Problem: Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere. 

Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya. 

If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way. 

Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.

Input

The first line contains the integer n (1 ≤ n ≤ 105).

n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.

Output

In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.

You can print the stones in arbitrary order. If there are several answers print any of them. 

Examples

Input

6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4


Output

1
1


Input

7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7


Output

2
1 5

Note

In the first example we can connect the pairs of stones:

  * 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
  * 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively. 
  * 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
  * 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
  * 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5



Or take only one stone:

  * 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
  * 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
  * 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
  * 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
  * 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
  * 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5



It is most profitable to take only the first stone. 

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.TreeMap;
import java.io.IOException;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Aman Kumar Singh
 */
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);
        DKostyaTheSculptor solver = new DKostyaTheSculptor();
        solver.solve(1, in, out);
        out.close();
    }

    static class DKostyaTheSculptor {
        int MAXN = 200005;
        PrintWriter out;
        InputReader in;
        final Comparator<Tuple> com = new Comparator<Tuple>() {
            public int compare(Tuple t1, Tuple t2) {
                if (t1.x != t2.x)
                    return Integer.compare(t1.x, t2.x);
                else
                    return Integer.compare(t1.y, t2.y);
            }
        };

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.out = out;
            this.in = in;
            int n = ni();
            int[][] max = new int[MAXN * 20][2];
            TreeMap<Tuple, Integer> tmap = new TreeMap<>(com);
            int i = 0;
            double mx = -1.0;
            int[] indexes = new int[2];
            Arrays.fill(indexes, -1);
            int[][] hola = new int[n][3];
            int c = 0;
            for (i = 0; i < n; i++) {
                TreeMap<Tuple, Integer> local = new TreeMap<>(com);
                hola[i][0] = ni();
                hola[i][1] = ni();
                hola[i][2] = ni();
                if (tmap.containsKey(new Tuple(Math.min(hola[i][0], hola[i][1]), Math.max(hola[i][0], hola[i][1])))) {
                    int ind = tmap.get(new Tuple(Math.min(hola[i][0], hola[i][1]), Math.max(hola[i][0], hola[i][1])));
                    double p = Math.min(max[ind][0] + hola[i][2], Math.min(hola[i][0], hola[i][1]));
                    if (mx < p / 2.0) {
                        mx = p / 2.0;
                        indexes = new int[]{max[ind][1] + 1, i + 1};
                    }
                }
                if (tmap.containsKey(new Tuple(Math.min(hola[i][0], hola[i][2]), Math.max(hola[i][0], hola[i][2])))) {
                    int ind = tmap.get(new Tuple(Math.min(hola[i][0], hola[i][2]), Math.max(hola[i][0], hola[i][2])));
                    double p = Math.min(max[ind][0] + hola[i][1], Math.min(hola[i][0], hola[i][2]));
                    if (mx < p / 2.0) {
                        mx = p / 2.0;
                        indexes = new int[]{max[ind][1] + 1, i + 1};
                    }
                }
                if (tmap.containsKey(new Tuple(Math.min(hola[i][1], hola[i][2]), Math.max(hola[i][1], hola[i][2])))) {
                    int ind = tmap.get(new Tuple(Math.min(hola[i][1], hola[i][2]), Math.max(hola[i][1], hola[i][2])));
                    double p = Math.min(max[ind][0] + hola[i][0], Math.min(hola[i][1], hola[i][2]));
                    if (mx < p / 2.0) {
                        mx = p / 2.0;
                        indexes = new int[]{max[ind][1] + 1, i + 1};
                    }
                }
                Integer x = local.get(new Tuple(Math.min(hola[i][0], hola[i][1]), Math.max(hola[i][0], hola[i][1])));
                if (x == null)
                    local.put(new Tuple(Math.min(hola[i][0], hola[i][1]), Math.max(hola[i][0], hola[i][1])), hola[i][2]);
                else
                    local.put(new Tuple(Math.min(hola[i][0], hola[i][1]), Math.max(hola[i][0], hola[i][1])), Math.max(hola[i][2], x));
                x = local.get(new Tuple(Math.min(hola[i][0], hola[i][2]), Math.max(hola[i][0], hola[i][2])));
                if (x == null)
                    local.put(new Tuple(Math.min(hola[i][0], hola[i][2]), Math.max(hola[i][0], hola[i][2])), hola[i][1]);
                else
                    local.put(new Tuple(Math.min(hola[i][0], hola[i][2]), Math.max(hola[i][0], hola[i][2])), Math.max(hola[i][1], x));
                x = local.get(new Tuple(Math.min(hola[i][1], hola[i][2]), Math.max(hola[i][1], hola[i][2])));
                if (x == null)
                    local.put(new Tuple(Math.min(hola[i][1], hola[i][2]), Math.max(hola[i][1], hola[i][2])), hola[i][0]);
                else
                    local.put(new Tuple(Math.min(hola[i][1], hola[i][2]), Math.max(hola[i][1], hola[i][2])), Math.max(hola[i][0], x));
                for (Tuple lol : local.keySet()) {
                    x = local.get(lol);
                    if (tmap.containsKey(lol)) {
                        int ind = tmap.get(lol);
                        if (max[ind][0] < x) {
                            max[ind][0] = x;
                            max[ind][1] = i;
                        }
                    } else {
                        tmap.put(lol, c++);
                        int ind = tmap.get(lol);
                        if (max[ind][0] < x) {
                            max[ind][0] = x;
                            max[ind][1] = i;
                        }
                    }
                }
            }
            double mx1 = -1.0;
            int mn_ind = -1;
            for (i = 0; i < n; i++) {
                double p = Math.min(hola[i][0], Math.min(hola[i][1], hola[i][2]));
                if (mx1 < p / 2.0) {
                    mx1 = p / 2.0;
                    mn_ind = i + 1;
                }
            }
            if (mx > mx1) {
                pn(2);
                pn(indexes[0] + " " + indexes[1]);
            } else {
                pn(1);
                pn(mn_ind);
            }
        }

        int ni() {
            return in.nextInt();
        }

        void pn(long zx) {
            out.println(zx);
        }

        void pn(String zx) {
            out.println(zx);
        }

        class Tuple {
            int x;
            int y;

            Tuple(int a, int b) {
                x = a;
                y = b;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new UnknownError();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}