Unique Pair Sum

You are given an array of n integers and an integer target value \(T\). Your task is to find all unique pairs \((a, b)\) such that

\(a + b = T\)

Each pair \((a, b)\) must be output in sorted order (i.e. the smaller number first) and the list of pairs should be sorted in lexicographical order. A pair is considered unique if no other pair contains the same two numbers, regardless of their order.

If no such pairs exist, output None.

inputFormat

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

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

outputFormat

Print each unique pair that sums up to the target on a new line. For each pair, print the two integers separated by a space. The pairs must be printed in lexicographical order (i.e. sorted by the first element, and then by the second element). If no valid pair exists, print None.

## sample

8
2 7 11 15 -2 2 8 1
9

-2 11
1 8
2 7

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