Kostya the Sculptor

题意翻译

Kostya 是一个雕刻家。他有一个主意：雕刻一个球形的雕塑。Kostya有n个长方体的石块，长，宽，高分别为a[i],b[i],c[i]。如果2个石块有一面完全相同，那么他可以将这两个石块拼在一起。石块可以翻转。他最多可以选择2个石块拼在一起。输出他可以做出的最大的球。（即长方体的内接球） ##### 输入 第一行一个正整数n，接下来n行，每行输入3个正整数a[i],b[i],c[i]，长，宽，高。 ##### 输出 第一行一个正整数k(k<=2)，Kostya使用的石块的个数。 第二行，Kostya使用的石块的编号。

题目描述

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 $ a_{i} $ , $ b_{i} $ and $ c_{i} $ . 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.

输入输出格式

输入格式

The first line contains the integer $ n $ ( $ 1<=n<=10^{5} $ ). $ n $ lines follow, in the $ i $ -th of which there are three integers $ a_{i},b_{i} $ and $ c_{i} $ ( $ 1<=a_{i},b_{i},c_{i}<=10^{9} $ ) — 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.

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

1
1

输入样例 #2

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

输出样例 #2

2
1 5

说明

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.