The secret code
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 data
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} = 1P_{ij} = 100.
1 \le N_ \le 100
1 \le M_ \le 20
1 \le K_ \le 100
0 \le P_{ij} \le 100
Output data
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
2 2 1 50 50 10 90
0.450000000