You have won the labour lottery and are now an apartment manager at 100 KRUSHVICE st. There, your job is to ensure that the ~N~ tenants are satisfied, and more important, following the government directives.

In order to do the latter, you plan to install ~K_i~ cameras in tenant ~i~'s room. Camera ~j~ in the ~i^\text{th}~ person's room has a probability of ~P_{i,j}~ of discovering that person doing something illegal. (Note that discovering a person twice has no additional effect). However, due to budget cuts, your number of cameras is limited to ~C~. Determine the maximum expected number of people caught doing something illegal if you only install up to ~C~ cameras, for ALL values of ~C~ from ~1~ to ~\sum_{i=0}^{N-1} K_i~.

Constraints

~1 \le N \le 5 \times 10^5~

~\sum_{i=0}^{N-1} K_i \le 5 \times 10^5~

The probability ~P_{i,j}~ is a real number between ~0~ and ~1~.

Input Specification

Line ~1~: An integer, ~N~, the number of tenants.
Next ~N~ lines: An integer ~K_i~, the number of cameras planned to be installed in the ~i^\text{th}~ person room, and ~K~ real numbers, the values of ~P_{i,j}~.

Output Specification

~\sum_{i=0}^{N-1} K_i~ lines, each with a single real number, the maximum expected value after installing ~C~ ~(1 \le C \le \sum_{i=0}^{N-1} K_i)~ cameras. Your answer will be accepted if it differs from the expected answer by up to ~10^{-6}~.

Sample Input

3
3 0.5 0.5 0.5
2 0.4 0.25
1 0.3

Sample Output

0.50000000
0.90000000
1.20000000
1.45000000
1.60000000
1.72500000

Also note that

0.50000000
0.90000000
1.20000000
1.44999999
1.60000000
1.72500001

is also a valid output, for example.