Output Specification

The output is one integer, the largest number of treats your Fox can gather.

Sample Input

5
5 8
4 10
3 1
3 2
3 3

Output for Sample Input

6

Explanation of Output for Sample Input

The Fox performs the visits in the following order (with the indicated distances):

• \((0, 0)\) to \((4, 10)\) with distance \(\sqrt{116}\) ;
• \((4, 10)\) to \((3, 1)\) with distance \(\sqrt{82}\) ;
• \((3, 1)\) to \((5, 8)\) with distance \(\sqrt{53}\) ;
• \((5, 8)\) to \((3, 3)\) with distance \(\sqrt{29}\) ;
• \((3, 3)\) to \((3, 1)\) with distance \(2\) ;
• \((3, 1)\) to \((3, 2)\) with distance \(1\) .