You are playing a video game where you are defending your city from a group of `n` monsters. You are given a 0-indexed integer array `dist` of size `n`, where `dist[i]` is the initial distance in kilometers of the `ith` monster from the city.

The monsters walk toward the city at a constant speed. The speed of each monster is given to you in an integer array `speed` of size `n`, where `speed[i]` is the speed of the `ith` monster in kilometers per minute.

You have a weapon that, once fully charged, can eliminate a single monster. However, the weapon takes one minute to charge.The weapon is fully charged at the very start.

You lose when any monster reaches your city. If a monster reaches the city at the exact moment the weapon is fully charged, it counts as a loss, and the game ends before you can use your weapon.

Return the maximum number of monsters that you can eliminate before you lose, or `n` if you can eliminate all the monsters before they reach the city.

Example 1:

    Input: dist = [1,3,4], speed = [1,1,1]
    Output: 3
    Explanation:
    In the beginning, the distances of the monsters are [1,3,4]. You eliminate the first monster.
    After a minute, the distances of the monsters are [X,2,3]. You eliminate the second monster.
    After a minute, the distances of the monsters are [X,X,2]. You eliminate the thrid monster.
    All 3 monsters can be eliminated.

Example 2:

    Input: dist = [1,1,2,3], speed = [1,1,1,1]
    Output: 1
    Explanation:
    In the beginning, the distances of the monsters are [1,1,2,3]. You eliminate the first monster.
    After a minute, the distances of the monsters are [X,0,1,2], so you lose.
    You can only eliminate 1 monster.

Example 3:

    Input: dist = [3,2,4], speed = [5,3,2]
    Output: 1
    Explanation:
    In the beginning, the distances of the monsters are [3,2,4]. You eliminate the first monster.
    After a minute, the distances of the monsters are [X,0,2], so you lose.
    You can only eliminate 1 monster.

Constraints:

- `n == dist.length == speed.length`
- `1 <= n <= 105`
- `1 <= dist[i], speed[i] <= 105`