Statement

Ookami is a werewolf girl. She studies in NFLS Class 8 Junior 3.

Having had too little for breakfast, she is hungry after 3 lessons in the morning. She wanted to have lunch ASAP. She remembered that in the ancient time, the werewolves would get together to eat when the hour hand coincides the minute hand on a simple round clock.

Now it is A:B in the morning, Ookami wants to know after how many minutes she would have her k-th meal if she lived in ancient time?

Input

In each testcase, there's one line contains 3 integers: A,B,K

Proceed to the EOF

Output

The answer. Your answer will be considered correct if it's relative error doesn't exceed 1e-6.

Example

In:
0 0 1
11 59 1
0 0 2
Out:
0.000000
1.000000
65.454545

Subtask

There are 11 testcases.

Testcase 1: $K=1$

Testcase 2-11: $1\leq K\leq 32768$

For all testcases, $0\leq A\leq 11,0\leq B\leq 59$

There will be no more than 1e5 cases in one testcase.