The secret code

After returning from the trip, Alex was unpleasantly surprised: his porch door had a new combination lock. Alex can not get into his house! Code lock contains $N$ disks, each of which can be in one of $M$ positions. There is only one correct position. Alex thoroughly inspected discs and by fingerprints and scratches determined the probability of each position for each disk. Now Alex has $K$ attempts to guess the correct code: if he fails, his vigilant neighbors will call the police, and Alex will have a hard time persuading cops that he is not a thief, but tried to get home. Help Alex to calculate the maximum probability of getting home, not to the police.

Input

The first line of input file contains three integers: $N$, $M$ та $K$.

Next $N$ lines contain $M$ integers each: $j$-th number $i$-th line ($P_{ij}$) – the probability of a situation where $i$-th disc's correct position is $j$. Given that $M_j=1$ $P_{ij}=100$.

$1\le N_{\le }100$

$1\le M_{\le }20$

$1\le K_{\le }100$

$0\le P_{ij}\le 100$

Output

Print a single number – Alex's chances to guess the correct code in time. Output result should have an absolute percentage error not grater than $10^{-7}$.

Examples