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Given three numbers such that $0 < a < b < c < 1$, define

$A = a^{a}b^{b}c^{c}, \quad B = a^{a}b^{c}c^{b} , \quad C = a^{b}b^{c}c^{a}.$

How do the values of $A, B, C$ compare to each other?

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