Total of a Fraction Chain

Medium

The string chain is a sum and difference of fractions written as numerator/denominator, for example "1/3-1/2+5/6". The first fraction may be preceded by a minus sign; a plus sign is never written in front of it. Evaluate it and return the result as a string holding a fully reduced fraction p/q with a positive denominator. A negative result starts with a minus sign, a positive one has no sign. A whole number is written with denominator 1, such as "2/1", and zero is "0/1".

Example 1

chain="3/4-1/6" → '7/12'

3/4 − 1/6 = 9/12 − 2/12 = 7/12.

Example 2

chain="-2/3+1/6+1/2" → '0/1'

−4/6 + 1/6 + 3/6 = 0, and zero is written as 0/1.

Example 3

chain="5/2+3/2" → '4/1'

The sum is 4, a whole number, so the answer is 4/1.

Constraints

the chain holds 1 to 10 fractions
every numerator and denominator is an integer from 1 to 10
the string contains only digits and the characters /, +, -

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Topics

Math String Simulation

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Input

chain="3/4-1/6"

Expected

'7/12'

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