409388: GYM103496 B1 Basketbology (Decision)

Cindy was tasked with organizing her school's sportsfest this year. In addition to normal competitions like volleyball, tug of war, and an actual basketball match, Cindy thinks that it would be exciting to start off the sportsfest with a special basketball jump shot competition.

She has chosen $$$n$$$ of her classmates to participate in the jump shot competition. There are $$$n$$$ marks on the ground (drawn in chalk), placed such that the $$$i$$$th mark is $$$x_i$$$ units away from the basket. Cindy will assign one person to each mark, and she tells each person to stand at their assigned mark. Each person will then be asked to try to shoot the ball into the basket from their respective locations. For each classmate, we know their "skill level" is some numerical value $$$c_i$$$, meaning that they will successfully land their shot if and only if they shoot from a distance of $$$c_i$$$ units from the basket or closer.

Cindy believes that the sportsfest will start with a bang if all her classmates successfully land their shot. Is it possible to assign the students to the marks in such a way that each of them successfully lands their shot?

The first line of input contains a single integer $$$n$$$.

The second line of input contains $$$n$$$ space-separated integers $$$x_1, x_2, \dots, x_n$$$, the distances of each mark from the basket.

The third line of input contains $$$n$$$ space-separated integers $$$c_1, c_2, \dots, c_n$$$, the skill levels of Cindy's classmates.

Output YES if it is possible to have every student successfully land their shot, and NO otherwise.

$$$$$$\begin{align*}

&\begin{array}{|l|} \hline \text{Constraints For All Subtasks} \\ \hline 1 \leq x_1 < x_2 < \dots < x_n \leq 12345 \\ \text{$1 \leq c_i \leq 12345$} \\ \hline \end{array}\\

&\begin{array}{|c|c|l|} \hline \text{Subtask} & \text{Points} & \text{Constraints} \\ \hline 1 & \mathbf{25} & 1 \leq n \leq 3 \\ \hline 2 & \mathbf{25} & 1 \leq n \leq 8 \\ \hline 3 & \mathbf{25} & 1 \leq n \leq 20 \\ \hline 4 & \mathbf{25} & 1 \leq n \leq 12345 \\ \hline \end{array}\\

\end{align*}$$$$$$

3
10 15 20
28 16 18

YES

3
10 15 20
24 13 13

NO

In the first sample input, one possible configuration is to assign the first student to the third mark (because $$$28 \geq 20$$$), the second student to the first mark (because $$$16 \geq 10$$$), and the third student to the second mark (because $$$18 \geq 15$$$).

In the second sample input, none of the assignments are valid.