Fun with fractions

A rational number is the ratio of two integers. Given a numerator $n$ and a denominator $d$, we write the fraction as $n/d$. A rational number has more than one representation. For example, $1/2$ and $2/4$ have the same value. A representation $n/d$ with $\gcd(|n|, |d|) = 1$ is in lowest terms. So $1/2$ is in lowest terms and $2/4$ is not.

Addition of rational numbers is defined below. The right side is not guaranteed to be in lowest terms.

$\frac{n_1}{d_1} + \frac{n_2}{d_2} = \frac{n_1 d_2 + n_2 d_1}{d_1 d_2}$

A rational number whose numerator is at least as large as its denominator can be written as a mixed number, which has an integer part and a fractional part. For example, $5\frac{1}{3}$ is the mixed number that equals $16/3$.

Read a sequence of rational numbers and print their sum.

The input holds several tests. The first line of each test has an integer $n$ ($1 \le n < 1000$). A line holding $n = 0$ ends the input.

The next $n$ lines each hold one string with no spaces. Each string is one rational number in one of the three forms below, and it may not be in lowest terms. $w$, $n$, and $d$ are integers with $0 \le w, n < 1000$ and $1 \le d < 1000$.

• w,n/d: a mixed number equal to $(w \times d + n) / d$
• n/d: a rational number whose integer part is 0
• w: an integer whose fractional part is 0

For each test print one line that begins with Test x: , followed by the sum in lowest terms. Here $x$ is the test number counting from 1.

If the sum has integer part $w$ and fractional part $n/d$, print it as w,n/d when both parts are present, as w when only the integer part is present, and as n/d when only the fractional part is present. If neither part is present, print 0.