Count Pairs with Target Sum

Given an array \( a \) of \( n \) integers and an integer \( T \), your task is to count the number of distinct pairs of indices \( (i, j) \) (with \( i < j \)) such that \( a_i + a_j = T \).

The problem requires you to efficiently calculate the number of pairs that add up to the target value. For example, consider the array [1, 5, 7, -1] with target \( T = 6 \). The valid pairs are (1, 5) and (7, -1), so the answer is 2.

Input Specification: The input is given in multiple lines. The first line contains an integer \( n \) representing the number of elements. The second line contains \( n \) space separated integers representing the array. The third line contains the integer \( T \), the target sum.

Output Specification: Output a single integer representing the number of distinct pairs of indices \( (i, j) \) such that \( a_i + a_j = T \).

inputFormat

The input is read from standard input and it has the following format:

n
 a1 a2 a3 ... an
 T

Where:

• n is the number of elements in the array.
• a1, a2, ..., an are the integers in the array.
• T is the target sum.

outputFormat

Output a single integer to standard output indicating the number of distinct pairs \( (i, j) \) such that their sum equals \( T \) and \( i < j \).

## sample

4
1 5 7 -1
6

2