Sticks

Little Johnny received a birthday present from his grandparents: a box of sticks of various lengths and colours. Johnny wonders whether he can pick three sticks that form a triangle whose three sides all have different colours. He only cares about non-degenerate triangles, that is, triangles with positive area.

Among all triangles that can be built from three sticks of three pairwise-different colours, find the one with the largest perimeter and report that perimeter.

The first line contains an integer $k$ ($3 \le k \le 50$), the number of different stick colours. The colours are numbered from $1$ to $k$.

Each of the next $k$ lines describes the sticks of one colour. Line $i+1$ describes the sticks of colour $i$: it begins with an integer $n_i$ ($1 \le n_i \le 1{,}000{,}000$), the number of sticks of that colour, followed on the same line by $n_i$ integers separated by single spaces, the lengths of those sticks. Every length is a positive integer not exceeding $1{,}000{,}000{,}000$. The total number of sticks does not exceed $1{,}000{,}000$.

Print a single line.

If at least one triangle with three pairwise-different-coloured sides and positive area can be formed, print the maximum possible perimeter of such a triangle (the sum of its three side lengths).

Otherwise, print -1.

A triangle with sides $a \le b \le c$ has positive area (is non-degenerate) exactly when $a + b > c$.