/******************************************************************************
 *  Compilation:  javac Markov.java
 *  Execution:    java Markov trials
 *  Data files:   https://introcs.cs.princeton.edu/java/16pagerank/tinyG.txt
 *                https://introcs.cs.princeton.edu/java/16pagerank/mediumG.txt
 *
 *  This program reads a transition matrix from standard input and
 *  computes the probabilities that a random surfer lands on each page
 *  (page ranks) after the specified number of matrix-vector multiplies.
 *
 *  % java Transition < tinyG.txt | java Markov 40
 *   0.27303 0.26573 0.14618 0.24723 0.06783
 *
 ******************************************************************************/

public class Markov {

    public static void main(String[] args) {
        int trials = Integer.parseInt(args[0]);  // number of iterations
        int n = StdIn.readInt();                 // number of pages
        StdIn.readInt();                         // ignore integer required by input format


        // Read p[][] from StdIn.
        double[][] p = new double[n][n];         // p[i][j] = prob. surfer moves from page i to page j
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                p[i][j] = StdIn.readDouble();

        // Use the power method to compute page ranks.
        double[] rank = new double[n];
        rank[0] = 1.0;
        for (int t = 0; t < trials; t++) {

            // Compute effect of next move on page ranks.
            double[] newRank = new double[n];
            for (int j = 0; j < n; j++) {
                //  New rank of page j is dot product of old ranks and column j of p[][].
                for (int k = 0; k < n; k++)
                   newRank[j] += rank[k]*p[k][j];
            }

            // Update page ranks.
            rank = newRank;
        }

        // print page ranks
        for (int i = 0; i < n; i++) {
            StdOut.printf("%8.5f", rank[i]);
        }
        StdOut.println();

        StdOut.println();
        // print page ranks
        for (int i = 0; i < n; i++) {
            StdOut.printf("%2d  %5.3f\n", i, rank[i]);
        }
    }
}