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E - Battles in a Row

Problem Statement

Takahashi is about to play a game where he fights N monsters in order. Initially, Takahashi's health is H and his magic power is M.

For the i-th monster he fights, he can choose one of the following actions:

Fight without using magic. This can only be chosen when his health is at least $A i$ , and his health decreases by $A i$ and the monster is defeated. Fight using magic. This can only be chosen when his magic power is at least $B i$ , and his magic power decreases by $B i$ and the monster is defeated. The game ends when all N monsters are defeated or when he cannot take any action. What is the maximum number of monsters he can defeat before the game ends?

Constraints

$1≤N≤3000$

$1≤H,M≤3000$

$1≤A_i ,B_i ≤3000$

All input values are integers.

Input

The input is given from Standard Input in the following format:

$N H M$

$A_1$ $B_1$
$A_2$ $B_2$

$A_N$ $B_N$

Output

Output the answer.

Sample Input 1

4 10 14
5 8
5 6
7 9
99 99

Sample Output 1

3

By taking the following actions, Takahashi can defeat 3 monsters before the game ends.

Initially, his health is 10 and his magic power is 14. Fight the 1st monster without using magic. His health decreases by 5, becoming health 5 and magic power 14. Fight the 2nd monster without using magic. His health decreases by 5, becoming health 0 and magic power 14. Fight the 3rd monster using magic. His magic power decreases by 9, becoming health 0 and magic power 5. For the 4th monster, he cannot choose either action, so the game ends.

Sample Input 2

3 3000 3000
3 3
3 3
3 3

Sample Output 2

3

He may be able to defeat all monsters.

Sample Input 3

10 8 8
2 2
2 3
2 2
1 2
2 3
1 2
3 3
3 2
3 1
3 2

Sample Output 3

9