Sign Profile

Consider a polynomial $f(x)$ like the one plotted below. For
sufficiently small (large negative magnitude) values of
$x$, the function
$f(x)$ has a negative
value. As $x$ gets larger
(more positive), $f(x)$
become positive, then negative again, then positive again. We
could describe the left-to-right behavior of this curve with
the string “`-+-+`”.

For curves like this, we say the sign profile is a string of
`+` and `-`
characters. If $\lim _{x
\rightarrow -\infty } f(x) < 0$, the string starts
with `-`. Otherwise, it starts with
`+`. Each time the curve crosses the
$X$ axis, we append
another character to the string that has the opposite sign of
its predecessor. Thus, the sign profile is a sequence of
alternating `+` and `-` characters that describes the sign of the
curve from left to right. If $\lim _{x \rightarrow \infty } f(x) <
0$, the string ends with `-`.
Otherwise it ends with `+`.

Input consists of up to 100 test cases, one per line. Each test case consists of four real numbers, $c_0$, $c_1$, $c_2$ and $c_3$, some of which may be zero. Each is in the range $[-100,100]$ with at most $8$ digits past the decimal point. These values give the coefficients of a polynomial $f( x ) = c_0 + c_1 x + c_2 x^2 + c_3 x^3$. The end of input is marked with values of zero for all coefficients. The input data will be such that the answer will not change if any of the non-zero coefficients are changed by $10^{-6}$ or less.

For each test case, print out a line giving the sign profile of $f(x)$.

Sample Input 1 | Sample Output 1 |
---|---|

-1 -3 4 -1 -1 0 -5 5 -0.2 0 1 0 0 0 0 0 |
+-+- -+ +-+ |