Given any integer base `b` >= 2, it is well known
that every positive integer `n` can be uniquely
represented in base `b`. That is, we can write

where the coefficientsn=a_{0}+a_{1}*b+a_{2}*b*b+a_{3}*b*b*b+ ...

What is less well known is that if `p`_{0},
`p`_{1}, `p`_{2}, ... are the first
primes (starting from 2, 3, 5, ...), every positive integer `n` can be
represented uniquely in the "mixed" bases as:

where each coefficientn=a_{0}+a_{1}*p_{0}+a_{2}*p_{0}*p_{1}+a_{3}*p_{0}*p_{1}*p_{2}+ ...

Given a positive integer `n`, you are asked to write
`n` in the representation above. Do not use more primes than
it is needed to represent `n`, and omit all terms in which the
coefficient is 0.

Each line of input consists of a single positive 32-bit signed integer. The end of input is indicated by a line containing the integer 0.

For each integer, print the integer, followed by a space, an equal sign, and a space, followed by the mixed base representation of the integer in the format shown below. The terms should be separated by a space, a plus sign, and a space. The output for each integer should appear on its own line.

123 456 123456 0

123 = 1 + 1*2 + 4*2*3*5 456 = 1*2*3 + 1*2*3*5 + 2*2*3*5*7 123456 = 1*2*3 + 6*2*3*5 + 4*2*3*5*7 + 1*2*3*5*7*11 + 4*2*3*5*7*11*13