\[ a^{200} \cdot b^{500} \cdot c^{16} \cdot d^{600} \cdot e^{700}\]

Let \(a,b,c,d\) and \(e\) be positive reals whose sum is 2016, and \(M\) the maximum value of the expression above. Then what is the highest power of 3 that divides \(M ?\)

**Tip** : Wait for the hardest version .

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