You have an $$$n \times n$$$ grid and two integers $$$a$$$ and $$$b$$$. Both the rows and the columns are numbered from $$$1$$$ to $$$n$$$. Let's denote the cell at the intersection of the $$$i$$$-th row and the $$$j$$$-th column as $$$(i, j)$$$.

You are standing in the cell $$$(1, 1)$$$ and want to move into the cell $$$(n, n)$$$.

Suppose you are in the cell $$$(i, j)$$$; in one step, you can move either into the cell $$$(i, j + 1)$$$ or into the cell $$$(i + 1, j)$$$ if the corresponding cells exist.

Let's define the cost of the cell $$$(i, j)$$$ as $$$c(i, j) = \gcd(i, a) + \gcd(j, b)$$$ (here, $$$\gcd(x,y)$$$ denotes the greatest common divisor of $$$x$$$ and $$$y$$$). The cost of the route from $$$(1, 1)$$$ to $$$(n, n)$$$ is the sum of costs of the visited cells (including the starting cell and the finishing cell).

Find the route with minimum possible cost and print its cost.

Input format:
The only line contains three integers $$$n$$$, $$$a$$$, and $$$b$$$ ($$$2 \le n \le 10^6$$$; $$$1 \le a, b \le 10^6$$$).
Output format:
Print one integer — the cost of the cheapest route from $$$(1, 1)$$$ to $$$(n, n)$$$.
Example Input 0:
4 2 4

Example Output 0:
21

Example Input 1:
10 210 420

Example Output 1:
125

Notes:
The first example is described in the picture above.

Example input:
4 2 4

10 210 420


Example output:
21

125