Problem: Harry Potter has a difficult homework. Given a rectangular table, consisting of n × m cells. Each cell of the table contains the integer. Harry knows how to use two spells: the first spell change the sign of the integers in the selected row, the second — in the selected column. Harry's task is to make non-negative the sum of the numbers in each row and each column using these spells.

Alone, the boy can not cope. Help the young magician!

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 100) — the number of rows and the number of columns. 

Next n lines follow, each contains m integers: j-th integer in the i-th line is ai, j (|ai, j| ≤ 100), the number in the i-th row and j-th column of the table.

The rows of the table numbered from 1 to n. The columns of the table numbered from 1 to m.

Output

In the first line print the number a — the number of required applications of the first spell. Next print a space-separated integers — the row numbers, you want to apply a spell. These row numbers must be distinct!

In the second line print the number b — the number of required applications of the second spell. Next print b space-separated integers — the column numbers, you want to apply a spell. These column numbers must be distinct!

If there are several solutions are allowed to print any of them.

Examples

Input

4 1
-1
-1
-1
-1


Output

4 1 2 3 4 
0 


Input

2 4
-1 -1 -1 2
1 1 1 1


Output

1 1 
1 4 

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    private int n, m;
    private int[][] a;
    private int[] col, row;
    private int[] sum_col, sum_row;

    private int FindRow() {
        for(int i = 0; i < n; ++i)
            if (sum_row[i] < 0) return i;
        return -1;
    }

    private int FindCol() {
        for(int j = 0; j < m; ++j)
            if (sum_col[j] < 0) return j;
        return -1;
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        n = in.nextInt(); m = in.nextInt();
        a = new int[n][m];
        col = new int[m];
        sum_col = new int[m];
        row = new int[n];
        sum_row = new int[n];
        for(int i = 0; i < n; ++i)
            for(int j = 0; j < m; ++j) {
                a[i][j] = in.nextInt();
                sum_col[j] += a[i][j];
                sum_row[i] += a[i][j];
            }

        do {
            int i = FindRow();
            if (i > -1) {
                for(int j = 0; j < m; ++j) {
                    sum_col[j] -= a[i][j];
                    a[i][j] *= -1;
                    sum_col[j] += a[i][j];
                }
                sum_row[i] *= -1;
                ++row[i];
                continue;
            }
            int j = FindCol();
            if (j > -1) {
                for(i = 0; i < n; ++i) {
                    sum_row[i] -= a[i][j];
                    a[i][j] *= -1;
                    sum_row[i] += a[i][j];
                }
                ++col[j];
                sum_col[j] *= -1;
                continue;
            }
            break;
        } while (true);

        int resr = 0, resc = 0;
        for(int i = 0; i < n; ++i)
            resr += row[i] % 2;
        for(int j = 0; j < m; ++j)
            resc += col[j] % 2;
        out.print(resr + " ");
        for(int i = 0; i < n; ++i)
            if (row[i] % 2 == 1) out.print((i + 1) + " ");
        out.println();
        out.print(resc + " ");
        for(int j = 0; j < m; ++j)
            if (col[j] % 2 == 1) out.print((j + 1) + " ");
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        } catch (Exception e) {
            throw new UnknownError(e.getMessage());
        }
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

}