 1][n - 1];
         int result = 0;
         for (int i = 0; i < n; i++) {            // 去除第0行第i列
             for (int j = 0; j < n-1; j++) {      
                 for (int p = 0; p < i; p++) {    // 上移一行
                     matrix2[j][p] = matrix[j + 1][p];
                 }
                 for (int q = i + 1; q < n; q++) { //右下往左上移
                     matrix2[j][q - 1] = matrix[j + 1][q];
                 }
             }
             result = result + (int) Math.pow(-1, i + 1) * matrix[0][i]  
                     * Det(n - 1, matrix2);
         }
         return result;
     }
     
     /*转置矩阵*/
     public static int[][] tranMatrix(int n,int[][] matrix){
         for(int i=0;i<n;i++)
             for(int j=i+1;j<n;j++){
                 int tmp=matrix[i][j];
                 matrix[i][j]=matrix[j][i];
                 matrix[j][i]=tmp;
             }
         return matrix;
     }
     
     /*代数余子式*/
     public static int getAdjunct(int n,int[][] matrix,int r,int c){
         int[][] matrix2 = new int[n - 1][n - 1];
         int result=0;
         for(int i=0;i<r;i++){                //上半部分
             for(int j=0;j<c;j++) {
                 matrix2[i][j]=matrix[i][j];
             }
             for(int j=c;j<n-1;j++){
                 matrix2[i][j]=matrix[i][j+1];
             }
         }
         for (int i = r; i < n-1; i++) {      //下半部分
             for (int p = 0; p < c; p++) {    
                 matrix2[i][p] = matrix[i + 1][p];
             }
             for (int q = c + 1; q < n; q++) { 
                 matrix2[i][q - 1] = matrix[i + 1][q];
             }
         }
         result=Det(n-1, matrix2);                 //对matrix2求n-1阶行列式
         if((r+c)%2==1) result=-result;
         return result;
     }
     
     /*
      * 矩阵的逆
      * 
 */
     public static int[][] ReverseMatrix(int n,int[][] matrix){
         int[][] matrix2=new int[n][n];
         for(int i=0;i<n;i++)
             for(int j=0;j<n;j++)
                 matrix2[i][j]=matrix[i][j];
         
         int det=Det(n, matrix);
         NumberTheory.extended_gcd(det, modular);
         int inverse=NumberTheory.x;       //乘法逆元
         while(inverse<0)
             inverse+=26;
         for (int i = 0; i < n; i++) {            
             for (int j = 0; j < n; j++) {      
                matrix2[i][j]=(inverse*getAdjunct(n, matrix, j, i))%modular;
                while(matrix2[i][j]<0){
                    matrix2[i][j]+=modular;
                }
             }
         }
         return matrix2;
     }
     private static int modular=26;
 }
 
 class NumberTheory {
     public static int extended_gcd(int a, int b) {
         int ret, tmp;
         if (b == 0) {
             x = 1;
             y = 0;
             return a;
         }
         ret = extended_gcd(b, a % b);
         tmp = x;
         x = y;
         y = tmp - a / b * y;
         return ret;
     }
     public static int x,y;
     public final static int modular=26;
 }