Score : $700$ points

Problem Statement

In the final of CODE FESTIVAL in some year, there are $N$ participants. The height and power of Participant $i$ is $H_i$ and $P_i$, respectively.

Ringo is hosting a game of stacking zabuton (cushions).

The participants will line up in a row in some order, and they will in turn try to add zabuton to the stack of zabuton. Initially, the stack is empty. When it is Participant $i$'s turn, if there are $H_i$ or less zabuton already stacked, he/she will add exactly $P_i$ zabuton to the stack. Otherwise, he/she will give up and do nothing.

Ringo wants to maximize the number of participants who can add zabuton to the stack. How many participants can add zabuton to the stack in the optimal order of participants?

Constraints

• $1 \leq N \leq 5000$
• $0 \leq H_i \leq 10^9$
• $1 \leq P_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$H_1$ $P_1$

$H_2$ $P_2$

$:$

$H_N$ $P_N$

Output

Print the maximum number of participants who can add zabuton to the stack.

3
0 2
1 3
3 4

2

When the participants line up in the same order as the input, Participants $1$ and $3$ will be able to add zabuton.

On the other hand, there is no order such that all three participants can add zabuton. Thus, the answer is $2$.

3
2 4
3 1
4 1

3

When the participants line up in the order $2$, $3$, $1$, all of them will be able to add zabuton.

10
1 3
8 4
8 3
9 1
6 4
2 3
4 2
9 2
8 3
0 1

5