# Arranging Coins

You have a total of *n* coins that you want to form in a staircase shape, where every *k*-th row must have exactly *k* coins.

Given *n*, find the total number of **full** staircase rows that can be formed.

*n* is a non-negative integer and fits within the range of a 32-bit signed integer.

**Example:**

n = 5

The coins can form the following rows:

¤

¤ ¤

¤ ¤

Because the 3rd row is incomplete, we return 2.

### Solution

Actually, this is the math problem.

The sum of length of each row of staircase shape is n(n + 1) / 2. So this question is to solve the inequality x² + x - 2n <= 0.

Use the formula : x = (-b +/- sqrt(b² - 4ac)) / 2a

The final answer will be x = sqrt(2*n + 0.25) - 0.5

```
import kotlin.math.sqrt
fun arrangeCoins(n: Int): Int {
return (sqrt(2 * n.toLong() +0.25) - 0.5).toInt()
}
```