Triangle Subsequence

Three numbers x, y, and z are said to be in a triangle relation if all of x + y > z, x + z > y, and y + z > x hold.

For a sequence B of length N, if B[i], B[j], and B[k] are in a triangle relation for every choice of three distinct positions i, j, and k, then B is called a triangle sequence.

You are given a sequence A. Delete any number of elements from A so that the remaining sequence is a triangle sequence. Find the maximum possible length of such a sequence.

The first line contains the size N of the sequence.

The second line contains the elements of sequence A, separated by spaces. N is a positive integer at most 50, and each element of A is a positive integer at most 10^9.

Print the length of the longest possible triangle subsequence.