Find the Minimum

Algebra Level 4

Let x,y,zx, y, z, and aa be positive real numbers such that x+y+z+a=1x + y + z + a = 1. What is the minimum value of

1x+1y+4z+16a\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{4}{z}+\dfrac{16}{a}

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