Cool Inequality #8 - Changing the rules

$\large{{ a }_{ 1 }^{ 2 }{ a }_{ 2 }+{ a }_{ 2 }^{ 2 }{ a }_{ 3 }+......+{ a }_{ 100 }^{ 2 }{ a }_{ 1 }}$

Let $a_{i}$ represent non-negative real numbers such that $a_{1}^{2}+a_{2}^{2}+......+a_{100}^{2}=1$ then find the maximum value of above expression. Answer upto 4 decimal places