Marinada '16

Dani su $a_1, a_2, \dots, a_{100} \in \mathbb{R}$ takvi da $$a_1 \geq a_2 \geq \dots \geq a_{100} \geq 0$$ $$a_1^2 + a_2^2 \geq 100$$ $$a_3^2 + \dots + a_{100}^2 \geq 100$$ Koliko najmanje može iznositi $a_1 + a_2 + \dots + a_{100}$?