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 9 2 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.
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.
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.