Problem Statement

We have $K$ sequences. The $i$-th sequence $A_i$ has the length of $N_i$.

Takahashi and Aoki will play a game using these. They will alternately do the following operation until the length of every sequence becomes $1$:

• Choose a sequence of length at least $2$, and delete its first or last element.

Takahashi goes first. Takahashi wants to maximize the sum of the $K$ elements remaining in the end, while Aoki wants to minimize it.

Find the sum of the $K$ elements remaining in the end when both players play optimally.

Constraints

• All values in input are integers.
• $1 \leq K \leq 2 \times 10^5$
• $1 \leq N_i$
• $\sum_i N_i \leq 2 \times 10^5$
• $1 \leq A_{i, j} \leq 10^9$

Input

Input is given from Standard Input in the following format:

K
N_1 A_{1, 1} A_{1, 2} \cdots A_{1, N_1}
N_2 A_{2, 1} A_{2, 2} \cdots A_{2, N_2}
\vdots
N_K A_{K, 1} A_{K, 2} \cdots A_{K, N_K}

Output

Print the answer.