Viva la Diferencia

Given four positive integers $a, b, c, d$, form four new numbers by taking the absolute differences of neighbours around a cycle:

$$(,|a-b|,\ |b-c|,\ |c-d|,\ |d-a|,)$$

Apply the same operation to the resulting four numbers, and keep repeating until all four numbers are equal.

For example, starting from $1, 3, 5, 9$:

1  3  5  9
2  2  4  8   (step 1)
0  2  4  6   (step 2)
2  2  2  6   (step 3)
0  0  4  4   (step 4)
0  4  0  4   (step 5)
4  4  4  4   (step 6)

Here the sequence reaches four equal numbers after 6 steps. Given $a, b, c, d$, determine how many steps it takes to converge. If the four numbers are already equal, the answer is $0$.

The input contains several test cases. Each test case is a single line with the four integers $a, b, c, d$ ($1 \le a, b, c, d \le 2 \times 10^9$). The last line contains four zeros and is not processed.

For each test case, print the number of steps until the four numbers become equal.

If all four integers are less than $2^n$, the sequence converges within $3n$ steps.