Telescope

Byteasar is going to watch a meteor shower tonight, and he has an exact forecast of its course. The shower is made up of $n$ meteors; the $i$-th meteor appears $t_i$ seconds after midnight, so it is visible during the time interval from moment $t_i - 1$ to moment $t_i$. Byteasar counts a meteor as observed only if he watches it for the entire time it is visible.

Byteasar will look at the sky from a nearby hill through a telescope. The telescope is coin-operated: for every $c$ bythalers inserted it lets him watch the sky for exactly $c$ seconds. The device is a little worn, so after a coin is inserted he must wait $r$ seconds before anything becomes visible. Only one coin is accepted at a time, so if he inserts a coin worth $c$, the next coin can be accepted only after at least $r + c$ seconds have passed.

Byteasar has $m$ coins in his pocket, worth $c_1, \dots, c_m$ bythalers, and will use them to pay for the telescope. Determine the maximum number of meteors he can observe.

The first line contains three integers $n$, $m$, and $r$ ($1 \le n \le 100$, $1 \le m \le 10$, $1 \le r \le 10^8$). The second line contains $n$ integers $t_1, \dots, t_n$ in increasing order ($1 \le t_i \le 10^8$). The third line contains $m$ integers $c_1, \dots, c_m$ ($1 \le c_i \le 10^8$).

Print one integer: the maximum number of meteors Byteasar can observe with the telescope.

In the figure above, the black rectangles mark the seconds during which each meteor is visible. To observe 6 meteors in the sample, Byteasar inserts his coins at moments $-2$, $2$, and $9$, using the values $1$, $5$, and $2$ bythalers in that order.