Two Sum Exists

You are given an array of integers and an integer target. Your task is to determine whether there exist two distinct indices i and j in the array such that the equation \(nums[i] + nums[j] = target\) holds.

The input format is as follows:

• The first line contains an integer \(n\), representing the number of elements in the array.
• The second line contains \(n\) space-separated integers representing the array elements.
• The third line contains an integer representing the target value.

Your program should output a single line: true if such a pair exists, and false otherwise.

inputFormat

The input is read from standard input (stdin) and has the following format:

n
nums[0] nums[1] ... nums[n-1]
target

Where:

• \(n\) is the number of elements in the array.
• \(nums[i]\) are the integer elements of the array.
• target is the integer target value.

outputFormat

The output is a single line to standard output (stdout) which is either:

• true if there exists a pair of distinct indices such that \(nums[i] + nums[j] = target\),
• or false otherwise.

## sample

4
2 7 11 15
9

true

</p>