Description:
Sam changed his school and on the first biology lesson he got a very interesting task about genes.
You are given $$$n$$$ arrays, the $$$i$$$-th of them contains $$$m$$$ different integers — $$$a_{i,1}, a_{i,2},\ldots,a_{i,m}$$$. Also you are given an array of integers $$$w$$$ of length $$$n$$$.
Find the minimum value of $$$w_i + w_j$$$ among all pairs of integers $$$(i, j)$$$ ($$$1 \le i, j \le n$$$), such that the numbers $$$a_{i,1}, a_{i,2},\ldots,a_{i,m}, a_{j,1}, a_{j,2},\ldots,a_{j,m}$$$ are distinct.
Input Format:
The first line contains two integers $$$n$$$, $$$m$$$ ($$$2 \leq n \leq 10^5$$$, $$$1 \le m \le 5$$$).
The $$$i$$$-th of the next $$$n$$$ lines starts with $$$m$$$ distinct integers $$$a_{i,1}, a_{i,2}, \ldots, a_{i,m}$$$ and then $$$w_i$$$ follows ($$$1\leq a_{i,j} \leq 10^9$$$, $$$1 \leq w_{i} \leq 10^9$$$).
Output Format:
Print a single number — the answer to the problem.
If there are no suitable pairs $$$(i, j)$$$, print $$$-1$$$.
Note:
In the first test the minimum value is $$$5 = w_3 + w_4$$$, because numbers $$$\{2, 3, 4, 5\}$$$ are distinct.
In the second test case, there are no suitable pair $$$(i, j)$$$.