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Formatted question description: https://leetcode.ca/all/2403.html

# 2403. Minimum Time to Kill All Monsters

## Description

You are given an integer array `power`

where `power[i]`

is the power of the `i`

monster.^{th}

You start with `0`

mana points, and each day you increase your mana points by `gain`

where `gain`

initially is equal to `1`

.

Each day, after gaining `gain`

mana, you can defeat a monster if your mana points are greater than or equal to the power of that monster. When you defeat a monster:

- your mana points will be reset to
`0`

, and - the value of
`gain`

increases by`1`

.

Return *the minimum number of days needed to defeat all the monsters.*

**Example 1:**

Input:power = [3,1,4]Output:4Explanation:The optimal way to beat all the monsters is to: - Day 1: Gain 1 mana point to get a total of 1 mana point. Spend all mana points to kill the 2^{nd}monster. - Day 2: Gain 2 mana points to get a total of 2 mana points. - Day 3: Gain 2 mana points to get a total of 4 mana points. Spend all mana points to kill the 3^{rd}monster. - Day 4: Gain 3 mana points to get a total of 3 mana points. Spend all mana points to kill the 1^{st}monster. It can be proven that 4 is the minimum number of days needed.

**Example 2:**

Input:power = [1,1,4]Output:4Explanation:The optimal way to beat all the monsters is to: - Day 1: Gain 1 mana point to get a total of 1 mana point. Spend all mana points to kill the 1^{st}monster. - Day 2: Gain 2 mana points to get a total of 2 mana points. Spend all mana points to kill the 2^{nd}monster. - Day 3: Gain 3 mana points to get a total of 3 mana points. - Day 4: Gain 3 mana points to get a total of 6 mana points. Spend all mana points to kill the 3^{rd}monster. It can be proven that 4 is the minimum number of days needed.

**Example 3:**

Input:power = [1,2,4,9]Output:6Explanation:The optimal way to beat all the monsters is to: - Day 1: Gain 1 mana point to get a total of 1 mana point. Spend all mana points to kill the 1st monster. - Day 2: Gain 2 mana points to get a total of 2 mana points. Spend all mana points to kill the 2nd monster. - Day 3: Gain 3 mana points to get a total of 3 mana points. - Day 4: Gain 3 mana points to get a total of 6 mana points. - Day 5: Gain 3 mana points to get a total of 9 mana points. Spend all mana points to kill the 4th monster. - Day 6: Gain 4 mana points to get a total of 4 mana points. Spend all mana points to kill the 3rd monster. It can be proven that 6 is the minimum number of days needed.

**Constraints:**

`1 <= power.length <= 17`

`1 <= power[i] <= 10`

^{9}