Problem Statement

There are $N$ bags numbered $1,2,\dots,N$ and $1$ box with nothing inside.
Bag $i$ $(1 \leq i \leq N)$ contains $T_{i}$ stones, and the mass of the $j$-th $(1 \leq j \leq T_{i})$ of these stones is $A_{i,j}$.

Using these bags, stones, and box, Koa performs the following operation for $i=1,2,\dots,N$ in this order.

1. First, freely choose $1$ bag containing at least $1$ stone, and put all the stones in it into the box.

2. Next, let $n$ be the number of stones in the box. Among these $n$ stones, choose $1$ stone at random from those satisfying the following condition.
   Here, let $x = \min(K_{i}, n)$.

   • When the masses of the $n$ stones are written in descending order as $a_{1}, a_{2}, \dots, a_{n}$ $(a_{1} \geq a_{2} \geq \cdots \geq a_{n})$, the stone's own mass is equal to $a_{x}$.

3. Finally, take all $n-1$ stones other than the chosen stone out of the box and eat them.

After the operations for all $i$ have been finished, find the maximum possible mass of the only $1$ stone remaining in the box.

Constraints

• $1 \leq N \leq 10^{5}$

• $1 \leq T_{i} \leq 10^{5}$ $(1 \leq i \leq N)$

• The sum of $T_{1}, T_{2}, \dots, T_{N}$ is at most $10^{5}$

• $1 \leq A_{i,j} \leq 10^{9}$ $(1 \leq i \leq N \text{ and } 1 \leq j \leq T_{i})$

• $1 \leq K_{i} \leq 3 \times 10^{5}$ $(1 \leq i \leq N)$

• All input values are integers

Input

The input is given in the following format.

$N$
$K_{1}$ $K_{2}$ $\cdots$ $K_{N}$
$T_{1}$
$A_{1,1}$ $A_{1,2}$ $\cdots$ $A_{1,T_{1}}$
$T_{2}$
$A_{2,1}$ $A_{2,2}$ $\cdots$ $A_{2,T_{2}}$
  $\vdots$
$T_{N}$
$A_{N,1}$ $A_{N,2}$ $\cdots$ $A_{N,T_{N}}$

• Line $1$ contains $N$

• Line $2$ contains $K_{1}, K_{2}, \dots, K_{N}$ in this order, separated by single-byte spaces

• Line $2 i + 1$ $(1 \leq i \leq N)$ contains $T_{i}$

• Line $2 i + 2$ $(1 \leq i \leq N)$ contains $A_{i,1}, A_{i,2}, \dots, A_{i,T_{i}}$ in this order, separated by single-byte spaces

Output

Output the answer on $1$ line.

Sample

3
3 1 2
2
1 2
5
7 9 5 3 9
4
10 8 6 4

9

5
2 2 2 1 2
1
1
1
10
1
100
1
1000
1
10000

1000

9
4 2 10 7 3 300000 7 1 5
5
7 1433 233 441445814 14
8
84906649 75121583 12 603415 10147 199004 65221 151278232
7
129002 468 235 250 1144 38994 1070804
10
122230317 19048460 168635 817 24296790 17 6404 49328 194386 61986
5
18 11 408 1 2
1
7
10
339112 57 159599 209673 234036624 277265898 34115930 17787 13825 20151
9
16 2337 557 185983 823 47160 712213 20538 100
3
829 10 9307

603415