1921 - Eliminate Maximum Number of Monsters.

Medium

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 <code>i^th</code> 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 <code>i^th</code> 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

• <code>1 <= n <= 10⁵</code>

• <code>1 <= disti, speedi<= 10⁵</code>