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.awt.Point;
import java.io.*;
import java.util.*;

public class Main implements Runnable {

    int maxn = (int)1e5+111;
    int mod = (int)1e9+7;
    int inf = (int)1e9;
    int n,m,k;
    Point a[] = new Point[maxn];

    void solve() throws Exception {

        HashMap<Pair, Point> map = new HashMap<>();

        n = in.nextInt();
        double maxR = 0;
        int id1 = 0;
        int id2 = 0;
        int k = 0;
        for (int i=1; i<=n; i++) {
            int x = in.nextInt();
            int y = in.nextInt();
            int z = in.nextInt();
            double radius = getRadius(x, y, z);
            if (maxR<radius) {
                maxR = radius;
                k = 1;
                id1 = i;
            }

            RadiusId radiusId = calculateAns(map,x,y,z);
            addNewValue(map, x, y, z, i);
            if (maxR<radiusId.r) {
                k = 2;
                id1 = i;
                id2 = radiusId.id;
                maxR = radiusId.r;
            }
        }

        out.println(k);
        if (k==1) {
            out.println(id1);
        } else {
            out.println(id1 + " " + id2);
        }

    }

    private RadiusId calculateAns(HashMap<Pair, Point> map, int x, int y, int z) {
        int id = 0;
        double R = 0.0;

        Pair p1 = new Pair(x,y);
        if (map.containsKey(p1)) {
            double curR = getRadius(x,y,z+ map.get(p1).x);
            if (R<curR) {
                R = curR;
                id = map.get(p1).y;
            }
        }

        Pair p2 = new Pair(y,z);
        if (map.containsKey(p2)) {
            double curR = getRadius(y,z,x + map.get(p2).x);
            if (R<curR) {
                R = curR;
                id = map.get(p2).y;
            }
        }


        Pair p3 = new Pair(x,z);
        if (map.containsKey(p3)) {
            double curR = getRadius(x,z, y+ map.get(p3).x);
            if (R<curR) {
                R = curR;
                id = map.get(p3).y;
            }
        }

        return new RadiusId(R, id);
    }

    class RadiusId {
        double r;
        int id;

        public RadiusId(double r, int id) {
            this.r = r;
            this.id = id;
        }
    }

    private double getRadius(int x, int y, int z) {
        double xR = (x*1.0)/2;
        double yR = (y*1.0)/2;
        double zR = (z*1.0)/2;
        double maxR = Math.min(xR, Math.min(yR, zR));
        return maxR;
    }

    private void addNewValue(HashMap<Pair, Point> map, int x, int y, int z, int i) {

        Pair p1 = new Pair(x,y);
        if (map.containsKey(p1)) {
            if (map.get(p1).x<z) {
                map.put(p1, new Point(z,i));
            }
        } else {
          map.put(p1, new Point(z,i));
        }

        Pair p2 = new Pair(y,x);
        if (map.containsKey(p2)) {
            if (map.get(p2).x<z) {
                map.put(p2, new Point(z,i));
            }
        }else {
          map.put(p2, new Point(z,i));
        }

        Pair p3 = new Pair(y,z);
        if (map.containsKey(p3)) {
            if (map.get(p3).x<x) {
                map.put(p3, new Point(x,i));
            }
        }else {
          map.put(p3, new Point(x,i));
        }

        Pair p4 = new Pair(z,y);
        if (map.containsKey(p4)) {
            if (map.get(p4).x<x) {
                map.put(p4, new Point(x,i));
            }
        } else {
          map.put(p4, new Point(x,i));
        }

        Pair p5 = new Pair(z,x);
        if (map.containsKey(p5)) {
            if (map.get(p5).x<y) {
                map.put(p5, new Point(y,i));
            }
        } else {
          map.put(p5, new Point(y,i));
        }

        Pair p6 = new Pair(x,z);
        if (map.containsKey(p6)) {
            if (map.get(p6).x<y) {
                map.put(p6, new Point(y,i));
            }
        } else {
          map.put(p6, new Point(y,i));
        }
    }

    class Pair {
        int x, y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            return (this.x==((Pair)o).x && this.y==((Pair)o).y);
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }
    }

    String fileInName = "network";
    boolean file = false;
    boolean isAcmp = true;

    static Throwable throwable;
    public static void main (String [] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }

    FastReader in;
    PrintWriter out;

    public void run() {
        String fileIn = "input.txt";
        String fileOut = "output.txt";

        try {
            if (isAcmp) {
                if (file) {
                    in = new FastReader(new BufferedReader(new FileReader(fileIn)));
                    out = new PrintWriter (fileOut);
                } else {
                    in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                    out = new PrintWriter(System.out);
                }
            } else if (file) {
                in = new FastReader(new BufferedReader(new FileReader(fileInName+".in")));
                out = new PrintWriter (fileInName + ".out");
            } else {
                in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                out = new PrintWriter(System.out);
            }

            solve();
        } catch(Exception e) {
            throwable = e;
        } finally {
            out.close();
        }

    }
}

class FastReader {
    BufferedReader bf;
    StringTokenizer tk = null;

    public FastReader(BufferedReader bf) {
        this.bf = bf;
    }

    public String nextToken () throws Exception {
        if (tk==null || !tk.hasMoreTokens()) {
            tk = new StringTokenizer(bf.readLine());
        }
        if (!tk.hasMoreTokens()) return nextToken();
        else
            return tk.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}