Triangle Sticks

Jaś loves building triangles out of sticks. He keeps the sticks in a bag and draws three of them at random. Because the sticks have different lengths, three drawn sticks cannot always form a triangle, and when they cannot, Jaś throws a tantrum. To prevent this, we want to throw away some of the sticks so that any three of the sticks left in the bag can form a triangle, while keeping as many sticks as possible.

Three sticks of lengths $a$, $b$, $c$ form a triangle when the sum of every two of them is greater than the third; equivalently, if $a \le b \le c$, they form a triangle exactly when $a + b > c$ (a flat, degenerate triangle does not count).

Write a program that:

• reads the number of sticks in the bag and the length of each stick,
• computes the maximum number of sticks that can be kept so that every three of the kept sticks form a triangle,
• prints that number.

The first line contains an integer $N$ ($5 \le N \le 30\,000$), the number of sticks in the bag. Each of the next $N$ lines contains one integer, the length of a stick. Every length is an integer between $1$ and $500$ inclusive.

Print one line: the maximum number of sticks that can remain in the bag so that any three of them form a triangle.