import java.util.ArrayList;
import java.util.Scanner;

public class MatrixChainMultiplicationTest {
	private static Scanner scan = new Scanner(System.in);
	private static ArrayList<Matrix> mArray = new ArrayList<>();
	private static int size;
	private static int[][] m;
	private static int[][] s;
	private static int[] p;
	
	public static void main(String[] args) {
		int count = 1;
		while(true) {
			String [] mSize = input("input size of matrix A("+count+") ( ex. 10 20 ) : ");
			int col = Integer.parseInt(mSize[0]);
			if (col==0) break;
			int row = Integer.parseInt(mSize[1]);
			
			Matrix matrix = new Matrix(count, col, row);
			mArray.add(matrix);
			count++;	
		}
		for(Matrix m : mArray) {
			System.out.format("A(%d)  =  %2d  x  %2d\n", m.count(), m.col(), m.row());
		}
		
		size = mArray.size();
		m = new int[size + 1][size + 1];
		s = new int[size + 1][size + 1];
		p = new int[size + 1];

		for (int i=0; i<size+1; i++) {
			for (int j=0; j<size+1; j++) {
				m[i][j] = -1;
				s[i][j] = -1;
			}
		}

		for (int i=0; i<p.length; i++) {
			if (i == 0) {
				p[i] = mArray.get(i).col();
			} else {
				p[i] = mArray.get(i-1).row();
			}
		}
		
		matrixChainOrder();
		for(int i=0; i<size; i++) { System.out.print("-------"); }
		System.out.println();
		printArray(m);
		for(int i=0; i<size; i++) { System.out.print("-------"); }
		System.out.println();
		printArray(s);
		for(int i=0; i<size; i++) { System.out.print("-------"); }
		System.out.println();
		
		System.out.println("Optimal solution : "+ m[1][size]);
		System.out.print("Optimal parens : ");
		printOptimalParens(1, size);
	}
	private static void printOptimalParens(int i, int j) {
		if (i == j) {
			System.out.print("A" + i);
		} else {
			System.out.print("(");
			printOptimalParens(i, s[i][j]);
			printOptimalParens(s[i][j] + 1, j);
			System.out.print(")");
		}
	}
	private static void printArray(int[][] array) {
		for (int i = 1; i < size+1; i++) {
			for (int j = 1; j < size+1; j++) {
				System.out.print(String.format("%7d", array[i][j]));
			}
			System.out.println();
		}
	}
	
	private static void matrixChainOrder() {
		for (int i = 1; i<size+1; i++) {
			m[i][i] = 0;
		}

		for (int l = 2; l <size+1; l++) {
			for (int i = 1; i<size-l+2; i++) {
				int j = i+l-1;
				m[i][j] = Integer.MAX_VALUE;

				for (int k = i; k < j; k++) {
					int q = m[i][k] + m[k+1][j] + p[i-1] * p[k] * p[j];
					if (q < m[i][j]) {
						m[i][j] = q;
						s[i][j] = k;
					}
				}
			}
		}
	}
	
	private static String[] input(String string) {
		System.out.print(string);
		return (scan.nextLine().split(" ") );
	}

}
class Matrix {
	private int count;
	private int col;
	private int row;
	public Matrix(int count, int col, int row) {
		this.count = count;
		this.col = col;
		this.row = row;
	}
	public int count() { return this.count; }
	public int col() { return this.col; }
	public int row() { return this.row; }
}