13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T58b,

You are given three integers $$$n$$$, $$$a$$$, $$$b$$$. Consider a weighted undirected graph with $$$n$$$ vertices, where for every pair of distinct vertices $$$(u, v)$$$ there is an edge with weight:

$$$$$$ w(u, v) = \frac{\max(u, v)}{\gcd(u, v)} $$$$$$

Here $$$\gcd(x, y)$$$ denotes the greatest common divisor (GCD) of integers $$$x$$$ and $$$y$$$.

Find the shortest path from vertex $$$a$$$ to vertex $$$b$$$ in this graph.

Input

The only line contains three integers $$$n$$$, $$$a$$$, $$$b$$$ ($$$2 \le n \le 10^{9}, 1 \le a, b \le n, a \neq b$$$).

Output

Print one integer — the length of the shortest path from vertex $$$a$$$ to vertex $$$b$$$.

Note

Consider the first example.

The shortest path in it is $$$9 \to 6 \to 8$$$ with total cost $$$w(9, 6) + w

Shortest GCD Paths

Examples