Club Room Repairs

A university had $N$ club rooms. One day a villain wrecked every one of them and drove the clubs out, leaving nothing but rubble.

$M$ clubs are now without a room, and club $i$ holds a budget of $S_i$ won. Each club wants to repair one room out of that budget and use it. Making room $j$ usable again costs $C_j$ won. A room takes at most one club, and a club takes at most one room. A club with money left over after a repair does not hand it to another club.

Jongbin knows how it feels to have no club room, so he helps the clubs that cannot cover a room on their own. When club $i$ is assigned room $j$, the club pays up to $S_i$ won from its own budget and Jongbin covers the shortfall of $\max(0, C_j - S_i)$ won. The total amount Jongbin pays out cannot exceed $X$ won.

Find the largest number of clubs that can end up with a room.

The first line contains $N$, $M$, and $X$. ($1 \le N \le 100000$, $1 \le M \le 100000$, $0 \le X \le 1000000000$)

The second line contains the repair costs $C_1, C_2, \dots, C_N$ of the $N$ rooms in order. ($0 \le C_j \le 1000000000$)

The third line contains the budgets $S_1, S_2, \dots, S_M$ of the $M$ clubs in order. ($0 \le S_i \le 1000000000$)

Print on one line the largest number of clubs that can end up with a room.

Take the case where the repair costs are $5, 8, 9, 1, 7$, the club budgets are $2, 10, 5, 3$, and $X = 3$.

Give the room costing $9$ to the club with budget $10$, the room costing $5$ to the club with budget $5$, and the room costing $1$ to the club with budget $3$. All three clubs cover their own repair, so Jongbin spends nothing and $3$ clubs get a room.

Seating all $4$ clubs would force Jongbin to pay at least $4$ won, which is over the limit of $3$, so four is impossible.