Rectangle

There is an infinitely large square grid. You want to place $N$ squares of size $1 \times 1$, each on a different cell of this grid.

Call a shape a minimum bounding rectangle if it satisfies the following conditions and has the shortest perimeter among such shapes.

• The shape is a rectangle whose sides are all parallel to the grid lines.
• The shape contains all of the placed squares.

Among all ways to place $N$ squares, in which case is the perimeter of the minimum bounding rectangle the shortest?

The first line contains the number of test cases $T$ ($1 \le T \le 2 \times 10^5$).

Each of the next $T$ lines contains one integer $N$, the number of squares to place ($1 \le N \le 10^9$).

For each test case, print the shortest possible perimeter of the minimum bounding rectangle.

This problem has a large input, so you may need to use fast I/O to avoid a time limit error.

• If you use C++ and want to use cin/cout:

  • Put cin.tie(nullptr) and ios::sync_with_stdio(false) at the top of main.
  • Use the newline character (\n) instead of endl.
  • In this case, you must not use C I/O such as scanf/printf/puts/getchar/putchar.

• If you use Java:

  • Use BufferedReader and BufferedWriter instead of Scanner and System.out.println.
  • Call BufferedWriter.flush once at the end.

• If you use Python:

  • Use sys.stdin.readline instead of input. Note that this function also reads the trailing newline.
  • It is a good idea to add .rstrip() if you want to store a string without the newline.