# Very Suspicious solution codeforces- Sehr Sus is an infinite hexagonal grid as pictured below, controlled by MennaFadali, ZerooCool and Hosssam.

## Very Suspicious solution codeforces

Sehr Sus is an infinite hexagonal grid as pictured below, controlled by MennaFadali, ZerooCool and Hosssam.

They love equilateral triangles and want to create nn equilateral triangles on the grid by adding some straight lines. The triangles must all be empty from the inside (in other words, no straight line or hexagon edge should pass through any of the triangles).

You are allowed to add straight lines parallel to the edges of the hexagons. Given nn, what is the minimum number of lines you need to add to create at least nn equilateral triangles as described?

Adding two red lines results in two new yellow equilateral triangles.
Input

The first line contains a single integer tt (1t1051≤t≤105) — the number of test cases. Then tt test cases follow.

Each test case contains a single integer nn (1n1091≤n≤109) — the required number of equilateral triangles.

Output

For each test case, print the minimum number of lines needed to have nn or more equilateral triangles.

Example

## Very Suspicious solution codeforces

input

Copy
4
1
2
3
4567


output

Copy
2
2
3
83

Note

## Very Suspicious solution codeforces

In the first and second test cases only 2 lines are needed. After adding the first line, no equilateral triangles will be created no matter where it is added. But after adding the second line, two more triangles will be created at once.

In the third test case, the minimum needed is 3 lines as shown below.