A zero-indexed array A consisting of N integers is given. A triplet (P, Q, R) is called a triangle if 0 ≤ P < Q < R < N and:

A[P] + A[Q] > A[R],

A[Q] + A[R] > A[P],

A[R] + A[P] > A[Q].

The perimeter of such a triangle equals A[P] + A[Q] + A[R]. For example, consider the following array A:

A[0] = 10

A[1] = 2

A[2] = 5

A[3] = 1

A[4] = 8

A[5] = 20

Triplet (0, 2, 4) is a triangle and its perimeter equals 10 + 5 + 8 = 23. There is no other triangle in this array with a larger perimeter.

Write a function:

class Solution { public int solution(int[] A); }

that, given a zero-indexed array A of N integers, returns the maximum perimeter of any triangle in this array. The function should return −1 if there are no triangles.

For example, given:

A[0] = 10

A[1] = 2

A[2] = 5

A[3] = 1

A[4] = 8

A[5] = 20

the function should return 23, as explained above.

Given array A such that:

A[0] = 5

A[1] = 10

A[2] = 18

A[3] = 7

A[4] = 8

A[5] = 3

the function should return 25: the triangle with the maximum perimeter is (1, 3, 4).

While for an array A:

A[0] = 10

A[1] = 20

A[2] = 30

the function should return −1, as it is impossible to create a triangle.

Assume that:

N is an integer within the range [0..100,000];

each element of array A is an integer within the range [1..100,000,000].

Complexity:

expected worst-case time complexity is O(N*log(N));

expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.