Triplet Sum Problem

You are given an array of N integers and an integer target value. Your task is to determine whether there exists a triplet of numbers in the array which adds up exactly to the target value.

You should design an efficient algorithm with a time complexity better than O(N³). A common approach is to first sort the array and then use the two-pointer technique for each element, which gives a time complexity of O(N²).

The problem includes negative numbers and zeros, so be cautious when handling these cases. The input is read from stdin and the answer should be output to stdout.

If a triplet exists whose sum equals the target, print True; otherwise, print False.

inputFormat

The input will be given in three lines:

1. The first line contains an integer N, the size of the array.
2. The second line contains N space-separated integers representing the elements of the array.
3. The third line contains an integer representing the target sum.

You should read the input from stdin.

outputFormat

Output a single line containing either True if there exists a triplet of numbers in the array that sum up to the target; otherwise, output False.

The output must be written to stdout.

## sample

6
12 3 4 1 6 9
24

True