Frog

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

The frog has a very busy weekend, it needs to jump over all \(n\) stones arranged in a row.

Initially, the frog is on the first stone and it wants to visit every other stone exactly once. To jump from stone \(x\) to stone \(y\), the frog spends \((|x-y|-3)^2\) energy. That is, if the distance between the stones is 3, no energy is required for such a jump.

Help the frog and find the minimum amount of energy it needs to spend to visit each stone exactly once.

Input

The first line gives a single integer \(n\) — the number of stones.

Output

Output a single number — the minimum amount of energy the frog needs to spend to visit each stone exactly once.

Constraints

\(2 \le n \le 10^5\).

Samples

Input (stdin) сopy	Output (stdout) сopy
4	5

Input (stdin) сopy	Output (stdout) сopy
7	2

Input (stdin) сopy	Output (stdout) сopy
10	3

Notes

In the first example, the optimal path of the frog is \(1 \to 4 \to 2 \to 3\). For this path, the frog spends 5 energy:

• Jump from stone 1 to stone 4 — 0 energy;

• Jump from stone 4 to stone 2 — 1 energy;

• Jump from stone 2 to stone 3 — 4 energy.