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 1:**

n = 5 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ Because the 3rd row is incomplete, we return 2.

**Example 2:**

n = 8 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Because the 4th row is incomplete, we return 3.

```
struct Solution;
impl Solution {
fn arrange_coins(n: i32) -> i32 {
(((2 * n as i64) as f64 + 0.25).sqrt() - 0.5).floor() as i32
}
}
#[test]
fn test() {
assert_eq!(Solution::arrange_coins(5), 2);
assert_eq!(Solution::arrange_coins(8), 3);
assert_eq!(Solution::arrange_coins(1_804_289_383), 60070);
}
```