Reverse Upper Triangle Pattern

You are given an integer n. Your task is to draw a reverse upper triangle pattern inside a square grid of size n × n. Each row of the grid must contain exactly two highlighted symbols ■ and the remaining positions must be filled with □. The two ■ symbols are placed such that in the i-th row (0-indexed) they occur at the i-th column and the (n-1-i)-th column. Note that when i equals n-1-i the symbol appears only once. All outputs should exactly match the pattern, including the newlines.

Example:

Input:
3
Output:
■□■
□■□
■□■

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Be sure to use LaTeX formatting for any mathematical expressions if needed. For instance, the positions of the highlighted symbols can be expressed by the formulas: $$i \quad \text{and} \quad n-1-i$$ for \(i = 0, 1, \ldots, n-1\).

inputFormat

The input consists of a single integer n (n ≥ 1), representing the dimensions of the square grid.

Input is provided via standard input.

outputFormat

The output should be the generated pattern with exactly n lines. Each line must consist of n characters, where two positions in each line are highlighted with the symbol ■ and the rest are the symbol □. Each line (except the last) should be terminated by a newline character. Output is produced on standard output.

## sample

3

■□■
□■□
■□■

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