\[\Large \lfloor \log (x) \rfloor + \lfloor \log (y) \rfloor + \lfloor \log (z) \rfloor = 140 \]

If the number of positive integral solutions to above equation can be expressed in the form of \(a^{b}\times c^{d} \times e^{f} \times g^{h} \times i^{j}\), where \(a\), \(c\), \(e\), \(g\) and \(i\) are distinct positive primes and \(b\), \(d\), \(f\), \(h\) and \(j\) are positive integers. Then find the value of

\[ a+b+c+d +e+f+g+h+i+j \]

**Details and Assumptions**

\(\lfloor k \rfloor \) represents the greatest integer less than or equal to \(k\).

\(\log k\) is the logarithm of \(k\) to the base 10.

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