Vive la Difference!
Take any four positive integers: a, b, c, d. Form four more, like this:
|a-b| |b-c| |c-d| |d-a|
That is, take the absolute value of the differences of a with b, b with c, c with d, and d with a. (Note that a zero could crop up, but they’ll all still be non-negative.) Then, do it again with these four new numbers. And then again. And again. Eventually, all four integers will be the same. For example, start with 1, 3, 5, 9:
1 3 5 92 2 4 8 (1)0 2 4 6 (2)2 2 2 6 (3)0 0 4 4 (4)0 4 0 4 (5)4 4 4 4 (6)
In this case, the sequence converged in 6 steps. It turns out that in all cases, the sequence converges very quickly. In fact, it can be shown that if all four integers are less than 2^n, then it will take no more than 3·n steps to converge!Given a, b, c and d, figure out just how quickly the sequence converges.
Input
There will be several test cases in the input. Each test case consists of four positive integers on a single line (1 ≤ a, b, c, d ≤ 2,000,000,000), with single spaces for separation. The input will end with a line with four 0s.
Output
For each test case, output a single integer on its own line, indicating the number of steps until convergence. Output no extra spaces, and do not separate answers with blank lines.