PAMO 2002 Problem 6

If $a_1 \geq a_2 \geq \cdots \geq a_n \geq 0$ and $a_1+a_2+\cdots+a_n=1$ , then prove: $$a_1^2+3a_2^2+5a_3^2+ \cdots +(2n-1)a_n^2 \leq 1$$