# Triangle of Wealth

In a wealthy family known for their extensive gold mines, a member today brought **N** gold coins and aimed to construct a triangle with them. Quite the unique endeavor, isn't it?

The method to create this golden triangle is as follows:

- Place
**1**coin in the**1st**row. - Follow with
**2**coins in the**2nd**row. - Next,
**3**coins in the**3rd**row. - Continue in this manner as depicted in the image below.

The goal is to form a triangle with the maximum possible height using no more than **N** coins. Can you determine the tallest triangle that can be built?

### Input

The input begins with a single integer **T**, indicating the number of test cases.

Each test case is described in one line, containing an integer **N** — the number of gold coins available.

### Output

For each test case, output a single line with one integer: the maximum height of the triangle that can be created.

### Constraints

**1 ≤ T ≤ 100****1 ≤ N ≤ 109**

### Subtasks

- Subtask 1 (48 points) :
**1 ≤ N ≤ 105** - Subtask 2 (52 points) :
**1 ≤ N ≤ 109**

## Sample Test Cases (and explanation)

### Case #1:

Input:

`3 3 5 7`

Output:

`2 2 3`

#### Explanation

**Test 1:** It's not possible to form a triangle taller than 2 levels with only 3 gold coins.

**Test 2:** Similarly, 5 gold coins are insufficient for a triangle taller than 2 levels.

**Test 3:** With 7 gold coins, a triangle of height 3 levels can be formed, requiring at least 10 gold coins for a taller structure.